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
51,001
Probabilities vs. Odds Ratios
In an observational study, the odds ratio can be calculated either by conditioning on exposure ($E$ and its complement $E'$) or outcome ($C$ and its complement $C'$): $\psi = \frac{P(C|E)/P(C'|E)}{P(C|E')/P(C'|E')} = \frac{P(E|C)/P(E'|C)}{P(E|C')/P(E'|C')}$ According to your observations, the binary outcome is whether ...
Probabilities vs. Odds Ratios
In an observational study, the odds ratio can be calculated either by conditioning on exposure ($E$ and its complement $E'$) or outcome ($C$ and its complement $C'$): $\psi = \frac{P(C|E)/P(C'|E)}{P(C
Probabilities vs. Odds Ratios In an observational study, the odds ratio can be calculated either by conditioning on exposure ($E$ and its complement $E'$) or outcome ($C$ and its complement $C'$): $\psi = \frac{P(C|E)/P(C'|E)}{P(C|E')/P(C'|E')} = \frac{P(E|C)/P(E'|C)}{P(E|C')/P(E'|C')}$ According to your observations, ...
Probabilities vs. Odds Ratios In an observational study, the odds ratio can be calculated either by conditioning on exposure ($E$ and its complement $E'$) or outcome ($C$ and its complement $C'$): $\psi = \frac{P(C|E)/P(C'|E)}{P(C
51,002
Probabilities vs. Odds Ratios
I think your confusion here is that sex is one binary variable. It has two levels, male and female, but they are not separate variables. So there aren't two variables to calculate the odds ratio of.
Probabilities vs. Odds Ratios
I think your confusion here is that sex is one binary variable. It has two levels, male and female, but they are not separate variables. So there aren't two variables to calculate the odds ratio of.
Probabilities vs. Odds Ratios I think your confusion here is that sex is one binary variable. It has two levels, male and female, but they are not separate variables. So there aren't two variables to calculate the odds ratio of.
Probabilities vs. Odds Ratios I think your confusion here is that sex is one binary variable. It has two levels, male and female, but they are not separate variables. So there aren't two variables to calculate the odds ratio of.
51,003
How to generate confidence bands for $\hat{Y}$
By fitting an lm object you obtain all the necessary components to do this. Mathematically you have estimates: $$\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right) ^{-1} \left( \mathbf{X}^T y \right) $$ and and estimate: $$\mbox{vcov}\left(\hat{\beta} \right) = \hat{\sigma}^2 \left( \mathbf{X}^T\mathbf{X} \right) ^{-...
How to generate confidence bands for $\hat{Y}$
By fitting an lm object you obtain all the necessary components to do this. Mathematically you have estimates: $$\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right) ^{-1} \left( \mathbf{X}^T y \right)
How to generate confidence bands for $\hat{Y}$ By fitting an lm object you obtain all the necessary components to do this. Mathematically you have estimates: $$\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right) ^{-1} \left( \mathbf{X}^T y \right) $$ and and estimate: $$\mbox{vcov}\left(\hat{\beta} \right) = \hat{\sig...
How to generate confidence bands for $\hat{Y}$ By fitting an lm object you obtain all the necessary components to do this. Mathematically you have estimates: $$\hat{\beta} = \left( \mathbf{X}^T\mathbf{X} \right) ^{-1} \left( \mathbf{X}^T y \right)
51,004
How to generate confidence bands for $\hat{Y}$
we have $$ \hat{\beta}\pm t_{\alpha/2,n-2} \sqrt{\frac{MSE}{\sum(x_i-\bar{x})^2}} $$ then l=lm(y~x) MSE=mean ( (l$residuals)^2) SSX=sum ( (x-mean(x))^2 ) U= l$coefficients + qt(1-alpha/2,n-2) * sqrt(MSE/SSX) L= l$coefficients - qt(1-alpha/2,n-2) * sqrt(MSE/SSX)
How to generate confidence bands for $\hat{Y}$
we have $$ \hat{\beta}\pm t_{\alpha/2,n-2} \sqrt{\frac{MSE}{\sum(x_i-\bar{x})^2}} $$ then l=lm(y~x) MSE=mean ( (l$residuals)^2) SSX=sum ( (x-mean(x))^2 ) U= l$coefficients + qt(1-alph
How to generate confidence bands for $\hat{Y}$ we have $$ \hat{\beta}\pm t_{\alpha/2,n-2} \sqrt{\frac{MSE}{\sum(x_i-\bar{x})^2}} $$ then l=lm(y~x) MSE=mean ( (l$residuals)^2) SSX=sum ( (x-mean(x))^2 ) U= l$coefficients + qt(1-alpha/2,n-2) * sqrt(MSE/SSX) L= l$coefficients - qt(1-alpha/2,n-2) * sqrt(M...
How to generate confidence bands for $\hat{Y}$ we have $$ \hat{\beta}\pm t_{\alpha/2,n-2} \sqrt{\frac{MSE}{\sum(x_i-\bar{x})^2}} $$ then l=lm(y~x) MSE=mean ( (l$residuals)^2) SSX=sum ( (x-mean(x))^2 ) U= l$coefficients + qt(1-alph
51,005
Choosing a method to solve a many-to-one mapping problem
One possible approach is to assume that, conditional on a device's features, each cookie appears independently. In that case, you can fit a SVM or decision tree or some other classifier (I don't recommend logistic regression for classification), with the appearance of each cookie being a binary outcome. This means you ...
