idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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13,801 | What tests do I use to confirm that residuals are normally distributed? | No test will tell you your residuals are normally distributed. In fact, you can reliably bet that they are not.
Hypothesis tests are not generally a good idea as checks on your assumptions. The effect of non-normality on your inference is not generally a function of sample size*, but the result of a significance test i... | What tests do I use to confirm that residuals are normally distributed? | No test will tell you your residuals are normally distributed. In fact, you can reliably bet that they are not.
Hypothesis tests are not generally a good idea as checks on your assumptions. The effect | What tests do I use to confirm that residuals are normally distributed?
No test will tell you your residuals are normally distributed. In fact, you can reliably bet that they are not.
Hypothesis tests are not generally a good idea as checks on your assumptions. The effect of non-normality on your inference is not gener... | What tests do I use to confirm that residuals are normally distributed?
No test will tell you your residuals are normally distributed. In fact, you can reliably bet that they are not.
Hypothesis tests are not generally a good idea as checks on your assumptions. The effect |
13,802 | What tests do I use to confirm that residuals are normally distributed? | The Shapiro-Wilk test is one possibility.
Shapiro-Wilk test
This test is implemented in almost all statistical software packages. The null hypothesis is the residuals are normally distributed, thus a small p-value indicates you should reject the null and conclude the residuals are not normally distributed.
Note that i... | What tests do I use to confirm that residuals are normally distributed? | The Shapiro-Wilk test is one possibility.
Shapiro-Wilk test
This test is implemented in almost all statistical software packages. The null hypothesis is the residuals are normally distributed, thus a | What tests do I use to confirm that residuals are normally distributed?
The Shapiro-Wilk test is one possibility.
Shapiro-Wilk test
This test is implemented in almost all statistical software packages. The null hypothesis is the residuals are normally distributed, thus a small p-value indicates you should reject the n... | What tests do I use to confirm that residuals are normally distributed?
The Shapiro-Wilk test is one possibility.
Shapiro-Wilk test
This test is implemented in almost all statistical software packages. The null hypothesis is the residuals are normally distributed, thus a |
13,803 | What tests do I use to confirm that residuals are normally distributed? | From wikipedia:
Tests of univariate normality include D'Agostino's K-squared test, the Jarque–Bera test, the Anderson–Darling test, the Cramér–von Mises criterion, the Lilliefors test for normality (itself an adaptation of the Kolmogorov–Smirnov test), the Shapiro–Wilk test, the Pearson's chi-squared test, and the Sha... | What tests do I use to confirm that residuals are normally distributed? | From wikipedia:
Tests of univariate normality include D'Agostino's K-squared test, the Jarque–Bera test, the Anderson–Darling test, the Cramér–von Mises criterion, the Lilliefors test for normality ( | What tests do I use to confirm that residuals are normally distributed?
From wikipedia:
Tests of univariate normality include D'Agostino's K-squared test, the Jarque–Bera test, the Anderson–Darling test, the Cramér–von Mises criterion, the Lilliefors test for normality (itself an adaptation of the Kolmogorov–Smirnov t... | What tests do I use to confirm that residuals are normally distributed?
From wikipedia:
Tests of univariate normality include D'Agostino's K-squared test, the Jarque–Bera test, the Anderson–Darling test, the Cramér–von Mises criterion, the Lilliefors test for normality ( |
13,804 | Why does increasing the sample size of coin flips not improve the normal curve approximation? | In the second case, by increasing the number of tosses, you increase the number of bins a single trial can fall into. While the first case of experiment 2 only has a maximum of 100 bins that can be filled, the last example has 10000 bins. You increased the "resolution" of your experiment by a factor 100 (i.e., one bin ... | Why does increasing the sample size of coin flips not improve the normal curve approximation? | In the second case, by increasing the number of tosses, you increase the number of bins a single trial can fall into. While the first case of experiment 2 only has a maximum of 100 bins that can be fi | Why does increasing the sample size of coin flips not improve the normal curve approximation?
In the second case, by increasing the number of tosses, you increase the number of bins a single trial can fall into. While the first case of experiment 2 only has a maximum of 100 bins that can be filled, the last example has... | Why does increasing the sample size of coin flips not improve the normal curve approximation?
In the second case, by increasing the number of tosses, you increase the number of bins a single trial can fall into. While the first case of experiment 2 only has a maximum of 100 bins that can be fi |
13,805 | Why does increasing the sample size of coin flips not improve the normal curve approximation? | You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be very close to 0.5, if the coin is fair.
Now if you increase the number of trials to 1,000 and... | Why does increasing the sample size of coin flips not improve the normal curve approximation? | You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the avera | Why does increasing the sample size of coin flips not improve the normal curve approximation?
You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the average number of heads will be... | Why does increasing the sample size of coin flips not improve the normal curve approximation?
You can think of an individual coin flip as an independent Bernoulli trial. One trial will give you either heads/tails or success/failure, respectively. If you repeat this say 100,000 times, the avera |
13,806 | Why does increasing the sample size of coin flips not improve the normal curve approximation? | I think the other answers here are great, but wanted to add an answer that extends to another statistical tool.
You're starting with a baseline that you think should approximate a normal curve, and then going from there to see if you can better approximate a normal curve. Try going the other direction, and see what yo... | Why does increasing the sample size of coin flips not improve the normal curve approximation? | I think the other answers here are great, but wanted to add an answer that extends to another statistical tool.
You're starting with a baseline that you think should approximate a normal curve, and th | Why does increasing the sample size of coin flips not improve the normal curve approximation?
I think the other answers here are great, but wanted to add an answer that extends to another statistical tool.
You're starting with a baseline that you think should approximate a normal curve, and then going from there to see... | Why does increasing the sample size of coin flips not improve the normal curve approximation?
I think the other answers here are great, but wanted to add an answer that extends to another statistical tool.
You're starting with a baseline that you think should approximate a normal curve, and th |
13,807 | Why does increasing the sample size of coin flips not improve the normal curve approximation? | To gain some additional intuition consider the following:
Imagine you do only one single repetition.
In that case you can increase the number of tosses all you want but it is not gonna resemble a normal distribution. And this makes sense since your histogram is only gonna have one single peak.
The normal distributi... | Why does increasing the sample size of coin flips not improve the normal curve approximation? | To gain some additional intuition consider the following:
Imagine you do only one single repetition.
In that case you can increase the number of tosses all you want but it is not gonna resemble a no | Why does increasing the sample size of coin flips not improve the normal curve approximation?
To gain some additional intuition consider the following:
Imagine you do only one single repetition.
In that case you can increase the number of tosses all you want but it is not gonna resemble a normal distribution. And thi... | Why does increasing the sample size of coin flips not improve the normal curve approximation?
To gain some additional intuition consider the following:
Imagine you do only one single repetition.
In that case you can increase the number of tosses all you want but it is not gonna resemble a no |
13,808 | Out of Bag Error makes CV unnecessary in Random Forests? | training error (as in predict(model, data=train)) is typically useless. Unless you do (non-standard) pruning of the trees, it cannot be much above 0 by design of the algorithm. Random forest uses bootstrap aggregation of decision trees, which are known to be overfit badly. This is like training error for a 1-nearest-ne... | Out of Bag Error makes CV unnecessary in Random Forests? | training error (as in predict(model, data=train)) is typically useless. Unless you do (non-standard) pruning of the trees, it cannot be much above 0 by design of the algorithm. Random forest uses boot | Out of Bag Error makes CV unnecessary in Random Forests?
training error (as in predict(model, data=train)) is typically useless. Unless you do (non-standard) pruning of the trees, it cannot be much above 0 by design of the algorithm. Random forest uses bootstrap aggregation of decision trees, which are known to be over... | Out of Bag Error makes CV unnecessary in Random Forests?
training error (as in predict(model, data=train)) is typically useless. Unless you do (non-standard) pruning of the trees, it cannot be much above 0 by design of the algorithm. Random forest uses boot |
13,809 | Out of Bag Error makes CV unnecessary in Random Forests? | Out-of-bag error is useful, and may replace other performance estimation protocols (like cross-validation), but should be used with care.
Like cross-validation, performance estimation using out-of-bag samples is computed using data that were not used for learning.
If the data have been processed in a way that transfers... | Out of Bag Error makes CV unnecessary in Random Forests? | Out-of-bag error is useful, and may replace other performance estimation protocols (like cross-validation), but should be used with care.
Like cross-validation, performance estimation using out-of-bag | Out of Bag Error makes CV unnecessary in Random Forests?
Out-of-bag error is useful, and may replace other performance estimation protocols (like cross-validation), but should be used with care.
Like cross-validation, performance estimation using out-of-bag samples is computed using data that were not used for learning... | Out of Bag Error makes CV unnecessary in Random Forests?
Out-of-bag error is useful, and may replace other performance estimation protocols (like cross-validation), but should be used with care.
Like cross-validation, performance estimation using out-of-bag |
13,810 | What is the interpretation of the covariance of regression coefficients? | The most basic use of the covariance matrix is to obtain the standard errors of regression estimates. If the researcher is only interested in the standard errors of the individual regression parameters themselves, they can just take the square root of the diagonal to get the individual standard errors.
However, often t... | What is the interpretation of the covariance of regression coefficients? | The most basic use of the covariance matrix is to obtain the standard errors of regression estimates. If the researcher is only interested in the standard errors of the individual regression parameter | What is the interpretation of the covariance of regression coefficients?
The most basic use of the covariance matrix is to obtain the standard errors of regression estimates. If the researcher is only interested in the standard errors of the individual regression parameters themselves, they can just take the square roo... | What is the interpretation of the covariance of regression coefficients?
The most basic use of the covariance matrix is to obtain the standard errors of regression estimates. If the researcher is only interested in the standard errors of the individual regression parameter |
13,811 | What is the interpretation of the covariance of regression coefficients? | There are two "kinds" of regression coefficients:
"True" regression coefficients (usually denoted $\beta$) that describe the underlying data-generating process of the data. These are fixed numbers, or "parameters." An example would be the speed of light $c$, which (we assume) is always the same everywhere in the acces... | What is the interpretation of the covariance of regression coefficients? | There are two "kinds" of regression coefficients:
"True" regression coefficients (usually denoted $\beta$) that describe the underlying data-generating process of the data. These are fixed numbers, o | What is the interpretation of the covariance of regression coefficients?
There are two "kinds" of regression coefficients:
"True" regression coefficients (usually denoted $\beta$) that describe the underlying data-generating process of the data. These are fixed numbers, or "parameters." An example would be the speed o... | What is the interpretation of the covariance of regression coefficients?
There are two "kinds" of regression coefficients:
"True" regression coefficients (usually denoted $\beta$) that describe the underlying data-generating process of the data. These are fixed numbers, o |
13,812 | How to sample from $c^a d^{a-1} / \Gamma(a)$? | Rejection sampling will work exceptionally well when $c d \ge \exp(5)$ and is reasonable for $c d \ge \exp(2)$.
To simplify the math a little, let $k = c d$, write $x = a$, and note that
$$f(x) \propto \frac{k^x}{\Gamma(x)} dx$$
for $x \ge 1$. Setting $x = u^{3/2}$ gives
$$f(u) \propto \frac{k^{u^{3/2}}}{\Gamma(u^{3/2... | How to sample from $c^a d^{a-1} / \Gamma(a)$? | Rejection sampling will work exceptionally well when $c d \ge \exp(5)$ and is reasonable for $c d \ge \exp(2)$.
To simplify the math a little, let $k = c d$, write $x = a$, and note that
$$f(x) \propt | How to sample from $c^a d^{a-1} / \Gamma(a)$?
Rejection sampling will work exceptionally well when $c d \ge \exp(5)$ and is reasonable for $c d \ge \exp(2)$.
To simplify the math a little, let $k = c d$, write $x = a$, and note that
$$f(x) \propto \frac{k^x}{\Gamma(x)} dx$$
for $x \ge 1$. Setting $x = u^{3/2}$ gives
$... | How to sample from $c^a d^{a-1} / \Gamma(a)$?
Rejection sampling will work exceptionally well when $c d \ge \exp(5)$ and is reasonable for $c d \ge \exp(2)$.
To simplify the math a little, let $k = c d$, write $x = a$, and note that
$$f(x) \propt |
13,813 | How to sample from $c^a d^{a-1} / \Gamma(a)$? | I like @whuber's answer very much; it's likely to be very efficient and has a beautiful analysis. But it requires some deep insight with respect to this particular distribution. For situations where you don't have that insight (so for different distributions), I also like the following approach which works for all dist... | How to sample from $c^a d^{a-1} / \Gamma(a)$? | I like @whuber's answer very much; it's likely to be very efficient and has a beautiful analysis. But it requires some deep insight with respect to this particular distribution. For situations where y | How to sample from $c^a d^{a-1} / \Gamma(a)$?
I like @whuber's answer very much; it's likely to be very efficient and has a beautiful analysis. But it requires some deep insight with respect to this particular distribution. For situations where you don't have that insight (so for different distributions), I also like t... | How to sample from $c^a d^{a-1} / \Gamma(a)$?
I like @whuber's answer very much; it's likely to be very efficient and has a beautiful analysis. But it requires some deep insight with respect to this particular distribution. For situations where y |
13,814 | How to sample from $c^a d^{a-1} / \Gamma(a)$? | You could do it by numerically executing the inversion method, which says that if you plug uniform(0,1) random variables in the inverse CDF, you get a draw from the distribution. I've included some R code below that does this, and from the few checks I've done, it is working well, but it is a bit sloppy and I'm sure yo... | How to sample from $c^a d^{a-1} / \Gamma(a)$? | You could do it by numerically executing the inversion method, which says that if you plug uniform(0,1) random variables in the inverse CDF, you get a draw from the distribution. I've included some R | How to sample from $c^a d^{a-1} / \Gamma(a)$?
You could do it by numerically executing the inversion method, which says that if you plug uniform(0,1) random variables in the inverse CDF, you get a draw from the distribution. I've included some R code below that does this, and from the few checks I've done, it is workin... | How to sample from $c^a d^{a-1} / \Gamma(a)$?
You could do it by numerically executing the inversion method, which says that if you plug uniform(0,1) random variables in the inverse CDF, you get a draw from the distribution. I've included some R |
13,815 | Avoid overfitting in regression: alternatives to regularization | Two important points that are not directly related to your question:
First, even the goal is accuracy instead of interpretation, regularization is still necessary in many cases, since, it will make sure the "high accuracy" on real testing / production data set, not the data used for modeling.
Second, if there are bill... | Avoid overfitting in regression: alternatives to regularization | Two important points that are not directly related to your question:
First, even the goal is accuracy instead of interpretation, regularization is still necessary in many cases, since, it will make s | Avoid overfitting in regression: alternatives to regularization
Two important points that are not directly related to your question:
First, even the goal is accuracy instead of interpretation, regularization is still necessary in many cases, since, it will make sure the "high accuracy" on real testing / production dat... | Avoid overfitting in regression: alternatives to regularization
Two important points that are not directly related to your question:
First, even the goal is accuracy instead of interpretation, regularization is still necessary in many cases, since, it will make s |
13,816 | Avoid overfitting in regression: alternatives to regularization | Two alternatives to regularization:
Have many, many observations
Use a simpler model
Geoff Hinton (co-inventor of back propogation) once told a story of engineers that told him (paraphrasing heavily), "Geoff, we don't need dropout in our deep nets because we have so much data." And his response, was, "Well, then you ... | Avoid overfitting in regression: alternatives to regularization | Two alternatives to regularization:
Have many, many observations
Use a simpler model
Geoff Hinton (co-inventor of back propogation) once told a story of engineers that told him (paraphrasing heavily | Avoid overfitting in regression: alternatives to regularization
Two alternatives to regularization:
Have many, many observations
Use a simpler model
Geoff Hinton (co-inventor of back propogation) once told a story of engineers that told him (paraphrasing heavily), "Geoff, we don't need dropout in our deep nets becaus... | Avoid overfitting in regression: alternatives to regularization
Two alternatives to regularization:
Have many, many observations
Use a simpler model
Geoff Hinton (co-inventor of back propogation) once told a story of engineers that told him (paraphrasing heavily |
13,817 | Avoid overfitting in regression: alternatives to regularization | Some additional possibilities to avoid overfitting
Dimensionality reduction
You can use an algorithm such as principal components analysis (PCA) to obtain a lower dimensional features subspace. The idea of PCA is that the variation of your $m$ dimensional feature space may be approximated well by an $l << m$ dimension... | Avoid overfitting in regression: alternatives to regularization | Some additional possibilities to avoid overfitting
Dimensionality reduction
You can use an algorithm such as principal components analysis (PCA) to obtain a lower dimensional features subspace. The i | Avoid overfitting in regression: alternatives to regularization
Some additional possibilities to avoid overfitting
Dimensionality reduction
You can use an algorithm such as principal components analysis (PCA) to obtain a lower dimensional features subspace. The idea of PCA is that the variation of your $m$ dimensional... | Avoid overfitting in regression: alternatives to regularization
Some additional possibilities to avoid overfitting
Dimensionality reduction
You can use an algorithm such as principal components analysis (PCA) to obtain a lower dimensional features subspace. The i |
13,818 | Avoid overfitting in regression: alternatives to regularization | Two thoughts:
I second the "use a simpler model" strategy proposed by Ben Ogorek.
I work on really sparse linear classification models with small integer coefficients (e.g. max 5 variables with integer coefficients between -5 and 5). The models generalize well in terms of accuracy and trickier performance metrics (e.... | Avoid overfitting in regression: alternatives to regularization | Two thoughts:
I second the "use a simpler model" strategy proposed by Ben Ogorek.
I work on really sparse linear classification models with small integer coefficients (e.g. max 5 variables with inte | Avoid overfitting in regression: alternatives to regularization
Two thoughts:
I second the "use a simpler model" strategy proposed by Ben Ogorek.
I work on really sparse linear classification models with small integer coefficients (e.g. max 5 variables with integer coefficients between -5 and 5). The models generaliz... | Avoid overfitting in regression: alternatives to regularization
Two thoughts:
I second the "use a simpler model" strategy proposed by Ben Ogorek.
I work on really sparse linear classification models with small integer coefficients (e.g. max 5 variables with inte |
13,819 | Avoid overfitting in regression: alternatives to regularization | If you are use a model with a solver, where you can define number of iterations/epochs, you can track validation error and apply early stopping: stop the algorithm, when validation error starts increasing. | Avoid overfitting in regression: alternatives to regularization | If you are use a model with a solver, where you can define number of iterations/epochs, you can track validation error and apply early stopping: stop the algorithm, when validation error starts increa | Avoid overfitting in regression: alternatives to regularization
If you are use a model with a solver, where you can define number of iterations/epochs, you can track validation error and apply early stopping: stop the algorithm, when validation error starts increasing. | Avoid overfitting in regression: alternatives to regularization
If you are use a model with a solver, where you can define number of iterations/epochs, you can track validation error and apply early stopping: stop the algorithm, when validation error starts increa |
13,820 | Avoid overfitting in regression: alternatives to regularization | What is regularization, really?
Perhaps you are conflating L1/L2 regularization (aka. Lasso/ridge regression, Tikhonov regularization...), the most ubiquitous type, as the only type of regularization 🤔
Regularization is actually anything that prevents overfitting, that you can do to a learning algorithm [Wikipedia]. D... | Avoid overfitting in regression: alternatives to regularization | What is regularization, really?
Perhaps you are conflating L1/L2 regularization (aka. Lasso/ridge regression, Tikhonov regularization...), the most ubiquitous type, as the only type of regularization | Avoid overfitting in regression: alternatives to regularization
What is regularization, really?
Perhaps you are conflating L1/L2 regularization (aka. Lasso/ridge regression, Tikhonov regularization...), the most ubiquitous type, as the only type of regularization 🤔
Regularization is actually anything that prevents ove... | Avoid overfitting in regression: alternatives to regularization
What is regularization, really?
Perhaps you are conflating L1/L2 regularization (aka. Lasso/ridge regression, Tikhonov regularization...), the most ubiquitous type, as the only type of regularization |
13,821 | Avoid overfitting in regression: alternatives to regularization | Other alternatives to regularization:
Using ensemble methods.
Oversampling and data augmentation.
Combine the variables to get new ones, for example with PCA.
Adding random noise at every step of the optimization.
Smoothing the data.
Dropout: typically used with NN, but could also be used with the covariates.
Standard... | Avoid overfitting in regression: alternatives to regularization | Other alternatives to regularization:
Using ensemble methods.
Oversampling and data augmentation.
Combine the variables to get new ones, for example with PCA.
Adding random noise at every step of the | Avoid overfitting in regression: alternatives to regularization
Other alternatives to regularization:
Using ensemble methods.
Oversampling and data augmentation.
Combine the variables to get new ones, for example with PCA.
Adding random noise at every step of the optimization.
Smoothing the data.
Dropout: typically us... | Avoid overfitting in regression: alternatives to regularization
Other alternatives to regularization:
Using ensemble methods.
Oversampling and data augmentation.
Combine the variables to get new ones, for example with PCA.
Adding random noise at every step of the |
13,822 | Bootstrap vs Monte Carlo, error estimation | As far as I understand your question, the difference between the "Monte Carlo" approach and the bootstrap approach is essentially the difference between parametric and non-parametric statistics.
In the parametric framework, one knows exactly how the data $x_1,\ldots,x_N$ is generated, that is, given the parameters of t... | Bootstrap vs Monte Carlo, error estimation | As far as I understand your question, the difference between the "Monte Carlo" approach and the bootstrap approach is essentially the difference between parametric and non-parametric statistics.
In th | Bootstrap vs Monte Carlo, error estimation
As far as I understand your question, the difference between the "Monte Carlo" approach and the bootstrap approach is essentially the difference between parametric and non-parametric statistics.
In the parametric framework, one knows exactly how the data $x_1,\ldots,x_N$ is ge... | Bootstrap vs Monte Carlo, error estimation
As far as I understand your question, the difference between the "Monte Carlo" approach and the bootstrap approach is essentially the difference between parametric and non-parametric statistics.
In th |
13,823 | Bootstrap vs Monte Carlo, error estimation | The Random Change in your Monte Carlo Model is represented by a bell curve and the computation probably assumes normally distributed "error" or "Change". At least, your computer needs some assumption about the distribution from which to draw the "change". Bootstrapping does not necessarily make such assumptions. It tak... | Bootstrap vs Monte Carlo, error estimation | The Random Change in your Monte Carlo Model is represented by a bell curve and the computation probably assumes normally distributed "error" or "Change". At least, your computer needs some assumption | Bootstrap vs Monte Carlo, error estimation
The Random Change in your Monte Carlo Model is represented by a bell curve and the computation probably assumes normally distributed "error" or "Change". At least, your computer needs some assumption about the distribution from which to draw the "change". Bootstrapping does no... | Bootstrap vs Monte Carlo, error estimation
The Random Change in your Monte Carlo Model is represented by a bell curve and the computation probably assumes normally distributed "error" or "Change". At least, your computer needs some assumption |
13,824 | Bootstrap vs Monte Carlo, error estimation | If the function relating the output Z to the inputs is
reasonably linear (i.e. within the variation range of
the inputs), the variance of Z is a combination of the
variances and covariances of the inputs. The details
of the distribution do not matter too much... So, both
methods should return similar results.
See the ... | Bootstrap vs Monte Carlo, error estimation | If the function relating the output Z to the inputs is
reasonably linear (i.e. within the variation range of
the inputs), the variance of Z is a combination of the
variances and covariances of the in | Bootstrap vs Monte Carlo, error estimation
If the function relating the output Z to the inputs is
reasonably linear (i.e. within the variation range of
the inputs), the variance of Z is a combination of the
variances and covariances of the inputs. The details
of the distribution do not matter too much... So, both
meth... | Bootstrap vs Monte Carlo, error estimation
If the function relating the output Z to the inputs is
reasonably linear (i.e. within the variation range of
the inputs), the variance of Z is a combination of the
variances and covariances of the in |
13,825 | Bootstrap vs Monte Carlo, error estimation | Bootstrap means letting the data speak for themselves.
With Monte Carlo method, you sample many random draws from the imposed CDF (normal; gamma; beta...) via uniform distribution and create an empirical PDF (provided that the CDF is continuous and derivable).
An interesting explanation of the whole Monte Carlo process... | Bootstrap vs Monte Carlo, error estimation | Bootstrap means letting the data speak for themselves.