Choosing a method to solve a many-to-one mapping problem
One possible approach is to assume that, conditional on a device's features, each cookie appears independently. In that case, you can fit a SVM or decision tree or some other classifier (I don't recom
Choosing a method to solve a many-to-one mapping problem One possible approach is to assume that, conditional on a device's features, each cookie appears independently. In that case, you can fit a SVM or decision tree or some other classifier (I don't recommend logistic regression for classification), with the appearan...
Choosing a method to solve a many-to-one mapping problem One possible approach is to assume that, conditional on a device's features, each cookie appears independently. In that case, you can fit a SVM or decision tree or some other classifier (I don't recom
51,006
Relationship between VC dimension and degrees of freedom
Yaser Abu-Mostafa --- Learning with data Degrees of freedom are an abstraction of the effective number of parameters. The effective number is based on how many dichotomies one can get, rather than how many real-valued parameters are used. In the case of 2-dimensional perceptron, one can think of slope and intercept (p...
Relationship between VC dimension and degrees of freedom
Yaser Abu-Mostafa --- Learning with data Degrees of freedom are an abstraction of the effective number of parameters. The effective number is based on how many dichotomies one can get, rather than ho
Relationship between VC dimension and degrees of freedom Yaser Abu-Mostafa --- Learning with data Degrees of freedom are an abstraction of the effective number of parameters. The effective number is based on how many dichotomies one can get, rather than how many real-valued parameters are used. In the case of 2-dimens...
Relationship between VC dimension and degrees of freedom Yaser Abu-Mostafa --- Learning with data Degrees of freedom are an abstraction of the effective number of parameters. The effective number is based on how many dichotomies one can get, rather than ho
51,007
Does one need to adjust for document length (in terms of pages) in topic modeling?
I haven't used topic models much, but I can say that if you are to apply usual clustering methods to un-normalized document-term matrices (even when the dimensionality of the data is reduced with LSA), you'll see that longer articles will tent to cluster together, just because they have more words. So you may take a l...
Does one need to adjust for document length (in terms of pages) in topic modeling?
I haven't used topic models much, but I can say that if you are to apply usual clustering methods to un-normalized document-term matrices (even when the dimensionality of the data is reduced with LSA)
Does one need to adjust for document length (in terms of pages) in topic modeling? I haven't used topic models much, but I can say that if you are to apply usual clustering methods to un-normalized document-term matrices (even when the dimensionality of the data is reduced with LSA), you'll see that longer articles wil...
Does one need to adjust for document length (in terms of pages) in topic modeling? I haven't used topic models much, but I can say that if you are to apply usual clustering methods to un-normalized document-term matrices (even when the dimensionality of the data is reduced with LSA)
51,008
How to make a two-tailed hypergeometric test?
I ended up considering the mass of probability on the shortest tail and multiplied this probability by 2 to account for the fact that it is a two-tailed test. I have no reference that this is the best method but it felt quite intuitive to me!
How to make a two-tailed hypergeometric test?
I ended up considering the mass of probability on the shortest tail and multiplied this probability by 2 to account for the fact that it is a two-tailed test. I have no reference that this is the best
How to make a two-tailed hypergeometric test? I ended up considering the mass of probability on the shortest tail and multiplied this probability by 2 to account for the fact that it is a two-tailed test. I have no reference that this is the best method but it felt quite intuitive to me!
How to make a two-tailed hypergeometric test? I ended up considering the mass of probability on the shortest tail and multiplied this probability by 2 to account for the fact that it is a two-tailed test. I have no reference that this is the best
51,009
anomaly detection with Markov chain
The final properties of the score may depend on the normalization procedure. Therefore, it may be better to keep using fixed length unix command sequences. However, something that offers "basic consistency" is geometric average. Most likely : $\hat{P}(S)=(q_{S_1}\prod_{t=2}^{|S|}p_{S_{t-1}S_t})^{1/S}$ Therefore, typing...
anomaly detection with Markov chain
The final properties of the score may depend on the normalization procedure. Therefore, it may be better to keep using fixed length unix command sequences. However, something that offers "basic consis
anomaly detection with Markov chain The final properties of the score may depend on the normalization procedure. Therefore, it may be better to keep using fixed length unix command sequences. However, something that offers "basic consistency" is geometric average. Most likely : $\hat{P}(S)=(q_{S_1}\prod_{t=2}^{|S|}p_{S...
anomaly detection with Markov chain The final properties of the score may depend on the normalization procedure. Therefore, it may be better to keep using fixed length unix command sequences. However, something that offers "basic consis
51,010
Estimating AR process for Logistic Regression
I do believe you should recode your values. They are not categorical, they are time-based. Say your first month is January 1995. THen that would be 1, then 2, then 3...January 1999 would take the value 4*12. This is what you should fit the AR(1) on. It is fine to fit the GLM part of the model with the categorical equiv...
Estimating AR process for Logistic Regression
I do believe you should recode your values. They are not categorical, they are time-based. Say your first month is January 1995. THen that would be 1, then 2, then 3...January 1999 would take the valu
Estimating AR process for Logistic Regression I do believe you should recode your values. They are not categorical, they are time-based. Say your first month is January 1995. THen that would be 1, then 2, then 3...January 1999 would take the value 4*12. This is what you should fit the AR(1) on. It is fine to fit the GL...
Estimating AR process for Logistic Regression I do believe you should recode your values. They are not categorical, they are time-based. Say your first month is January 1995. THen that would be 1, then 2, then 3...January 1999 would take the valu
51,011
Finding the support of transformations of random variables
$\DeclareMathOperator{\support}{support}$The general question here is a very hard problem, for the following reason. Let $f(x_1, \dots, x_n)$ be any function, and let $X_1, \dots, X_n$ be Gaussian random variables. Then the r.v. $f(X_1, \dots, X_n)$ has support at 0 if and only if the equation $f(x_1, \dots, x_n) = 0$ ...
Finding the support of transformations of random variables
$\DeclareMathOperator{\support}{support}$The general question here is a very hard problem, for the following reason. Let $f(x_1, \dots, x_n)$ be any function, and let $X_1, \dots, X_n$ be Gaussian ran
Finding the support of transformations of random variables $\DeclareMathOperator{\support}{support}$The general question here is a very hard problem, for the following reason. Let $f(x_1, \dots, x_n)$ be any function, and let $X_1, \dots, X_n$ be Gaussian random variables. Then the r.v. $f(X_1, \dots, X_n)$ has support...
Finding the support of transformations of random variables $\DeclareMathOperator{\support}{support}$The general question here is a very hard problem, for the following reason. Let $f(x_1, \dots, x_n)$ be any function, and let $X_1, \dots, X_n$ be Gaussian ran
51,012
Will normalizing training and testing data separately cause under/overfitting?
In general, this should be avoided. The basic assumption of learning algorithms is that all data come from the same distribution. Applying different normalization procedures (or with different parameters) on the training and test data violates this. There are cases however where this may be appropriate. If it is known ...
Will normalizing training and testing data separately cause under/overfitting?
In general, this should be avoided. The basic assumption of learning algorithms is that all data come from the same distribution. Applying different normalization procedures (or with different paramet
Will normalizing training and testing data separately cause under/overfitting? In general, this should be avoided. The basic assumption of learning algorithms is that all data come from the same distribution. Applying different normalization procedures (or with different parameters) on the training and test data violat...
Will normalizing training and testing data separately cause under/overfitting? In general, this should be avoided. The basic assumption of learning algorithms is that all data come from the same distribution. Applying different normalization procedures (or with different paramet
51,013
Will normalizing training and testing data separately cause under/overfitting?
I don't see any relation with underfitting or overfitting. It is more about applying the same type of transformation with different parameters. I've tried ZCAWhitening on MNIST data with various datasize m = 10k, 10k, 100. My intuition was that the same transformation with the same parameters(mu,sigma) must be applied....
Will normalizing training and testing data separately cause under/overfitting?
I don't see any relation with underfitting or overfitting. It is more about applying the same type of transformation with different parameters. I've tried ZCAWhitening on MNIST data with various datas
Will normalizing training and testing data separately cause under/overfitting? I don't see any relation with underfitting or overfitting. It is more about applying the same type of transformation with different parameters. I've tried ZCAWhitening on MNIST data with various datasize m = 10k, 10k, 100. My intuition was t...
Will normalizing training and testing data separately cause under/overfitting? I don't see any relation with underfitting or overfitting. It is more about applying the same type of transformation with different parameters. I've tried ZCAWhitening on MNIST data with various datas
51,014
Population version of Kendall's tau
Yes, we are measuring the difference between the probability of concordance and discordance for two observations coming from different distribution. I think $ Q(C_1,C_2) $ does not give you many informations (it turns out $ Q $ depends on the copulas, hence I used this notation) unless one of the copulas represents a "...
Population version of Kendall's tau
Yes, we are measuring the difference between the probability of concordance and discordance for two observations coming from different distribution. I think $ Q(C_1,C_2) $ does not give you many infor
Population version of Kendall's tau Yes, we are measuring the difference between the probability of concordance and discordance for two observations coming from different distribution. I think $ Q(C_1,C_2) $ does not give you many informations (it turns out $ Q $ depends on the copulas, hence I used this notation) unle...
Population version of Kendall's tau Yes, we are measuring the difference between the probability of concordance and discordance for two observations coming from different distribution. I think $ Q(C_1,C_2) $ does not give you many infor
51,015
Extrapolation of 2d movement
This is the approach I used to impute missing values in IMU (Inertial Measurement Unit) data: Build trajectory matrix out of time-series Run the missing value imputation algorithm from the TFOCS library (MATLAB) Extract the time-series from the filled trajectory matrix The function you want to use is the Nuclear Norm...
Extrapolation of 2d movement
This is the approach I used to impute missing values in IMU (Inertial Measurement Unit) data: Build trajectory matrix out of time-series Run the missing value imputation algorithm from the TFOCS libr
Extrapolation of 2d movement This is the approach I used to impute missing values in IMU (Inertial Measurement Unit) data: Build trajectory matrix out of time-series Run the missing value imputation algorithm from the TFOCS library (MATLAB) Extract the time-series from the filled trajectory matrix The function you wa...