With Monte Carlo method, you sample many random draws from the imposed CDF (normal; gamma; beta...) via uniform distribution and create an empiri | Bootstrap vs Monte Carlo, error estimation
Bootstrap means letting the data speak for themselves.
With Monte Carlo method, you sample many random draws from the imposed CDF (normal; gamma; beta...) via uniform distribution and create an empirical PDF (provided that the CDF is continuous and derivable).
An interesting e... | Bootstrap vs Monte Carlo, error estimation
Bootstrap means letting the data speak for themselves.
With Monte Carlo method, you sample many random draws from the imposed CDF (normal; gamma; beta...) via uniform distribution and create an empiri |
13,826 | RNNs: When to apply BPTT and/or update weights? | I'll assume we're talking about recurrent neural nets (RNNs) that produce an output at every time step (if output is only available at the end of the sequence, it only makes sense to run backprop at the end). RNNs in this setting are often trained using truncated backpropagation through time (BPTT), operating sequentia... | RNNs: When to apply BPTT and/or update weights? | I'll assume we're talking about recurrent neural nets (RNNs) that produce an output at every time step (if output is only available at the end of the sequence, it only makes sense to run backprop at t | RNNs: When to apply BPTT and/or update weights?
I'll assume we're talking about recurrent neural nets (RNNs) that produce an output at every time step (if output is only available at the end of the sequence, it only makes sense to run backprop at the end). RNNs in this setting are often trained using truncated backprop... | RNNs: When to apply BPTT and/or update weights?
I'll assume we're talking about recurrent neural nets (RNNs) that produce an output at every time step (if output is only available at the end of the sequence, it only makes sense to run backprop at t |
13,827 | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation? | Let's just go through the parameters one by one:
data doesn't require explanation
m is the number of imputations, generally speaking, the more the better. Originally (following Rubin, 1987) 5 was considered to be enough (hence the default). So from an accuracy point of view, 5 may be sufficient. However, this was base... | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation? | Let's just go through the parameters one by one:
data doesn't require explanation
m is the number of imputations, generally speaking, the more the better. Originally (following Rubin, 1987) 5 was con | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation?
Let's just go through the parameters one by one:
data doesn't require explanation
m is the number of imputations, generally speaking, the more the better. Originally (following Rubin, 1987) 5 was considered to be enough (... | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation?
Let's just go through the parameters one by one:
data doesn't require explanation
m is the number of imputations, generally speaking, the more the better. Originally (following Rubin, 1987) 5 was con |
13,828 | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation? | Until 5 years ago, the most popular rule of thumb was that the number of imputations should be equal to the % of missing information, but it turns out it's not a linear relationship. It's quadratic. Plus the number of imputations depends on how much random noise you can tolerate in your estimates; more imputations-->le... | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation? | Until 5 years ago, the most popular rule of thumb was that the number of imputations should be equal to the % of missing information, but it turns out it's not a linear relationship. It's quadratic. P | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation?
Until 5 years ago, the most popular rule of thumb was that the number of imputations should be equal to the % of missing information, but it turns out it's not a linear relationship. It's quadratic. Plus the number of impu... | How do the number of imputations & the maximum iterations affect accuracy in multiple imputation?
Until 5 years ago, the most popular rule of thumb was that the number of imputations should be equal to the % of missing information, but it turns out it's not a linear relationship. It's quadratic. P |
13,829 | Qualitative variable coding in regression leads to "singularities" | The problem you are having (i.e., "singularities") can be thought of as an instance of multicollinearity. Multicollinearity is often defined as:
One or more predictor variables are a linear combination of other predictor variables.
This is, in fact, a rather strict definition; it is perfect multicollinearity, an... | Qualitative variable coding in regression leads to "singularities" | The problem you are having (i.e., "singularities") can be thought of as an instance of multicollinearity. Multicollinearity is often defined as:
One or more predictor variables are a linear combin | Qualitative variable coding in regression leads to "singularities"
The problem you are having (i.e., "singularities") can be thought of as an instance of multicollinearity. Multicollinearity is often defined as:
One or more predictor variables are a linear combination of other predictor variables.
This is, in fa... | Qualitative variable coding in regression leads to "singularities"
The problem you are having (i.e., "singularities") can be thought of as an instance of multicollinearity. Multicollinearity is often defined as:
One or more predictor variables are a linear combin |
13,830 | Qualitative variable coding in regression leads to "singularities" | @gung has explained the theory clearly. Here's a practical example to illustrate:
set.seed(1)
pred1 <- factor(c("bad", "med", "high"), levels=c("bad", "med", "high"))
df1 <- data.frame(y=20*abs(runif(6)),
x=rnorm(6),
q=sample(pred1, 6, replace=TRUE)
)
l1 <- lm(y ~ x... | Qualitative variable coding in regression leads to "singularities" | @gung has explained the theory clearly. Here's a practical example to illustrate:
set.seed(1)
pred1 <- factor(c("bad", "med", "high"), levels=c("bad", "med", "high"))
df1 <- data.frame(y=20*abs(runif( | Qualitative variable coding in regression leads to "singularities"
@gung has explained the theory clearly. Here's a practical example to illustrate:
set.seed(1)
pred1 <- factor(c("bad", "med", "high"), levels=c("bad", "med", "high"))
df1 <- data.frame(y=20*abs(runif(6)),
x=rnorm(6),
... | Qualitative variable coding in regression leads to "singularities"
@gung has explained the theory clearly. Here's a practical example to illustrate:
set.seed(1)
pred1 <- factor(c("bad", "med", "high"), levels=c("bad", "med", "high"))
df1 <- data.frame(y=20*abs(runif( |
13,831 | Using lmer for prediction | Expressing factors relationships using R formulas follows from Wilkinson's notation, where '*' denotes crossing and '/' nesting, but there are some particularities in the way formula for mixed-effects models, or more generally random effects, are handled. For example, two crossed random effects might be represented as ... | Using lmer for prediction | Expressing factors relationships using R formulas follows from Wilkinson's notation, where '*' denotes crossing and '/' nesting, but there are some particularities in the way formula for mixed-effects | Using lmer for prediction
Expressing factors relationships using R formulas follows from Wilkinson's notation, where '*' denotes crossing and '/' nesting, but there are some particularities in the way formula for mixed-effects models, or more generally random effects, are handled. For example, two crossed random effect... | Using lmer for prediction
Expressing factors relationships using R formulas follows from Wilkinson's notation, where '*' denotes crossing and '/' nesting, but there are some particularities in the way formula for mixed-effects |
13,832 | Using lmer for prediction | The ez package contains the ezPredict() function, which obtains predictions from lmer models where prediction is based on the fixed effects only. It's really just a wrapper around the approach detailed in the glmm wiki. | Using lmer for prediction | The ez package contains the ezPredict() function, which obtains predictions from lmer models where prediction is based on the fixed effects only. It's really just a wrapper around the approach detaile | Using lmer for prediction
The ez package contains the ezPredict() function, which obtains predictions from lmer models where prediction is based on the fixed effects only. It's really just a wrapper around the approach detailed in the glmm wiki. | Using lmer for prediction
The ez package contains the ezPredict() function, which obtains predictions from lmer models where prediction is based on the fixed effects only. It's really just a wrapper around the approach detaile |
13,833 | Using lmer for prediction | I would use the "logit.mixed" function in Zelig, which is a wrapper for lime4 and makes it very convenient to do prediction and simulation. | Using lmer for prediction | I would use the "logit.mixed" function in Zelig, which is a wrapper for lime4 and makes it very convenient to do prediction and simulation. | Using lmer for prediction
I would use the "logit.mixed" function in Zelig, which is a wrapper for lime4 and makes it very convenient to do prediction and simulation. | Using lmer for prediction
I would use the "logit.mixed" function in Zelig, which is a wrapper for lime4 and makes it very convenient to do prediction and simulation. |
13,834 | Using lmer for prediction | The development version of lme4 has a built-in predict function (predict.merMod). It can be found on https://github.com/lme4/lme4/.
The code to install the "Nearly up-to-date development binaries from lme4 r-forge repository" can be found on above page and is:
install.packages("lme4", repos=c("http://lme4.r-forge.r-pr... | Using lmer for prediction | The development version of lme4 has a built-in predict function (predict.merMod). It can be found on https://github.com/lme4/lme4/.
The code to install the "Nearly up-to-date development binaries fro | Using lmer for prediction
The development version of lme4 has a built-in predict function (predict.merMod). It can be found on https://github.com/lme4/lme4/.
The code to install the "Nearly up-to-date development binaries from lme4 r-forge repository" can be found on above page and is:
install.packages("lme4", repos=c... | Using lmer for prediction
The development version of lme4 has a built-in predict function (predict.merMod). It can be found on https://github.com/lme4/lme4/.
The code to install the "Nearly up-to-date development binaries fro |
13,835 | Using lmer for prediction | Stephen Raudenbush has a book chapter in the Handbook of Multilevel Analysis on "Many Small Groups". If you are only interested in the effects of x on y and have no interest in higher level effects, his suggestion is simply to estimate a fixed effects model (i.e. a dummy variable for all possible higher level groupings... | Using lmer for prediction | Stephen Raudenbush has a book chapter in the Handbook of Multilevel Analysis on "Many Small Groups". If you are only interested in the effects of x on y and have no interest in higher level effects, h | Using lmer for prediction
Stephen Raudenbush has a book chapter in the Handbook of Multilevel Analysis on "Many Small Groups". If you are only interested in the effects of x on y and have no interest in higher level effects, his suggestion is simply to estimate a fixed effects model (i.e. a dummy variable for all possi... | Using lmer for prediction
Stephen Raudenbush has a book chapter in the Handbook of Multilevel Analysis on "Many Small Groups". If you are only interested in the effects of x on y and have no interest in higher level effects, h |
13,836 | Post-hocs for within subjects tests? | Have a look at the multcomp-package and its vignette Simultaneous Inference in General Parametric Models. I think it should do what wan't and the vignette has very good examples and extensive references. | Post-hocs for within subjects tests? | Have a look at the multcomp-package and its vignette Simultaneous Inference in General Parametric Models. I think it should do what wan't and the vignette has very good examples and extensive referenc | Post-hocs for within subjects tests?
Have a look at the multcomp-package and its vignette Simultaneous Inference in General Parametric Models. I think it should do what wan't and the vignette has very good examples and extensive references. | Post-hocs for within subjects tests?
Have a look at the multcomp-package and its vignette Simultaneous Inference in General Parametric Models. I think it should do what wan't and the vignette has very good examples and extensive referenc |
13,837 | Post-hocs for within subjects tests? | I am currently writing a paper in which I have the pleasure to conduct both between and within subjects comparisons. After discussion with my supervisor we decided to run t-tests and use the pretty simple Holm-Bonferroni method (wikipedia) for correcting for alpha error cumulation. It controls for familwise error rate ... | Post-hocs for within subjects tests? | I am currently writing a paper in which I have the pleasure to conduct both between and within subjects comparisons. After discussion with my supervisor we decided to run t-tests and use the pretty si | Post-hocs for within subjects tests?
I am currently writing a paper in which I have the pleasure to conduct both between and within subjects comparisons. After discussion with my supervisor we decided to run t-tests and use the pretty simple Holm-Bonferroni method (wikipedia) for correcting for alpha error cumulation. ... | Post-hocs for within subjects tests?
I am currently writing a paper in which I have the pleasure to conduct both between and within subjects comparisons. After discussion with my supervisor we decided to run t-tests and use the pretty si |
13,838 | Post-hocs for within subjects tests? | I recall some discussion on this in the past; I'm not aware of any implementation of Maxwell & Delaney's approach, although it shouldn't be too difficult to do. Have a look at "Repeated Measures ANOVA using R" which also shows one method of addressing the sphericity issue in Tukey's HSD.
You might also find this descr... | Post-hocs for within subjects tests? | I recall some discussion on this in the past; I'm not aware of any implementation of Maxwell & Delaney's approach, although it shouldn't be too difficult to do. Have a look at "Repeated Measures ANOV | Post-hocs for within subjects tests?
I recall some discussion on this in the past; I'm not aware of any implementation of Maxwell & Delaney's approach, although it shouldn't be too difficult to do. Have a look at "Repeated Measures ANOVA using R" which also shows one method of addressing the sphericity issue in Tukey'... | Post-hocs for within subjects tests?