Extrapolation of 2d movement This is the approach I used to impute missing values in IMU (Inertial Measurement Unit) data: Build trajectory matrix out of time-series Run the missing value imputation algorithm from the TFOCS libr
51,016
Extrapolation of 2d movement
You can assume a constant acceleration... V0=Initial Velocity VF= Final Velocity t= time elapsed a=(Vf-V0)/t Then use the same equation but that constant acceleration to solve for the velocity at each interpolated timepoint: V(t)=a*t+V0 Perhaps instead you do not want to make that assumption, you want to guess a "tr...
Extrapolation of 2d movement
You can assume a constant acceleration... V0=Initial Velocity VF= Final Velocity t= time elapsed a=(Vf-V0)/t Then use the same equation but that constant acceleration to solve for the velocity at ea
Extrapolation of 2d movement You can assume a constant acceleration... V0=Initial Velocity VF= Final Velocity t= time elapsed a=(Vf-V0)/t Then use the same equation but that constant acceleration to solve for the velocity at each interpolated timepoint: V(t)=a*t+V0 Perhaps instead you do not want to make that assump...
Extrapolation of 2d movement You can assume a constant acceleration... V0=Initial Velocity VF= Final Velocity t= time elapsed a=(Vf-V0)/t Then use the same equation but that constant acceleration to solve for the velocity at ea
51,017
Prove $X_i$ in Span of $ X_k, k \neq i$
Based on @whuber's hint, I came up with the following. Please do let me know if I made a mistake somewhere. Let $\alpha^{m}:=\left(a_{1}^{m},\dots, a_{n}^{m}\right)/\left\Vert \left(a_{1}^{m},\dots\,a_{n}^{m}\right)\right\Vert$. Since every bounded sequence in $\mathbb{R}^{n}$ has a convergent sub-sequence (Bolzano-Wei...
Prove $X_i$ in Span of $ X_k, k \neq i$
Based on @whuber's hint, I came up with the following. Please do let me know if I made a mistake somewhere. Let $\alpha^{m}:=\left(a_{1}^{m},\dots, a_{n}^{m}\right)/\left\Vert \left(a_{1}^{m},\dots\,a
Prove $X_i$ in Span of $ X_k, k \neq i$ Based on @whuber's hint, I came up with the following. Please do let me know if I made a mistake somewhere. Let $\alpha^{m}:=\left(a_{1}^{m},\dots, a_{n}^{m}\right)/\left\Vert \left(a_{1}^{m},\dots\,a_{n}^{m}\right)\right\Vert$. Since every bounded sequence in $\mathbb{R}^{n}$ ha...
Prove $X_i$ in Span of $ X_k, k \neq i$ Based on @whuber's hint, I came up with the following. Please do let me know if I made a mistake somewhere. Let $\alpha^{m}:=\left(a_{1}^{m},\dots, a_{n}^{m}\right)/\left\Vert \left(a_{1}^{m},\dots\,a
51,018
is there a book on stats similar to Kallenberg's on probability?
Presumably the person who asked this question is long gone, but for future reference I will mention a book here. Note: I have not read this book. Theoretical Statistics: Topics for a Core Course, by Robert W. Keener. Amazon: link. I quote the last three lines of the review by Amazon user Der Boandlkramer: This book is...
is there a book on stats similar to Kallenberg's on probability?
Presumably the person who asked this question is long gone, but for future reference I will mention a book here. Note: I have not read this book. Theoretical Statistics: Topics for a Core Course, by R
is there a book on stats similar to Kallenberg's on probability? Presumably the person who asked this question is long gone, but for future reference I will mention a book here. Note: I have not read this book. Theoretical Statistics: Topics for a Core Course, by Robert W. Keener. Amazon: link. I quote the last three l...
is there a book on stats similar to Kallenberg's on probability? Presumably the person who asked this question is long gone, but for future reference I will mention a book here. Note: I have not read this book. Theoretical Statistics: Topics for a Core Course, by R
51,019
is there a book on stats similar to Kallenberg's on probability?
Peter Bickel and Kjell Doksum wrote Mathematical Statistics Volume 1 and Volume 2. The two books form a comprehensive guide to modern (frequentist) statistical methods at a level of mathematical sophistication similar to Kallenberg.
is there a book on stats similar to Kallenberg's on probability?
Peter Bickel and Kjell Doksum wrote Mathematical Statistics Volume 1 and Volume 2. The two books form a comprehensive guide to modern (frequentist) statistical methods at a level of mathematical sophi
is there a book on stats similar to Kallenberg's on probability? Peter Bickel and Kjell Doksum wrote Mathematical Statistics Volume 1 and Volume 2. The two books form a comprehensive guide to modern (frequentist) statistical methods at a level of mathematical sophistication similar to Kallenberg.
is there a book on stats similar to Kallenberg's on probability? Peter Bickel and Kjell Doksum wrote Mathematical Statistics Volume 1 and Volume 2. The two books form a comprehensive guide to modern (frequentist) statistical methods at a level of mathematical sophi
51,020
Practical collaborative filtering application for large database
A simple approach would be: Let's say that you 5 items you can train on and 3 that you are recommending: 1) create a similarity matrix between active items and training items, so you similarity matrix is 5 x 3. Similarity can be based on just item attributes, or/and other user's activities on these items. 2) Each time ...