I recall some discussion on this in the past; I'm not aware of any implementation of Maxwell & Delaney's approach, although it shouldn't be too difficult to do. Have a look at "Repeated Measures ANOV |
13,839 | Post-hocs for within subjects tests? | There are TWO options for the inferential F-tests In SPSS.
Multivariate does NOT assume sphericity, adn so makes use of a different pairwise correlation for each pair of variables.
The "tests of within subjects effects", including any post hoc tests, assumes sphericity and makes some corrections for using a common co... | Post-hocs for within subjects tests? | There are TWO options for the inferential F-tests In SPSS.
Multivariate does NOT assume sphericity, adn so makes use of a different pairwise correlation for each pair of variables.
The "tests of wit | Post-hocs for within subjects tests?
There are TWO options for the inferential F-tests In SPSS.
Multivariate does NOT assume sphericity, adn so makes use of a different pairwise correlation for each pair of variables.
The "tests of within subjects effects", including any post hoc tests, assumes sphericity and makes s... | Post-hocs for within subjects tests?
There are TWO options for the inferential F-tests In SPSS.
Multivariate does NOT assume sphericity, adn so makes use of a different pairwise correlation for each pair of variables.
The "tests of wit |
13,840 | Post-hocs for within subjects tests? | I shall use R function qtukey(1-alpha, means, df) to make family-wise CIs.
For example, R function qtukey(1-0.05, nmeans=4, df=16) gave the critical value $tukey_{0.05,4,16}$=4.046093.
Given a between-subject design with k=4 groups, 5*k=20 sample size e.g. (5-1)*k=16 df for $MS_{Error}$,
$\begin{align}
& Tuke{{y}_{k... | Post-hocs for within subjects tests? | I shall use R function qtukey(1-alpha, means, df) to make family-wise CIs.
For example, R function qtukey(1-0.05, nmeans=4, df=16) gave the critical value $tukey_{0.05,4,16}$=4.046093.
Given a between | Post-hocs for within subjects tests?
I shall use R function qtukey(1-alpha, means, df) to make family-wise CIs.
For example, R function qtukey(1-0.05, nmeans=4, df=16) gave the critical value $tukey_{0.05,4,16}$=4.046093.
Given a between-subject design with k=4 groups, 5*k=20 sample size e.g. (5-1)*k=16 df for $MS_{Err... | Post-hocs for within subjects tests?
I shall use R function qtukey(1-alpha, means, df) to make family-wise CIs.
For example, R function qtukey(1-0.05, nmeans=4, df=16) gave the critical value $tukey_{0.05,4,16}$=4.046093.
Given a between |
13,841 | How does random forest generate the random forest | Implementations of RF differ slightly. I know that Salford Systems' proprietary implementation is supposed to be better than the vanilla one in R. A description of the algorithm is in ESL by Friedman-Hastie-Tibshirani, 2nd ed, 3rd printing. An entire chapter (15th) is devoted to RF, and I find it actually clearer than ... | How does random forest generate the random forest | Implementations of RF differ slightly. I know that Salford Systems' proprietary implementation is supposed to be better than the vanilla one in R. A description of the algorithm is in ESL by Friedman- | How does random forest generate the random forest
Implementations of RF differ slightly. I know that Salford Systems' proprietary implementation is supposed to be better than the vanilla one in R. A description of the algorithm is in ESL by Friedman-Hastie-Tibshirani, 2nd ed, 3rd printing. An entire chapter (15th) is d... | How does random forest generate the random forest
Implementations of RF differ slightly. I know that Salford Systems' proprietary implementation is supposed to be better than the vanilla one in R. A description of the algorithm is in ESL by Friedman- |
13,842 | How does random forest generate the random forest | The main idea is the bagging procedure, not making trees random. In detail, each tree is built on a sample of objects drawn with replacement from the original set; thus each tree has some objects that it hasn't seen, which is what makes the whole ensemble more heterogeneous and thus better in generalizing.
Furthermore,... | How does random forest generate the random forest | The main idea is the bagging procedure, not making trees random. In detail, each tree is built on a sample of objects drawn with replacement from the original set; thus each tree has some objects that | How does random forest generate the random forest
The main idea is the bagging procedure, not making trees random. In detail, each tree is built on a sample of objects drawn with replacement from the original set; thus each tree has some objects that it hasn't seen, which is what makes the whole ensemble more heterogen... | How does random forest generate the random forest
The main idea is the bagging procedure, not making trees random. In detail, each tree is built on a sample of objects drawn with replacement from the original set; thus each tree has some objects that |
13,843 | What is predicted and controlled in reinforcement Learning? | The difference between prediction and control is to do with goals regarding the policy. The policy describes the way of acting depending on current state, and in the literature is often noted as $\pi(a|s)$, the probability of taking action $a$ when in state $s$.
So, my question is for prediction, predict what?
A pre... | What is predicted and controlled in reinforcement Learning? | The difference between prediction and control is to do with goals regarding the policy. The policy describes the way of acting depending on current state, and in the literature is often noted as $\pi( | What is predicted and controlled in reinforcement Learning?
The difference between prediction and control is to do with goals regarding the policy. The policy describes the way of acting depending on current state, and in the literature is often noted as $\pi(a|s)$, the probability of taking action $a$ when in state $s... | What is predicted and controlled in reinforcement Learning?
The difference between prediction and control is to do with goals regarding the policy. The policy describes the way of acting depending on current state, and in the literature is often noted as $\pi( |
13,844 | What is predicted and controlled in reinforcement Learning? | The term control comes from dynamical systems theory, specifically, optimal control. As Richard Sutton writes in the 1.7 Early History of Reinforcement Learning section of his book [1]
Connections between optimal control and dynamic programming, on the
one hand, and learning, on the other, were slow to be recognized... | What is predicted and controlled in reinforcement Learning? | The term control comes from dynamical systems theory, specifically, optimal control. As Richard Sutton writes in the 1.7 Early History of Reinforcement Learning section of his book [1]
Connections be | What is predicted and controlled in reinforcement Learning?
The term control comes from dynamical systems theory, specifically, optimal control. As Richard Sutton writes in the 1.7 Early History of Reinforcement Learning section of his book [1]
Connections between optimal control and dynamic programming, on the
one ... | What is predicted and controlled in reinforcement Learning?
The term control comes from dynamical systems theory, specifically, optimal control. As Richard Sutton writes in the 1.7 Early History of Reinforcement Learning section of his book [1]
Connections be |
13,845 | How can we judge the accuracy of Nate Silver's predictions? | Probabilistic forecasts (or, as they are also known, density forecasts) can be evaluated using scoring-rules, i.e., functions that map a density forecast and an observed outcome to a so-called score, which is minimized in expectation if the density forecast indeed is the true density to be forecasted. Proper scoring ru... | How can we judge the accuracy of Nate Silver's predictions? | Probabilistic forecasts (or, as they are also known, density forecasts) can be evaluated using scoring-rules, i.e., functions that map a density forecast and an observed outcome to a so-called score, | How can we judge the accuracy of Nate Silver's predictions?
Probabilistic forecasts (or, as they are also known, density forecasts) can be evaluated using scoring-rules, i.e., functions that map a density forecast and an observed outcome to a so-called score, which is minimized in expectation if the density forecast in... | How can we judge the accuracy of Nate Silver's predictions?
Probabilistic forecasts (or, as they are also known, density forecasts) can be evaluated using scoring-rules, i.e., functions that map a density forecast and an observed outcome to a so-called score, |
13,846 | How can we judge the accuracy of Nate Silver's predictions? | In Nate Silver's book The Signal and the Noise he writes the following, which may provide some insight for your question:
One of the most important tests of a forecast - I would argue that it is the single most important one - is called calibration. Out of all the times you said there was a 40% chance of rain, how of... | How can we judge the accuracy of Nate Silver's predictions? | In Nate Silver's book The Signal and the Noise he writes the following, which may provide some insight for your question:
One of the most important tests of a forecast - I would argue that it is the | How can we judge the accuracy of Nate Silver's predictions?
In Nate Silver's book The Signal and the Noise he writes the following, which may provide some insight for your question:
One of the most important tests of a forecast - I would argue that it is the single most important one - is called calibration. Out of a... | How can we judge the accuracy of Nate Silver's predictions?
In Nate Silver's book The Signal and the Noise he writes the following, which may provide some insight for your question:
One of the most important tests of a forecast - I would argue that it is the |
13,847 | How can we judge the accuracy of Nate Silver's predictions? | For any single prediction you can't, any more than we can tell if the claim "this coin has a 60% chance of coming up heads" is close to correct from a single toss.
However, you can assess his methodology across many predictions -- for a given election he makes lots of predictions, not just of the presidential race over... | How can we judge the accuracy of Nate Silver's predictions? | For any single prediction you can't, any more than we can tell if the claim "this coin has a 60% chance of coming up heads" is close to correct from a single toss.
However, you can assess his methodol | How can we judge the accuracy of Nate Silver's predictions?
For any single prediction you can't, any more than we can tell if the claim "this coin has a 60% chance of coming up heads" is close to correct from a single toss.
However, you can assess his methodology across many predictions -- for a given election he makes... | How can we judge the accuracy of Nate Silver's predictions?
For any single prediction you can't, any more than we can tell if the claim "this coin has a 60% chance of coming up heads" is close to correct from a single toss.
However, you can assess his methodol |
13,848 | Classification with Gradient Boosting : How to keep the prediction in [0,1] | I like to think of this in analogy with the case of linear models, and their extension to GLMs (generalized linear models).
In a linear model, we fit a linear function to predict our response
$$ \hat y = \beta_0 + \beta_1 x_1 + \cdots \beta_n x_n $$
To generalize to other situations, we introduce a link function, which... | Classification with Gradient Boosting : How to keep the prediction in [0,1] | I like to think of this in analogy with the case of linear models, and their extension to GLMs (generalized linear models).
In a linear model, we fit a linear function to predict our response
$$ \hat | Classification with Gradient Boosting : How to keep the prediction in [0,1]
I like to think of this in analogy with the case of linear models, and their extension to GLMs (generalized linear models).
In a linear model, we fit a linear function to predict our response
$$ \hat y = \beta_0 + \beta_1 x_1 + \cdots \beta_n x... | Classification with Gradient Boosting : How to keep the prediction in [0,1]
I like to think of this in analogy with the case of linear models, and their extension to GLMs (generalized linear models).
In a linear model, we fit a linear function to predict our response
$$ \hat |
13,849 | Classification with Gradient Boosting : How to keep the prediction in [0,1] | After some research, is seems that my intuition and Alex R. comment are right.
In order to build a continuous model with predictions in $[0,1]$, one can put the model $H$ into a logistic function (Wikipedia), such that for $H \in \mathbb{R}$, we have
$$\frac{1}{1 + e^{-H}} \in [0,1]$$
The gradient boosting steps then t... | Classification with Gradient Boosting : How to keep the prediction in [0,1] | After some research, is seems that my intuition and Alex R. comment are right.
In order to build a continuous model with predictions in $[0,1]$, one can put the model $H$ into a logistic function (Wik | Classification with Gradient Boosting : How to keep the prediction in [0,1]
After some research, is seems that my intuition and Alex R. comment are right.
In order to build a continuous model with predictions in $[0,1]$, one can put the model $H$ into a logistic function (Wikipedia), such that for $H \in \mathbb{R}$, w... | Classification with Gradient Boosting : How to keep the prediction in [0,1]
After some research, is seems that my intuition and Alex R. comment are right.
In order to build a continuous model with predictions in $[0,1]$, one can put the model $H$ into a logistic function (Wik |
13,850 | Item Response Theory vs Confirmatory Factor Analysis | @Philchalmers answer is on point, and if you want a reference from one of the leaders in the field, Muthen (creator of Mplus), here you go:
(Edited to include direct quote)
An MPlus user asks: I am trying to describe and illustrate current
similarities and differences between binary CFA and IRT for my thesis.
The... | Item Response Theory vs Confirmatory Factor Analysis | @Philchalmers answer is on point, and if you want a reference from one of the leaders in the field, Muthen (creator of Mplus), here you go:
(Edited to include direct quote)
An MPlus user asks: I am | Item Response Theory vs Confirmatory Factor Analysis
@Philchalmers answer is on point, and if you want a reference from one of the leaders in the field, Muthen (creator of Mplus), here you go:
(Edited to include direct quote)
An MPlus user asks: I am trying to describe and illustrate current
similarities and differ... | Item Response Theory vs Confirmatory Factor Analysis
@Philchalmers answer is on point, and if you want a reference from one of the leaders in the field, Muthen (creator of Mplus), here you go:
(Edited to include direct quote)
An MPlus user asks: I am |
13,851 | Item Response Theory vs Confirmatory Factor Analysis | In some ways you are right, CFA and IRT are cut from the same cloth. But it many ways they are quite different as well. CFA, or more appropriately item CFA, is an adaption of the structural equation/covariance modeling framework to account for a specific type of covariation between categorical items. IRT is more direct... | Item Response Theory vs Confirmatory Factor Analysis | In some ways you are right, CFA and IRT are cut from the same cloth. But it many ways they are quite different as well. CFA, or more appropriately item CFA, is an adaption of the structural equation/c | Item Response Theory vs Confirmatory Factor Analysis
In some ways you are right, CFA and IRT are cut from the same cloth. But it many ways they are quite different as well. CFA, or more appropriately item CFA, is an adaption of the structural equation/covariance modeling framework to account for a specific type of cova... | Item Response Theory vs Confirmatory Factor Analysis
In some ways you are right, CFA and IRT are cut from the same cloth. But it many ways they are quite different as well. CFA, or more appropriately item CFA, is an adaption of the structural equation/c |
13,852 | Item Response Theory vs Confirmatory Factor Analysis | I believe Yves Rosseel discusses it briefly in slides 91-93 of his 2014 workshop:
http://www.personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf
Taken from Rosseel (2014, link above):
Full information approach: marginal maximum likelihood
origins: IRT models (eg Bock & Lieberman, 1970) and GLMM... | Item Response Theory vs Confirmatory Factor Analysis | I believe Yves Rosseel discusses it briefly in slides 91-93 of his 2014 workshop:
http://www.personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf
Taken from Rosseel (2014, link abo | Item Response Theory vs Confirmatory Factor Analysis
I believe Yves Rosseel discusses it briefly in slides 91-93 of his 2014 workshop:
http://www.personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf
Taken from Rosseel (2014, link above):
Full information approach: marginal maximum likelihood
ori... | Item Response Theory vs Confirmatory Factor Analysis
I believe Yves Rosseel discusses it briefly in slides 91-93 of his 2014 workshop:
http://www.personality-project.org/r/tutorials/summerschool.14/rosseel_sem_cat.pdf
Taken from Rosseel (2014, link abo |
13,853 | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks? | The operational meaning of the IID condition is given by the celebrated "representation theorem" of Bruno de Finetti (which, in my humble opinion, is one of the greatest innovations of probability theory ever discovered). According to this brilliant theorem, if we have a sequence $\mathbf{X}=(X_1,X_2,X_3,...)$ with em... | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks? | The operational meaning of the IID condition is given by the celebrated "representation theorem" of Bruno de Finetti (which, in my humble opinion, is one of the greatest innovations of probability the | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?
The operational meaning of the IID condition is given by the celebrated "representation theorem" of Bruno de Finetti (which, in my humble opinion, is one of the greatest innovations of probability theory ever discovered).... | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?
The operational meaning of the IID condition is given by the celebrated "representation theorem" of Bruno de Finetti (which, in my humble opinion, is one of the greatest innovations of probability the |
13,854 | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks? | Yes, samples in the dataset may not be completely iid, but the assumption is present to ease the modelling. To maximize the data likelihood (in almost all models this is explicitly or implicitly part of the optimization), i.e. $P(\mathcal{D}|\theta)$, without the iid assumption, we'd have to model the dependence betwee... | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks? | Yes, samples in the dataset may not be completely iid, but the assumption is present to ease the modelling. To maximize the data likelihood (in almost all models this is explicitly or implicitly part | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?
Yes, samples in the dataset may not be completely iid, but the assumption is present to ease the modelling. To maximize the data likelihood (in almost all models this is explicitly or implicitly part of the optimization),... | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?
Yes, samples in the dataset may not be completely iid, but the assumption is present to ease the modelling. To maximize the data likelihood (in almost all models this is explicitly or implicitly part |
13,855 | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks? | For me, the notion of what i.i.d really is and why it is, in many cases, a necessary assumption makes more sense from the Bayesian perspective. Here, instead of data being thought of as i.i.d in an absolute sense, they are though of as conditionally i.i.d. given model parameters.
For instance, consider a normal model ... | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks? | For me, the notion of what i.i.d really is and why it is, in many cases, a necessary assumption makes more sense from the Bayesian perspective. Here, instead of data being thought of as i.i.d in an ab | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?
For me, the notion of what i.i.d really is and why it is, in many cases, a necessary assumption makes more sense from the Bayesian perspective. Here, instead of data being thought of as i.i.d in an absolute sense, they ar... | Realistically, does the i.i.d. assumption hold for the vast majority of supervised learning tasks?
For me, the notion of what i.i.d really is and why it is, in many cases, a necessary assumption makes more sense from the Bayesian perspective. Here, instead of data being thought of as i.i.d in an ab |
13,856 | Likelihood-free inference - what does it mean? | There are many examples of methods not based on likelihoods in statistics (I don't know about machine learning). Some examples:
Fisher's pure significance tests. Based only on a sharply defined null hypothesis (such as no difference between milk first and milk last in the Lady Tasting Tea experiment. This assumption... | Likelihood-free inference - what does it mean? | There are many examples of methods not based on likelihoods in statistics (I don't know about machine learning). Some examples:
Fisher's pure significance tests. Based only on a sharply defined nul | Likelihood-free inference - what does it mean?
There are many examples of methods not based on likelihoods in statistics (I don't know about machine learning). Some examples:
Fisher's pure significance tests. Based only on a sharply defined null hypothesis (such as no difference between milk first and milk last in t... | Likelihood-free inference - what does it mean?
There are many examples of methods not based on likelihoods in statistics (I don't know about machine learning). Some examples:
Fisher's pure significance tests. Based only on a sharply defined nul |
13,857 | Likelihood-free inference - what does it mean? | Specifically, [the recent] likelihood-free methods are a rewording of the ABC algorithms, where ABC stands for approximate Bayesian computation. This intends to cover inference methods that do not require the use of a closed-form likelihood function, but still intend to study a specific statistical model. They are free... | Likelihood-free inference - what does it mean? | Specifically, [the recent] likelihood-free methods are a rewording of the ABC algorithms, where ABC stands for approximate Bayesian computation. This intends to cover inference methods that do not req | Likelihood-free inference - what does it mean?
Specifically, [the recent] likelihood-free methods are a rewording of the ABC algorithms, where ABC stands for approximate Bayesian computation. This intends to cover inference methods that do not require the use of a closed-form likelihood function, but still intend to st... | Likelihood-free inference - what does it mean?
Specifically, [the recent] likelihood-free methods are a rewording of the ABC algorithms, where ABC stands for approximate Bayesian computation. This intends to cover inference methods that do not req |
13,858 | Likelihood-free inference - what does it mean? | On the machine learning side:
In machine learning, you usually try to maximize $p(y|x)$, where $x$ is the target, and $y$ is the input (for example, x could be some random noise, and y would be an image). Now, how do we optimize this? A common way to do it, is to assume, that $p(y|x) = N(y|\mu(x), \sigma)$. If we assum... | Likelihood-free inference - what does it mean? | On the machine learning side:
In machine learning, you usually try to maximize $p(y|x)$, where $x$ is the target, and $y$ is the input (for example, x could be some random noise, and y would be an ima | Likelihood-free inference - what does it mean?
On the machine learning side:
In machine learning, you usually try to maximize $p(y|x)$, where $x$ is the target, and $y$ is the input (for example, x could be some random noise, and y would be an image). Now, how do we optimize this? A common way to do it, is to assume, t... | Likelihood-free inference - what does it mean?
On the machine learning side:
In machine learning, you usually try to maximize $p(y|x)$, where $x$ is the target, and $y$ is the input (for example, x could be some random noise, and y would be an ima |
13,859 | Likelihood-free inference - what does it mean? | To add to the litany of answers, asymptotic statistics are in fact free of likelihoods.
A "likelihood" here refers to the probability model for the data. I may not care about that. But I may find some simple estimator, like the mean, that is an adequate summary of the data and I want to perform inference about the mea... | Likelihood-free inference - what does it mean? | To add to the litany of answers, asymptotic statistics are in fact free of likelihoods.
A "likelihood" here refers to the probability model for the data. I may not care about that. But I may find som | Likelihood-free inference - what does it mean?
To add to the litany of answers, asymptotic statistics are in fact free of likelihoods.
A "likelihood" here refers to the probability model for the data. I may not care about that. But I may find some simple estimator, like the mean, that is an adequate summary of the dat... | Likelihood-free inference - what does it mean?
To add to the litany of answers, asymptotic statistics are in fact free of likelihoods.
A "likelihood" here refers to the probability model for the data. I may not care about that. But I may find som |
13,860 | Can an instrumental variable equation be written as a directed acyclic graph (DAG)? | Yes.
For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$.
The instrumental variable model for this DAG would be to estimate the causal effect of $X$ on $O$ using $E(O|\widehat{X})$, where $\widehat{X} = E(X|Z)$.
This estimate i... | Can an instrumental variable equation be written as a directed acyclic graph (DAG)? | Yes.
For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$.
The instrumental variable model for this DAG woul | Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Yes.
For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$.
The instrumental variable model for this DAG would be to estimate the causal effect o... | Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Yes.
For example in the DAG below, the instrumental variable $Z$ causes $X$, while the effect of $X$ on $O$ is confounded by unmeasured variable $U$.
The instrumental variable model for this DAG woul |
13,861 | Can an instrumental variable equation be written as a directed acyclic graph (DAG)? | Yes, they surely can.
As a matter of fact, the SCM/DAG literature has been working on generalized notions of instrumental variables, you might want to check Brito and Pearl, or Chen, Kumor and Bareinboim.
The basic IV dag is usually represented as:
Where $U$ is unobserved and $Z$ is an instrument for the effect of $X$... | Can an instrumental variable equation be written as a directed acyclic graph (DAG)? | Yes, they surely can.
As a matter of fact, the SCM/DAG literature has been working on generalized notions of instrumental variables, you might want to check Brito and Pearl, or Chen, Kumor and Bareinb | Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Yes, they surely can.
As a matter of fact, the SCM/DAG literature has been working on generalized notions of instrumental variables, you might want to check Brito and Pearl, or Chen, Kumor and Bareinboim.
The basic IV dag is usually rep... | Can an instrumental variable equation be written as a directed acyclic graph (DAG)?
Yes, they surely can.