Practical collaborative filtering application for large database
A simple approach would be: Let's say that you 5 items you can train on and 3 that you are recommending: 1) create a similarity matrix between active items and training items, so you similarity matrix
Practical collaborative filtering application for large database A simple approach would be: Let's say that you 5 items you can train on and 3 that you are recommending: 1) create a similarity matrix between active items and training items, so you similarity matrix is 5 x 3. Similarity can be based on just item attribu...
Practical collaborative filtering application for large database A simple approach would be: Let's say that you 5 items you can train on and 3 that you are recommending: 1) create a similarity matrix between active items and training items, so you similarity matrix
51,021
Interpretation P value one sample KS test
So, since P > α, I can not reject the null? That's correct, you wouldn't reject the null with that test. The Kolmogorov-Smirnov can detect scale shifts, but not nearly as efficiently as something specifically designed to pick them up. and hence assume my date follows a exponential distribution with rate 1/117.5? Fa...
Interpretation P value one sample KS test
So, since P > α, I can not reject the null? That's correct, you wouldn't reject the null with that test. The Kolmogorov-Smirnov can detect scale shifts, but not nearly as efficiently as something sp
Interpretation P value one sample KS test So, since P > α, I can not reject the null? That's correct, you wouldn't reject the null with that test. The Kolmogorov-Smirnov can detect scale shifts, but not nearly as efficiently as something specifically designed to pick them up. and hence assume my date follows a expon...
Interpretation P value one sample KS test So, since P > α, I can not reject the null? That's correct, you wouldn't reject the null with that test. The Kolmogorov-Smirnov can detect scale shifts, but not nearly as efficiently as something sp
51,022
Interpretation P value one sample KS test
if you want exponential distribution , I think try to transform exponential to normal, with ln your data I think you should change your data ln your data ln(data) run your code with ks.test(x, "pnorm",mean=0,sd=1)
Interpretation P value one sample KS test
if you want exponential distribution , I think try to transform exponential to normal, with ln your data I think you should change your data ln your data ln(data) run your code with ks.test(x, "pnorm
Interpretation P value one sample KS test if you want exponential distribution , I think try to transform exponential to normal, with ln your data I think you should change your data ln your data ln(data) run your code with ks.test(x, "pnorm",mean=0,sd=1)
Interpretation P value one sample KS test if you want exponential distribution , I think try to transform exponential to normal, with ln your data I think you should change your data ln your data ln(data) run your code with ks.test(x, "pnorm
51,023
Model Stacking algorithm
If I understand your pseudo-code correctly, I don't see where the stacking model is being tested in the cross validation loop. I would expect to see something like model4 = fitmodel4(model1, model2, model3, train) y4 = predict(model4, test) Similar to how the base models' hyper-parameters are being tuned using cross ...
Model Stacking algorithm
If I understand your pseudo-code correctly, I don't see where the stacking model is being tested in the cross validation loop. I would expect to see something like model4 = fitmodel4(model1, model2,
Model Stacking algorithm If I understand your pseudo-code correctly, I don't see where the stacking model is being tested in the cross validation loop. I would expect to see something like model4 = fitmodel4(model1, model2, model3, train) y4 = predict(model4, test) Similar to how the base models' hyper-parameters are...
Model Stacking algorithm If I understand your pseudo-code correctly, I don't see where the stacking model is being tested in the cross validation loop. I would expect to see something like model4 = fitmodel4(model1, model2,
51,024
Correct standard errors for weighted linear regression
These two expressions disagree, as you note, in terms of the use of the residuals in calculation: the difference of $Y$ from the predicted values, being included or omitted from the calculation of the standard errors. They are indeed different estimators but they converge to the same thing in the long run. They also ca...
Correct standard errors for weighted linear regression
These two expressions disagree, as you note, in terms of the use of the residuals in calculation: the difference of $Y$ from the predicted values, being included or omitted from the calculation of the
Correct standard errors for weighted linear regression These two expressions disagree, as you note, in terms of the use of the residuals in calculation: the difference of $Y$ from the predicted values, being included or omitted from the calculation of the standard errors. They are indeed different estimators but they c...
Correct standard errors for weighted linear regression These two expressions disagree, as you note, in terms of the use of the residuals in calculation: the difference of $Y$ from the predicted values, being included or omitted from the calculation of the
51,025
Expectation maxmisation algorithm increases true likelihood at each iteration
I think your picture is misleading you. Rather than envisioning a single orange lower-bound approximation to the true blue likelihood, instead you should be thinking of a series of orange lower-bounds that are approximations about particular points $\theta_t$. In particular, the approximation is necessarily tightest ...
Expectation maxmisation algorithm increases true likelihood at each iteration
I think your picture is misleading you. Rather than envisioning a single orange lower-bound approximation to the true blue likelihood, instead you should be thinking of a series of orange lower-bound
Expectation maxmisation algorithm increases true likelihood at each iteration I think your picture is misleading you. Rather than envisioning a single orange lower-bound approximation to the true blue likelihood, instead you should be thinking of a series of orange lower-bounds that are approximations about particular...