As a matter of fact, the SCM/DAG literature has been working on generalized notions of instrumental variables, you might want to check Brito and Pearl, or Chen, Kumor and Bareinb |
13,862 | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | One way to approach the problem is to start with the survival function. In order to have to wait at least $t$ minutes you have to wait for at least $t$ minutes for both the red and the blue train. Thus the overall survival function is just the product of the individual survival functions:
$$ S(t) = \left( 1 - \frac{... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | One way to approach the problem is to start with the survival function. In order to have to wait at least $t$ minutes you have to wait for at least $t$ minutes for both the red and the blue train. | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
One way to approach the problem is to start with the survival function. In order to have to wait at least $t$ minutes you have to wait for at least $t$ minutes for both the red and the blue train. Thus the overall survival ... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
One way to approach the problem is to start with the survival function. In order to have to wait at least $t$ minutes you have to wait for at least $t$ minutes for both the red and the blue train. |
13,863 | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | The answer is $$E[t]=\int_x\int_y \min(x,y)\frac 1 {10} \frac 1 {15}dx dy=\int_x\left(\int_{y<x}ydy+\int_{y>x}xdy\right)\frac 1 {10} \frac 1 {15}dx$$
Get the parts inside the parantheses:
$$\int_{y<x}ydy=y^2/2|_0^x=x^2/2$$
$$\int_{y>x}xdy=xy|_x^{15}=15x-x^2$$
So, the part is:
$$(.)=\left(\int_{y<x}ydy+\int_{y>x}xdy\rig... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | The answer is $$E[t]=\int_x\int_y \min(x,y)\frac 1 {10} \frac 1 {15}dx dy=\int_x\left(\int_{y<x}ydy+\int_{y>x}xdy\right)\frac 1 {10} \frac 1 {15}dx$$
Get the parts inside the parantheses:
$$\int_{y<x} | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
The answer is $$E[t]=\int_x\int_y \min(x,y)\frac 1 {10} \frac 1 {15}dx dy=\int_x\left(\int_{y<x}ydy+\int_{y>x}xdy\right)\frac 1 {10} \frac 1 {15}dx$$
Get the parts inside the parantheses:
$$\int_{y<x}ydy=y^2/2|_0^x=x^2/2$$
$$\... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
The answer is $$E[t]=\int_x\int_y \min(x,y)\frac 1 {10} \frac 1 {15}dx dy=\int_x\left(\int_{y<x}ydy+\int_{y>x}xdy\right)\frac 1 {10} \frac 1 {15}dx$$
Get the parts inside the parantheses:
$$\int_{y<x} |
13,864 | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | Assuming each train is on a fixed timetable independent of the other and of the traveller's arrival time, the probability neither train arrives in the first $x$ minutes is $\frac{10-x}{10} \times \frac{15-x}{15}$ for $0 \le x \le 10$, which when integrated gives $\frac{35}9\approx 3.889$ minutes
Alternatively, assuming... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | Assuming each train is on a fixed timetable independent of the other and of the traveller's arrival time, the probability neither train arrives in the first $x$ minutes is $\frac{10-x}{10} \times \fra | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
Assuming each train is on a fixed timetable independent of the other and of the traveller's arrival time, the probability neither train arrives in the first $x$ minutes is $\frac{10-x}{10} \times \frac{15-x}{15}$ for $0 \le x ... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
Assuming each train is on a fixed timetable independent of the other and of the traveller's arrival time, the probability neither train arrives in the first $x$ minutes is $\frac{10-x}{10} \times \fra |
13,865 | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | I am probably wrong but assuming that each train's starting-time follows a uniform distribution, I would say that when arriving at the station at a random time the expected waiting time for:
the $R$ed train is $\mathbb{E}[R] = 5$ mins
the $B$lue train is $\mathbb{E}[B] = 7.5$ mins
the train that comes the first is $\m... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | I am probably wrong but assuming that each train's starting-time follows a uniform distribution, I would say that when arriving at the station at a random time the expected waiting time for:
the $R$e | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
I am probably wrong but assuming that each train's starting-time follows a uniform distribution, I would say that when arriving at the station at a random time the expected waiting time for:
the $R$ed train is $\mathbb{E}[R] ... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
I am probably wrong but assuming that each train's starting-time follows a uniform distribution, I would say that when arriving at the station at a random time the expected waiting time for:
the $R$e |
13,866 | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | Suppose that red and blue trains arrive on time according to schedule, with the red schedule beginning $\Delta$ minutes after the blue schedule, for some $0\le\Delta<10$. For definiteness suppose the first blue train arrives at time $t=0$.
Assume for now that $\Delta$ lies between $0$ and $5$ minutes. Between $t=0$ and... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | Suppose that red and blue trains arrive on time according to schedule, with the red schedule beginning $\Delta$ minutes after the blue schedule, for some $0\le\Delta<10$. For definiteness suppose the | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
Suppose that red and blue trains arrive on time according to schedule, with the red schedule beginning $\Delta$ minutes after the blue schedule, for some $0\le\Delta<10$. For definiteness suppose the first blue train arrives a... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
Suppose that red and blue trains arrive on time according to schedule, with the red schedule beginning $\Delta$ minutes after the blue schedule, for some $0\le\Delta<10$. For definiteness suppose the |
13,867 | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | This is a Poisson process.
The red train arrives according to a Poisson distribution wIth rate parameter 6/hour.
The blue train also arrives according to a Poisson distribution with rate 4/hour.
Red train arrivals and blue train arrivals are independent.
Total number of train arrivals Is also Poisson with rate 10/ho... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes | This is a Poisson process.
The red train arrives according to a Poisson distribution wIth rate parameter 6/hour.
The blue train also arrives according to a Poisson distribution with rate 4/hour.
Red | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
This is a Poisson process.
The red train arrives according to a Poisson distribution wIth rate parameter 6/hour.
The blue train also arrives according to a Poisson distribution with rate 4/hour.
Red train arrivals and blue t... | Expected value of waiting time for the first of the two buses running every 10 and 15 minutes
This is a Poisson process.
The red train arrives according to a Poisson distribution wIth rate parameter 6/hour.
The blue train also arrives according to a Poisson distribution with rate 4/hour.
Red |
13,868 | R package for Weighted Random Forest? classwt option? | This thread refers to two other threads and a fine article on this matter. It seems classweighting and downsampling are equally good. I use downsampling as described below.
Remember the training set must be large as only 1% will characterize the rare class. Less than 25~50 samples of this class probably will be problem... | R package for Weighted Random Forest? classwt option? | This thread refers to two other threads and a fine article on this matter. It seems classweighting and downsampling are equally good. I use downsampling as described below.
Remember the training set m | R package for Weighted Random Forest? classwt option?
This thread refers to two other threads and a fine article on this matter. It seems classweighting and downsampling are equally good. I use downsampling as described below.
Remember the training set must be large as only 1% will characterize the rare class. Less tha... | R package for Weighted Random Forest? classwt option?
This thread refers to two other threads and a fine article on this matter. It seems classweighting and downsampling are equally good. I use downsampling as described below.
Remember the training set m |
13,869 | How to predict or extend regression lines in ggplot2? | As @Glen mentions you have to use a stat_smooth method which supports extrapolations, which loess does not. lm does however. What you need to do is use the fullrange parameter of stat_smooth and expand the x-axis to include the range you want to predict over. I don't have your data, but here's an example using the mtca... | How to predict or extend regression lines in ggplot2? | As @Glen mentions you have to use a stat_smooth method which supports extrapolations, which loess does not. lm does however. What you need to do is use the fullrange parameter of stat_smooth and expan | How to predict or extend regression lines in ggplot2?
As @Glen mentions you have to use a stat_smooth method which supports extrapolations, which loess does not. lm does however. What you need to do is use the fullrange parameter of stat_smooth and expand the x-axis to include the range you want to predict over. I don'... | How to predict or extend regression lines in ggplot2?
As @Glen mentions you have to use a stat_smooth method which supports extrapolations, which loess does not. lm does however. What you need to do is use the fullrange parameter of stat_smooth and expan |
13,870 | How to predict or extend regression lines in ggplot2? | You would have to predict the values for future observations outside of ggplot2 and then plot the predicted values, you could also get a confidence interval for these predictions.
Look at the loess function, although I'm not sure if it does predictions outside your data range, I'm sure some smooth function does however... | How to predict or extend regression lines in ggplot2? | You would have to predict the values for future observations outside of ggplot2 and then plot the predicted values, you could also get a confidence interval for these predictions.
Look at the loess fu | How to predict or extend regression lines in ggplot2?
You would have to predict the values for future observations outside of ggplot2 and then plot the predicted values, you could also get a confidence interval for these predictions.
Look at the loess function, although I'm not sure if it does predictions outside your ... | How to predict or extend regression lines in ggplot2?
You would have to predict the values for future observations outside of ggplot2 and then plot the predicted values, you could also get a confidence interval for these predictions.
Look at the loess fu |
13,871 | Whether a AR(P) process is stationary or not? | Extract the roots of the polynomial. If all the roots are outside the unit circle then the process is stationary. Model identification aids can be found on the web. Fundamentally the pattern of the ACF's and the pattern of the PACF's are used to identify which model might be a good starting model. If there are more sig... | Whether a AR(P) process is stationary or not? | Extract the roots of the polynomial. If all the roots are outside the unit circle then the process is stationary. Model identification aids can be found on the web. Fundamentally the pattern of the AC | Whether a AR(P) process is stationary or not?
Extract the roots of the polynomial. If all the roots are outside the unit circle then the process is stationary. Model identification aids can be found on the web. Fundamentally the pattern of the ACF's and the pattern of the PACF's are used to identify which model might b... | Whether a AR(P) process is stationary or not?
Extract the roots of the polynomial. If all the roots are outside the unit circle then the process is stationary. Model identification aids can be found on the web. Fundamentally the pattern of the AC |
13,872 | Whether a AR(P) process is stationary or not? | If you have an AR(p) process like this:
$$
y_t = c + \alpha_1 y_{t - 1} + \cdots + \alpha_p y_{t - p}
$$
Then you can build an equation like this:
$$
z^p - \alpha_1 z^{p - 1} - \cdots - \alpha_{p - 1} z - \alpha_p = 0
$$
Find the roots of this equation, and if all of them are less than 1 in absolute value, then the... | Whether a AR(P) process is stationary or not? | If you have an AR(p) process like this:
$$
y_t = c + \alpha_1 y_{t - 1} + \cdots + \alpha_p y_{t - p}
$$
Then you can build an equation like this:
$$
z^p - \alpha_1 z^{p - 1} - \cdots - \alpha_{p - | Whether a AR(P) process is stationary or not?
If you have an AR(p) process like this:
$$
y_t = c + \alpha_1 y_{t - 1} + \cdots + \alpha_p y_{t - p}
$$
Then you can build an equation like this:
$$
z^p - \alpha_1 z^{p - 1} - \cdots - \alpha_{p - 1} z - \alpha_p = 0
$$
Find the roots of this equation, and if all of th... | Whether a AR(P) process is stationary or not?
If you have an AR(p) process like this:
$$
y_t = c + \alpha_1 y_{t - 1} + \cdots + \alpha_p y_{t - p}
$$
Then you can build an equation like this:
$$
z^p - \alpha_1 z^{p - 1} - \cdots - \alpha_{p - |
13,873 | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | Unbiased estimates are typical in introductory statistics courses because they are: 1) classic, 2) easy to analyze mathematically. The Cramer-Rao lower bound is one of the main tools for 2). Away from unbiased estimates there is possible improvement. The bias-variance trade off is an important concept in statistics ... | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | Unbiased estimates are typical in introductory statistics courses because they are: 1) classic, 2) easy to analyze mathematically. The Cramer-Rao lower bound is one of the main tools for 2). Away fr | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
Unbiased estimates are typical in introductory statistics courses because they are: 1) classic, 2) easy to analyze mathematically. The Cramer-Rao lower bound is one of the main tools for 2). Away from unbiased estimates there is possible improvem... | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
Unbiased estimates are typical in introductory statistics courses because they are: 1) classic, 2) easy to analyze mathematically. The Cramer-Rao lower bound is one of the main tools for 2). Away fr |
13,874 | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | I don't know if you are OK with the Bayes Estimate? If yes, then depending on the Loss function you can obtain different Bayes Estimates. A theorem by Blackwell states that Bayes Estimates are never unbiased. A decision theoretic argument states that every admissible rule ((i.e. or every other rule against which it is ... | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | I don't know if you are OK with the Bayes Estimate? If yes, then depending on the Loss function you can obtain different Bayes Estimates. A theorem by Blackwell states that Bayes Estimates are never u | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
I don't know if you are OK with the Bayes Estimate? If yes, then depending on the Loss function you can obtain different Bayes Estimates. A theorem by Blackwell states that Bayes Estimates are never unbiased. A decision theoretic argument states th... | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
I don't know if you are OK with the Bayes Estimate? If yes, then depending on the Loss function you can obtain different Bayes Estimates. A theorem by Blackwell states that Bayes Estimates are never u |
13,875 | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | There is a nice review paper by Kay and Eldar on biased estimation for the purpose of finding estimators with minimum mean square error. | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | There is a nice review paper by Kay and Eldar on biased estimation for the purpose of finding estimators with minimum mean square error. | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
There is a nice review paper by Kay and Eldar on biased estimation for the purpose of finding estimators with minimum mean square error. | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
There is a nice review paper by Kay and Eldar on biased estimation for the purpose of finding estimators with minimum mean square error. |
13,876 | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | “Best” in BLUE means the minimum variance.
Variance is a non-negative quantity, so its lowest value is zero.
If you estimate the coefficients by picking a constant every time, then your estimator has zero variance.
In other words, just estimating the coefficients as zero every time, regardless of the data, is a zero-va... | OLS is BLUE. But what if I don't care about unbiasedness and linearity? | “Best” in BLUE means the minimum variance.
Variance is a non-negative quantity, so its lowest value is zero.
If you estimate the coefficients by picking a constant every time, then your estimator has | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
“Best” in BLUE means the minimum variance.
Variance is a non-negative quantity, so its lowest value is zero.