Expectation maxmisation algorithm increases true likelihood at each iteration I think your picture is misleading you. Rather than envisioning a single orange lower-bound approximation to the true blue likelihood, instead you should be thinking of a series of orange lower-bound
51,026
Expectation maxmisation algorithm increases true likelihood at each iteration
The EM algorithm directly maximizes the expected complete data likelihood, but can guarantee the increase of observed data likelihood. The correct version of the proof is in the following reference. Statistical Inference by Casella and Berger also addresses this problem. Wu, C. F. Jeff (1983). "On the Convergence Prope...
Expectation maxmisation algorithm increases true likelihood at each iteration
The EM algorithm directly maximizes the expected complete data likelihood, but can guarantee the increase of observed data likelihood. The correct version of the proof is in the following reference. S
Expectation maxmisation algorithm increases true likelihood at each iteration The EM algorithm directly maximizes the expected complete data likelihood, but can guarantee the increase of observed data likelihood. The correct version of the proof is in the following reference. Statistical Inference by Casella and Berger...
Expectation maxmisation algorithm increases true likelihood at each iteration The EM algorithm directly maximizes the expected complete data likelihood, but can guarantee the increase of observed data likelihood. The correct version of the proof is in the following reference. S
51,027
LASSO closed form with two regressors, JRSSB eq. (6)
If $$\max[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2,0]=0$$ then $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 \leq 0.$$ But you wrote $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 < 0.$$ Now $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 \leq 0$$ implies $$s/2\leq (\hat\beta^{(ols)}_1-\hat\beta^{(ols)...
LASSO closed form with two regressors, JRSSB eq. (6)
If $$\max[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2,0]=0$$ then $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 \leq 0.$$ But you wrote $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 < 0.$$
LASSO closed form with two regressors, JRSSB eq. (6) If $$\max[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2,0]=0$$ then $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 \leq 0.$$ But you wrote $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 < 0.$$ Now $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 \leq 0$$ imp...
LASSO closed form with two regressors, JRSSB eq. (6) If $$\max[s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2,0]=0$$ then $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 \leq 0.$$ But you wrote $$s/2-(\hat\beta^{(ols)}_1-\hat\beta^{(ols)}_2)/2 < 0.$$
51,028
Asymptotic distribution of $\chi^2_{(1)}$
If you want the limiting distribution of the minimum of a collection of non-identically distributed chi-squares (each with a different degrees-of-freedom parameter), then this thread, Order statistics (e.g., minimum) of infinite collection of chi-square variates? I believe answers exactly the question. If you want to s...
Asymptotic distribution of $\chi^2_{(1)}$
If you want the limiting distribution of the minimum of a collection of non-identically distributed chi-squares (each with a different degrees-of-freedom parameter), then this thread, Order statistics
Asymptotic distribution of $\chi^2_{(1)}$ If you want the limiting distribution of the minimum of a collection of non-identically distributed chi-squares (each with a different degrees-of-freedom parameter), then this thread, Order statistics (e.g., minimum) of infinite collection of chi-square variates? I believe answ...
Asymptotic distribution of $\chi^2_{(1)}$ If you want the limiting distribution of the minimum of a collection of non-identically distributed chi-squares (each with a different degrees-of-freedom parameter), then this thread, Order statistics
51,029
Distinguish an ARMA and an ARIMA model graphically
It is not easy to distinguish an ARMA model from an ARIMA model graphically. The problem is that the stationary ARMA form can be made arbitrarily close to the ARIMA form by setting one of the roots of the auto-regressive characteristic polynomial arbitrarily close to one. Trying to distinguish between these models is...
Distinguish an ARMA and an ARIMA model graphically
It is not easy to distinguish an ARMA model from an ARIMA model graphically. The problem is that the stationary ARMA form can be made arbitrarily close to the ARIMA form by setting one of the roots o
Distinguish an ARMA and an ARIMA model graphically It is not easy to distinguish an ARMA model from an ARIMA model graphically. The problem is that the stationary ARMA form can be made arbitrarily close to the ARIMA form by setting one of the roots of the auto-regressive characteristic polynomial arbitrarily close to ...
Distinguish an ARMA and an ARIMA model graphically It is not easy to distinguish an ARMA model from an ARIMA model graphically. The problem is that the stationary ARMA form can be made arbitrarily close to the ARIMA form by setting one of the roots o
51,030
Distinguish an ARMA and an ARIMA model graphically
Given that are no Pulses, Level Shifts, Seasonal Pulses, Local Time Trends AND the ultimate ARIMA parameters and model error variance are constant over time AND that you have suitably (not over) differenced the series to obtain stationarity THEN: compare the acf and the pacf for dominance. Examine the dominant one and ...
Distinguish an ARMA and an ARIMA model graphically
Given that are no Pulses, Level Shifts, Seasonal Pulses, Local Time Trends AND the ultimate ARIMA parameters and model error variance are constant over time AND that you have suitably (not over) diffe
Distinguish an ARMA and an ARIMA model graphically Given that are no Pulses, Level Shifts, Seasonal Pulses, Local Time Trends AND the ultimate ARIMA parameters and model error variance are constant over time AND that you have suitably (not over) differenced the series to obtain stationarity THEN: compare the acf and th...