If you estimate the coefficients by picking a constant every time, then your estimator has zero variance.
In other words, just estimating t... | OLS is BLUE. But what if I don't care about unbiasedness and linearity?
“Best” in BLUE means the minimum variance.
Variance is a non-negative quantity, so its lowest value is zero.
If you estimate the coefficients by picking a constant every time, then your estimator has |
13,877 | Relationship between Cholesky decomposition and matrix inversion? | Gaussian process models often involve computing some quadratic form, such as
$$
y = x^\top\Sigma^{-1}x
$$
where $\Sigma$ is positive definite, $x$ is a vector of appropriate dimension, and we wish to compute scalar $y$. Typically, you don't want to compute $\Sigma^{-1}$ directly because of cost or loss of precision. Us... | Relationship between Cholesky decomposition and matrix inversion? | Gaussian process models often involve computing some quadratic form, such as
$$
y = x^\top\Sigma^{-1}x
$$
where $\Sigma$ is positive definite, $x$ is a vector of appropriate dimension, and we wish to | Relationship between Cholesky decomposition and matrix inversion?
Gaussian process models often involve computing some quadratic form, such as
$$
y = x^\top\Sigma^{-1}x
$$
where $\Sigma$ is positive definite, $x$ is a vector of appropriate dimension, and we wish to compute scalar $y$. Typically, you don't want to compu... | Relationship between Cholesky decomposition and matrix inversion?
Gaussian process models often involve computing some quadratic form, such as
$$
y = x^\top\Sigma^{-1}x
$$
where $\Sigma$ is positive definite, $x$ is a vector of appropriate dimension, and we wish to |
13,878 | How to choose random- and fixed-effects structure in linear mixed models? | I'm not sure there's really a canonical answer to this, but I'll give it a shot.
What is the recommended way to select the best fitting model in this context? When using log-likelihood ratio tests what is the recommended procedure? Generating models upwards (from null model to most complex model) or downwards (from mo... | How to choose random- and fixed-effects structure in linear mixed models? | I'm not sure there's really a canonical answer to this, but I'll give it a shot.
What is the recommended way to select the best fitting model in this context? When using log-likelihood ratio tests wh | How to choose random- and fixed-effects structure in linear mixed models?
I'm not sure there's really a canonical answer to this, but I'll give it a shot.
What is the recommended way to select the best fitting model in this context? When using log-likelihood ratio tests what is the recommended procedure? Generating mo... | How to choose random- and fixed-effects structure in linear mixed models?
I'm not sure there's really a canonical answer to this, but I'll give it a shot.
What is the recommended way to select the best fitting model in this context? When using log-likelihood ratio tests wh |
13,879 | How to choose random- and fixed-effects structure in linear mixed models? | Update May 2017: As it turns out, a lof of what I have written here is kind of wrongish. Some updates are made throughout the post.
I agree a lot with what has been said by Ben Bolker already (thanks for the shout-out to afex::mixed()) but let me add a few more general and specific thoughts on this issue.
Focus on fix... | How to choose random- and fixed-effects structure in linear mixed models? | Update May 2017: As it turns out, a lof of what I have written here is kind of wrongish. Some updates are made throughout the post.
I agree a lot with what has been said by Ben Bolker already (thanks | How to choose random- and fixed-effects structure in linear mixed models?
Update May 2017: As it turns out, a lof of what I have written here is kind of wrongish. Some updates are made throughout the post.
I agree a lot with what has been said by Ben Bolker already (thanks for the shout-out to afex::mixed()) but let m... | How to choose random- and fixed-effects structure in linear mixed models?
Update May 2017: As it turns out, a lof of what I have written here is kind of wrongish. Some updates are made throughout the post.
I agree a lot with what has been said by Ben Bolker already (thanks |
13,880 | Interpreting output from anova() when using lm() as input [duplicate] | The anova() function call returns an ANOVA table. You can use it to get an ANOVA table any time you want one. Thus, the question becomes, 'why might I want an ANOVA table when I can just get $t$-tests of my variables with standard output (i.e., the summary.lm() command)?'
First of all, you may be perfectly satisfie... | Interpreting output from anova() when using lm() as input [duplicate] | The anova() function call returns an ANOVA table. You can use it to get an ANOVA table any time you want one. Thus, the question becomes, 'why might I want an ANOVA table when I can just get $t$-tes | Interpreting output from anova() when using lm() as input [duplicate]
The anova() function call returns an ANOVA table. You can use it to get an ANOVA table any time you want one. Thus, the question becomes, 'why might I want an ANOVA table when I can just get $t$-tests of my variables with standard output (i.e., the... | Interpreting output from anova() when using lm() as input [duplicate]
The anova() function call returns an ANOVA table. You can use it to get an ANOVA table any time you want one. Thus, the question becomes, 'why might I want an ANOVA table when I can just get $t$-tes |
13,881 | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation prediction error of the model | The LASSO and forward/backward model selection both have strengths and limitations. No far sweeping recommendation can be made. Simulation can always be explored to address this.
Both can be understood in the sense of dimensionality: referring to $p$ the number of model parameters and $n$ the number of observations. I... | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation pr | The LASSO and forward/backward model selection both have strengths and limitations. No far sweeping recommendation can be made. Simulation can always be explored to address this.
Both can be understo | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation prediction error of the model
The LASSO and forward/backward model selection both have strengths and limitations. No far sweeping recommendation can be made. Simulation can always be explored to address this.
Both can be ... | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation pr
The LASSO and forward/backward model selection both have strengths and limitations. No far sweeping recommendation can be made. Simulation can always be explored to address this.
Both can be understo |
13,882 | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation prediction error of the model | You want to choose a subset of predictors according to some criteria. Might be in-sample AIC or adjusted R^2, or cross-validation, doesn't matter.
You could test every single predictor subset combination and pick the best subset. However
Very time-consuming due to combinatorial explosion of parameters.
Works if you ha... | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation pr | You want to choose a subset of predictors according to some criteria. Might be in-sample AIC or adjusted R^2, or cross-validation, doesn't matter.
You could test every single predictor subset combinat | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation prediction error of the model
You want to choose a subset of predictors according to some criteria. Might be in-sample AIC or adjusted R^2, or cross-validation, doesn't matter.
You could test every single predictor subset ... | Superiority of LASSO over forward selection/backward elimination in terms of the cross validation pr
You want to choose a subset of predictors according to some criteria. Might be in-sample AIC or adjusted R^2, or cross-validation, doesn't matter.
You could test every single predictor subset combinat |
13,883 | MCMC on a bounded parameter space? | You have several nice, more-or-less simple, options. Your uniform prior helps make them simpler.
Option 1: Independence sampler. You can just set your proposal distribution equal to a uniform distribution over the unit square, which ensures that samples won't fall outside the restricted zone, as you call it. Potenti... | MCMC on a bounded parameter space? | You have several nice, more-or-less simple, options. Your uniform prior helps make them simpler.
Option 1: Independence sampler. You can just set your proposal distribution equal to a uniform distri | MCMC on a bounded parameter space?
You have several nice, more-or-less simple, options. Your uniform prior helps make them simpler.
Option 1: Independence sampler. You can just set your proposal distribution equal to a uniform distribution over the unit square, which ensures that samples won't fall outside the restri... | MCMC on a bounded parameter space?
You have several nice, more-or-less simple, options. Your uniform prior helps make them simpler.
Option 1: Independence sampler. You can just set your proposal distribution equal to a uniform distri |
13,884 | How do I interpret Exp(B) in Cox regression? | Generally speaking, $\exp(\hat\beta_1)$ is the ratio of the hazards between two individuals whose values of $x_1$ differ by one unit when all other covariates are held constant. The parallel with other linear models is that in Cox regression the hazard function is modeled as $h(t)=h_0(t)\exp(\beta'x)$, where $h_0(t)$ i... | How do I interpret Exp(B) in Cox regression? | Generally speaking, $\exp(\hat\beta_1)$ is the ratio of the hazards between two individuals whose values of $x_1$ differ by one unit when all other covariates are held constant. The parallel with othe | How do I interpret Exp(B) in Cox regression?
Generally speaking, $\exp(\hat\beta_1)$ is the ratio of the hazards between two individuals whose values of $x_1$ differ by one unit when all other covariates are held constant. The parallel with other linear models is that in Cox regression the hazard function is modeled as... | How do I interpret Exp(B) in Cox regression?
Generally speaking, $\exp(\hat\beta_1)$ is the ratio of the hazards between two individuals whose values of $x_1$ differ by one unit when all other covariates are held constant. The parallel with othe |
13,885 | How do I interpret Exp(B) in Cox regression? | I am not a statistician, but an MD, trying to sort things out in the world of statistics.
The way you have to interpret this output is by looking at the $\exp(B)$ values. A value of < 1 says that an increase in one unit for that particular variable, will decrease the probability of experiencing an end point throughout... | How do I interpret Exp(B) in Cox regression? | I am not a statistician, but an MD, trying to sort things out in the world of statistics.
The way you have to interpret this output is by looking at the $\exp(B)$ values. A value of < 1 says that an | How do I interpret Exp(B) in Cox regression?
I am not a statistician, but an MD, trying to sort things out in the world of statistics.
The way you have to interpret this output is by looking at the $\exp(B)$ values. A value of < 1 says that an increase in one unit for that particular variable, will decrease the probab... | How do I interpret Exp(B) in Cox regression?
I am not a statistician, but an MD, trying to sort things out in the world of statistics.
The way you have to interpret this output is by looking at the $\exp(B)$ values. A value of < 1 says that an |
13,886 | Conflict between Poisson confidence interval and p-value | There are several ways to define two-sided $p$-values in this case. Michael Fay lists three in his article. The following is mostly taken from his article.
Suppose you have a discrete test statistic $t$ with random variable $T$ such that larger values of $T$ imply larger values of a parameter of interest, $\theta$. Let... | Conflict between Poisson confidence interval and p-value | There are several ways to define two-sided $p$-values in this case. Michael Fay lists three in his article. The following is mostly taken from his article.
Suppose you have a discrete test statistic $ | Conflict between Poisson confidence interval and p-value
There are several ways to define two-sided $p$-values in this case. Michael Fay lists three in his article. The following is mostly taken from his article.
Suppose you have a discrete test statistic $t$ with random variable $T$ such that larger values of $T$ impl... | Conflict between Poisson confidence interval and p-value
There are several ways to define two-sided $p$-values in this case. Michael Fay lists three in his article. The following is mostly taken from his article.
Suppose you have a discrete test statistic $ |
13,887 | Conflict between Poisson confidence interval and p-value | The correct exact two-sided 95% confidence interval $[\lambda^{-},\lambda^{+}]$ is computed from an observation $x$ of a Poisson variable $X$ using the defining relationships
$$\Pr(X\lt x;\lambda^{-}) = \alpha/2$$
and
$$\Pr(X \gt x; \lambda^{+}) = 1 - \alpha/2.$$
We may find these limits by exploiting
$$e^{-\lambda}\su... | Conflict between Poisson confidence interval and p-value | The correct exact two-sided 95% confidence interval $[\lambda^{-},\lambda^{+}]$ is computed from an observation $x$ of a Poisson variable $X$ using the defining relationships
$$\Pr(X\lt x;\lambda^{-}) | Conflict between Poisson confidence interval and p-value
The correct exact two-sided 95% confidence interval $[\lambda^{-},\lambda^{+}]$ is computed from an observation $x$ of a Poisson variable $X$ using the defining relationships
$$\Pr(X\lt x;\lambda^{-}) = \alpha/2$$
and
$$\Pr(X \gt x; \lambda^{+}) = 1 - \alpha/2.$$... | Conflict between Poisson confidence interval and p-value
The correct exact two-sided 95% confidence interval $[\lambda^{-},\lambda^{+}]$ is computed from an observation $x$ of a Poisson variable $X$ using the defining relationships
$$\Pr(X\lt x;\lambda^{-}) |
13,888 | Conflict between Poisson confidence interval and p-value | There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-sided tests. The second would be that the p-value and the interval are using different loss functions, but I would suspe... | Conflict between Poisson confidence interval and p-value | There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-s | Conflict between Poisson confidence interval and p-value
There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-sided tests. The second would be that the p-value and the inter... | Conflict between Poisson confidence interval and p-value
There are two possibilities. The first, and most obvious, is that it is a bug. I looked up the documentation for poisson.test in R and, originally, it was a one-sided test. It did not support two-s |
13,889 | Definition and delimitation of regression model | I would say that "regression model" is a kind of meta-concept, in the sense that you will not find a definition of "regression model", but more concrete concepts such as "linear regression", "non-linear regression", "robust regression" and so on. This in the same way as in mathemathics we usually do not define "number... | Definition and delimitation of regression model | I would say that "regression model" is a kind of meta-concept, in the sense that you will not find a definition of "regression model", but more concrete concepts such as "linear regression", "non-line | Definition and delimitation of regression model
I would say that "regression model" is a kind of meta-concept, in the sense that you will not find a definition of "regression model", but more concrete concepts such as "linear regression", "non-linear regression", "robust regression" and so on. This in the same way as ... | Definition and delimitation of regression model
I would say that "regression model" is a kind of meta-concept, in the sense that you will not find a definition of "regression model", but more concrete concepts such as "linear regression", "non-line |
13,890 | Definition and delimitation of regression model | Two nice answers were already given, but I'd like to add my two cents.