Distinguish an ARMA and an ARIMA model graphically Given that are no Pulses, Level Shifts, Seasonal Pulses, Local Time Trends AND the ultimate ARIMA parameters and model error variance are constant over time AND that you have suitably (not over) diffe
51,031
Estimate mean & standard deviation of set S if I know stats of an inner set and outer set
I'm going to solve this by calculation. I'm sure there's some clever statistics way to figure this out -- if you know, please make a post and I'll probably accept it :p. Until then, this will have to do. Problem statement We know $\mu_1=\mu(S_1)$, $\sigma_1=\sigma(S_1)$, and $N_1=\lvert S_1\rvert$, as well as the equ...
Estimate mean & standard deviation of set S if I know stats of an inner set and outer set
I'm going to solve this by calculation. I'm sure there's some clever statistics way to figure this out -- if you know, please make a post and I'll probably accept it :p. Until then, this will have t
Estimate mean & standard deviation of set S if I know stats of an inner set and outer set I'm going to solve this by calculation. I'm sure there's some clever statistics way to figure this out -- if you know, please make a post and I'll probably accept it :p. Until then, this will have to do. Problem statement We kno...
Estimate mean & standard deviation of set S if I know stats of an inner set and outer set I'm going to solve this by calculation. I'm sure there's some clever statistics way to figure this out -- if you know, please make a post and I'll probably accept it :p. Until then, this will have t
51,032
Time series with multiple subjects and multiple variables in R
The Arima function in the forecast package can fit a regression model to the data with an ARIMA model for the errors. The order argument specifies the orders of the ARIMA model, while the argument xreg defines which data object contains the observations of the predictors. E.g., if xreg is a matrix of predictors: model ...
Time series with multiple subjects and multiple variables in R
The Arima function in the forecast package can fit a regression model to the data with an ARIMA model for the errors. The order argument specifies the orders of the ARIMA model, while the argument xre
Time series with multiple subjects and multiple variables in R The Arima function in the forecast package can fit a regression model to the data with an ARIMA model for the errors. The order argument specifies the orders of the ARIMA model, while the argument xreg defines which data object contains the observations of ...
Time series with multiple subjects and multiple variables in R The Arima function in the forecast package can fit a regression model to the data with an ARIMA model for the errors. The order argument specifies the orders of the ARIMA model, while the argument xre
51,033
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained?
I've heard all three but I don't particularly like any of them (with variance being at the bottom of the list ). Really, I prefer calling $R^{2}$ a measure of fit for our model to the data (and if you really want to use $R^{2}$, use its adjusted version instead.) The reason I don't like calling it a variance is because...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance*
I've heard all three but I don't particularly like any of them (with variance being at the bottom of the list ). Really, I prefer calling $R^{2}$ a measure of fit for our model to the data (and if you
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained? I've heard all three but I don't particularly like any of them (with variance being at the bottom of the list ). Really, I prefer calling $R^{2}$ a measure of fit for our model to the data (and if you really ...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* I've heard all three but I don't particularly like any of them (with variance being at the bottom of the list ). Really, I prefer calling $R^{2}$ a measure of fit for our model to the data (and if you
51,034
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained?
I like to explain R-squared to clients as follows - it's just the squared correlation between the predicted values of the Dependent Variable and the actual values of the Dependent Variable. if you plot the former against the latter as a scatter chart, and fit a regression line, then the R-squared of that regression lin...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance*
I like to explain R-squared to clients as follows - it's just the squared correlation between the predicted values of the Dependent Variable and the actual values of the Dependent Variable. if you plo
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained? I like to explain R-squared to clients as follows - it's just the squared correlation between the predicted values of the Dependent Variable and the actual values of the Dependent Variable. if you plot the fo...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* I like to explain R-squared to clients as follows - it's just the squared correlation between the predicted values of the Dependent Variable and the actual values of the Dependent Variable. if you plo
51,035
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained?
Informally, R2 is a measure for the variation or variability. In this context, variation measures the size of the residuals. Clearly, variation isn't equal to the variance. Variance is simply a measure of the deviation from the sample mean.
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance*
Informally, R2 is a measure for the variation or variability. In this context, variation measures the size of the residuals. Clearly, variation isn't equal to the variance. Variance is simply a measur
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained? Informally, R2 is a measure for the variation or variability. In this context, variation measures the size of the residuals. Clearly, variation isn't equal to the variance. Variance is simply a measure of the...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* Informally, R2 is a measure for the variation or variability. In this context, variation measures the size of the residuals. Clearly, variation isn't equal to the variance. Variance is simply a measur
51,036
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained?
In the context of linear regression, $R^2$ is a measure (estimate?) of the proportion of variance explained by the model. It seems to me that if we want to be precise, variance is the only word that can be used. To say that it is a measure of proportion of response variation is at best informal; the quote from Wikipe...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance*
In the context of linear regression, $R^2$ is a measure (estimate?) of the proportion of variance explained by the model. It seems to me that if we want to be precise, variance is the only word that
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained? In the context of linear regression, $R^2$ is a measure (estimate?) of the proportion of variance explained by the model. It seems to me that if we want to be precise, variance is the only word that can be u...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* In the context of linear regression, $R^2$ is a measure (estimate?) of the proportion of variance explained by the model. It seems to me that if we want to be precise, variance is the only word that
51,037
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained?