In regression case we have some random variables $Y$ and $X_1,\dots,X_k$. The variables have some unknown distribution and complicated covariance structure. We simplify this problem to focusing solely on conditional distribution, or more precisely o... | Definition and delimitation of regression model | Two nice answers were already given, but I'd like to add my two cents.
In regression case we have some random variables $Y$ and $X_1,\dots,X_k$. The variables have some unknown distribution and compli | Definition and delimitation of regression model
Two nice answers were already given, but I'd like to add my two cents.
In regression case we have some random variables $Y$ and $X_1,\dots,X_k$. The variables have some unknown distribution and complicated covariance structure. We simplify this problem to focusing solely ... | Definition and delimitation of regression model
Two nice answers were already given, but I'd like to add my two cents.
In regression case we have some random variables $Y$ and $X_1,\dots,X_k$. The variables have some unknown distribution and compli |
13,891 | Definition and delimitation of regression model | Some thoughts based on the literature:
F. Hayashi in Chapter 1 of his classic graduate textbook "Econometrics" (2000) states that the following assumptions comprise the classical linear regression model:
Linearity
Strict exogeneity
No multicollinearity
Spherical error variance
"Fixed" regressors
Wooldridge in Chapter... | Definition and delimitation of regression model | Some thoughts based on the literature:
F. Hayashi in Chapter 1 of his classic graduate textbook "Econometrics" (2000) states that the following assumptions comprise the classical linear regression mod | Definition and delimitation of regression model
Some thoughts based on the literature:
F. Hayashi in Chapter 1 of his classic graduate textbook "Econometrics" (2000) states that the following assumptions comprise the classical linear regression model:
Linearity
Strict exogeneity
No multicollinearity
Spherical error va... | Definition and delimitation of regression model
Some thoughts based on the literature:
F. Hayashi in Chapter 1 of his classic graduate textbook "Econometrics" (2000) states that the following assumptions comprise the classical linear regression mod |
13,892 | Definition and delimitation of regression model | Definition and delimitation of regression model
In the past me too shared your perplexity about this point. You refers on econometrics literature and me too refers primarily on that. Unfortunately most econometrics books do not helped much. However I achieved a clearer view that seems me consistent.
What is the defin... | Definition and delimitation of regression model | Definition and delimitation of regression model
In the past me too shared your perplexity about this point. You refers on econometrics literature and me too refers primarily on that. Unfortunately mo | Definition and delimitation of regression model
Definition and delimitation of regression model
In the past me too shared your perplexity about this point. You refers on econometrics literature and me too refers primarily on that. Unfortunately most econometrics books do not helped much. However I achieved a clearer v... | Definition and delimitation of regression model
Definition and delimitation of regression model
In the past me too shared your perplexity about this point. You refers on econometrics literature and me too refers primarily on that. Unfortunately mo |
13,893 | Definition and delimitation of regression model | You can split the question into:
(i) "What is a model? and (ii)"What is regression?"
A "model" is any given way of making a prediction, in the sense of "all models are wrong, but some are useful".
"Regression" is the process of adjusting a model with the intention that its predictions become useful.
Typically some clas... | Definition and delimitation of regression model | You can split the question into:
(i) "What is a model? and (ii)"What is regression?"
A "model" is any given way of making a prediction, in the sense of "all models are wrong, but some are useful".
"Re | Definition and delimitation of regression model
You can split the question into:
(i) "What is a model? and (ii)"What is regression?"
A "model" is any given way of making a prediction, in the sense of "all models are wrong, but some are useful".
"Regression" is the process of adjusting a model with the intention that it... | Definition and delimitation of regression model
You can split the question into:
(i) "What is a model? and (ii)"What is regression?"
A "model" is any given way of making a prediction, in the sense of "all models are wrong, but some are useful".
"Re |
13,894 | R: geom_density values in y-axis [duplicate] | Or you can just used the computed ..scaled.. value stat_density provides:
library(ggplot2)
set.seed(1)
vals1 <- rbeta(1000, 0.5, 0.1)
vals2 <- rbeta(1000, 0.25, 0.3)
gg <- ggplot(data.frame(x=c(vals1, vals2),
grp=c(rep("a", 1000), rep("b", 1000))))
gg <- gg + geom_density(aes(x=x, y=..scaled..... | R: geom_density values in y-axis [duplicate] | Or you can just used the computed ..scaled.. value stat_density provides:
library(ggplot2)
set.seed(1)
vals1 <- rbeta(1000, 0.5, 0.1)
vals2 <- rbeta(1000, 0.25, 0.3)
gg <- ggplot(data.frame(x=c(vals | R: geom_density values in y-axis [duplicate]
Or you can just used the computed ..scaled.. value stat_density provides:
library(ggplot2)
set.seed(1)
vals1 <- rbeta(1000, 0.5, 0.1)
vals2 <- rbeta(1000, 0.25, 0.3)
gg <- ggplot(data.frame(x=c(vals1, vals2),
grp=c(rep("a", 1000), rep("b", 1000))))
... | R: geom_density values in y-axis [duplicate]
Or you can just used the computed ..scaled.. value stat_density provides:
library(ggplot2)
set.seed(1)
vals1 <- rbeta(1000, 0.5, 0.1)
vals2 <- rbeta(1000, 0.25, 0.3)
gg <- ggplot(data.frame(x=c(vals |
13,895 | R: geom_density values in y-axis [duplicate] | It looks like geom_density() is displaying the appropriate values. The area under that whole curve should be 1.
To get an estimate of the probability of certain values, you'd have to integrate over an interval on your 'y' axis, and that value should never be greater than 1. | R: geom_density values in y-axis [duplicate] | It looks like geom_density() is displaying the appropriate values. The area under that whole curve should be 1.
To get an estimate of the probability of certain values, you'd have to integrate over an | R: geom_density values in y-axis [duplicate]
It looks like geom_density() is displaying the appropriate values. The area under that whole curve should be 1.
To get an estimate of the probability of certain values, you'd have to integrate over an interval on your 'y' axis, and that value should never be greater than 1. | R: geom_density values in y-axis [duplicate]
It looks like geom_density() is displaying the appropriate values. The area under that whole curve should be 1.
To get an estimate of the probability of certain values, you'd have to integrate over an |
13,896 | Why is the error "estimated adjustment 'a' is NA" generated from R boot package when calculating confidence intervals using the bca method? | As you can see from your error message, boot.ci calls bca.ci. Because the boot.out object doesn't supply L, the empirical influence values for the statistic you're calculating on the data, bca.ci tries to calculate them using the empinf function, and then (as Michael says) it uses them to calculate the acceleration con... | Why is the error "estimated adjustment 'a' is NA" generated from R boot package when calculating con | As you can see from your error message, boot.ci calls bca.ci. Because the boot.out object doesn't supply L, the empirical influence values for the statistic you're calculating on the data, bca.ci trie | Why is the error "estimated adjustment 'a' is NA" generated from R boot package when calculating confidence intervals using the bca method?
As you can see from your error message, boot.ci calls bca.ci. Because the boot.out object doesn't supply L, the empirical influence values for the statistic you're calculating on t... | Why is the error "estimated adjustment 'a' is NA" generated from R boot package when calculating con
As you can see from your error message, boot.ci calls bca.ci. Because the boot.out object doesn't supply L, the empirical influence values for the statistic you're calculating on the data, bca.ci trie |
13,897 | What is the exact definition of profile likelihood? | I would suggest
Sprott, D. A. (2000). Statistical Inference in Science. Springer. Chapter 4
Next, I am going to summarise the definition of the Profile or maximised likelihood.
Let $\theta$ be a vector parameter that can be decomposed as $\theta = (\delta,\xi)$, where $\delta$ is a vector parameter of interest and $\xi... | What is the exact definition of profile likelihood? | I would suggest
Sprott, D. A. (2000). Statistical Inference in Science. Springer. Chapter 4
Next, I am going to summarise the definition of the Profile or maximised likelihood.
Let $\theta$ be a vecto | What is the exact definition of profile likelihood?
I would suggest
Sprott, D. A. (2000). Statistical Inference in Science. Springer. Chapter 4
Next, I am going to summarise the definition of the Profile or maximised likelihood.
Let $\theta$ be a vector parameter that can be decomposed as $\theta = (\delta,\xi)$, where... | What is the exact definition of profile likelihood?
I would suggest
Sprott, D. A. (2000). Statistical Inference in Science. Springer. Chapter 4
Next, I am going to summarise the definition of the Profile or maximised likelihood.
Let $\theta$ be a vecto |
13,898 | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model? | The AIC is sensitive to the sample size used to train the models. At small sample sizes, "there is a substantial probability that AIC will select models that have too many parameters, i.e. that AIC will overfit". [1] The reference goes on to suggest AICc in this scenario, which introduces an extra penalty term for the ... | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model? | The AIC is sensitive to the sample size used to train the models. At small sample sizes, "there is a substantial probability that AIC will select models that have too many parameters, i.e. that AIC wi | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model?
The AIC is sensitive to the sample size used to train the models. At small sample sizes, "there is a substantial probability that AIC will select models that have too many parameters, i.e. that AIC will overfit". [1] The reference goes... | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model?
The AIC is sensitive to the sample size used to train the models. At small sample sizes, "there is a substantial probability that AIC will select models that have too many parameters, i.e. that AIC wi |
13,899 | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model? | Disclaimer: I didn't go through your code line-by-line. At first sight, it seems legit, so I'll assume it is.
AIC is just the log-likelihood penalized by the number of parameters $k$
$$
2k - 2\ln(\hat L)
$$
$2$ is a constant. $\ln(\hat L)$ is a sum of the unnormalized likelihood function evaluations over all the data p... | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model? | Disclaimer: I didn't go through your code line-by-line. At first sight, it seems legit, so I'll assume it is.
AIC is just the log-likelihood penalized by the number of parameters $k$
$$
2k - 2\ln(\hat | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model?
Disclaimer: I didn't go through your code line-by-line. At first sight, it seems legit, so I'll assume it is.
AIC is just the log-likelihood penalized by the number of parameters $k$
$$
2k - 2\ln(\hat L)
$$
$2$ is a constant. $\ln(\hat... | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model?
Disclaimer: I didn't go through your code line-by-line. At first sight, it seems legit, so I'll assume it is.
AIC is just the log-likelihood penalized by the number of parameters $k$
$$
2k - 2\ln(\hat |
13,900 | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model? | The problem with AIC is that it does not take into account the stochastics of the parameter vector ${\boldsymbol { \beta}}$. Recall that in multiple regression, each estimate of the regression parameters $\beta_0,\ldots,\beta_p$, follow the distribution $\;\hat{\beta_j} \; \sim T(n-p-1)$. Here $n$ is the number of dat... | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model? | The problem with AIC is that it does not take into account the stochastics of the parameter vector ${\boldsymbol { \beta}}$. Recall that in multiple regression, each estimate of the regression paramet | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model?
The problem with AIC is that it does not take into account the stochastics of the parameter vector ${\boldsymbol { \beta}}$. Recall that in multiple regression, each estimate of the regression parameters $\beta_0,\ldots,\beta_p$, follo... | Why does the Akaike Information Criterion (AIC) sometimes favor an overfitted model?
The problem with AIC is that it does not take into account the stochastics of the parameter vector ${\boldsymbol { \beta}}$. Recall that in multiple regression, each estimate of the regression paramet |
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