“Variation” and “variability” are English words that have colloquial meanings that basically everyone more-or-less understands: the extent to which the values are different. If there is minimal variability, the values are close together; is there is extensive variation, the values are far apart. “Variance” is technical...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance*
“Variation” and “variability” are English words that have colloquial meanings that basically everyone more-or-less understands: the extent to which the values are different. If there is minimal variab
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* explained? “Variation” and “variability” are English words that have colloquial meanings that basically everyone more-or-less understands: the extent to which the values are different. If there is minimal variability, t...
Does $R^2$ interpretable as the proportion of *variation* explained, or the proportion of *variance* “Variation” and “variability” are English words that have colloquial meanings that basically everyone more-or-less understands: the extent to which the values are different. If there is minimal variab
51,038
Probability of getting $k$ answers correct in an exam with 4 and 2 questions on $N$ possible subjects?
Consider each section of the exam as containing the result of several draws (without replacement) from an urn. The urn contains the K subjects the student studied, and the N - K subjects he/she skipped. Let J = N - K, for convenience. Part A contains between 0 and 4 subjects that the student studied, while part B con...
Probability of getting $k$ answers correct in an exam with 4 and 2 questions on $N$ possible subject
Consider each section of the exam as containing the result of several draws (without replacement) from an urn. The urn contains the K subjects the student studied, and the N - K subjects he/she skipp
Probability of getting $k$ answers correct in an exam with 4 and 2 questions on $N$ possible subjects? Consider each section of the exam as containing the result of several draws (without replacement) from an urn. The urn contains the K subjects the student studied, and the N - K subjects he/she skipped. Let J = N - ...
Probability of getting $k$ answers correct in an exam with 4 and 2 questions on $N$ possible subject Consider each section of the exam as containing the result of several draws (without replacement) from an urn. The urn contains the K subjects the student studied, and the N - K subjects he/she skipp
51,039
Is using PCA then autoencoders for pre-processing useful?
I'm not a deep learning expert by any means, but my guess is that the PCA serves two functions: computational improvements if the input dimensionality is significantly reduced, and a kind of preconditioning for the optimization problem. Although a normal autoencoder setup certainly can learn the linear relationships, i...
Is using PCA then autoencoders for pre-processing useful?
I'm not a deep learning expert by any means, but my guess is that the PCA serves two functions: computational improvements if the input dimensionality is significantly reduced, and a kind of precondit
Is using PCA then autoencoders for pre-processing useful? I'm not a deep learning expert by any means, but my guess is that the PCA serves two functions: computational improvements if the input dimensionality is significantly reduced, and a kind of preconditioning for the optimization problem. Although a normal autoenc...
Is using PCA then autoencoders for pre-processing useful? I'm not a deep learning expert by any means, but my guess is that the PCA serves two functions: computational improvements if the input dimensionality is significantly reduced, and a kind of precondit
51,040
Power martingales for change detection: M goes to zero?
Your implementation is correct. The power martingale tends to get very small (closer to 0) when p-values are uniformly distributed. To avoid that, you just need to restart your martingale from 1 as soon as it gets smaller than 1. So just add: Mtest[i] = max(Mtest[i], 1) This will keep your martingale small (but not le...
Power martingales for change detection: M goes to zero?
Your implementation is correct. The power martingale tends to get very small (closer to 0) when p-values are uniformly distributed. To avoid that, you just need to restart your martingale from 1 as so
Power martingales for change detection: M goes to zero? Your implementation is correct. The power martingale tends to get very small (closer to 0) when p-values are uniformly distributed. To avoid that, you just need to restart your martingale from 1 as soon as it gets smaller than 1. So just add: Mtest[i] = max(Mtest[...
Power martingales for change detection: M goes to zero? Your implementation is correct. The power martingale tends to get very small (closer to 0) when p-values are uniformly distributed. To avoid that, you just need to restart your martingale from 1 as so
51,041
Power martingales for change detection: M goes to zero?
I think you can see the nature of the problem if you calculate how many "strange" data points you need, given that you've observed a long run of "not-strange" data points (using the language of Ho and Wechsler here). Let's do some back-of-the-envelope calculations: for a stream of $k$ data points with constant $p_i = p...
Power martingales for change detection: M goes to zero?
I think you can see the nature of the problem if you calculate how many "strange" data points you need, given that you've observed a long run of "not-strange" data points (using the language of Ho and
Power martingales for change detection: M goes to zero? I think you can see the nature of the problem if you calculate how many "strange" data points you need, given that you've observed a long run of "not-strange" data points (using the language of Ho and Wechsler here). Let's do some back-of-the-envelope calculations...
Power martingales for change detection: M goes to zero? I think you can see the nature of the problem if you calculate how many "strange" data points you need, given that you've observed a long run of "not-strange" data points (using the language of Ho and
51,042
Power martingales for change detection: M goes to zero?
In my opinion you don't understand change concept. Try to do this: You must implement a dataset with at least 2 clusters with n-dimension vectors (for a test is better 2-dimesion). Your code must reads one-to-one all the dates from cluster #1. When your code starts to read dates from cluster #2 your martigale must det...
Power martingales for change detection: M goes to zero?
In my opinion you don't understand change concept. Try to do this: You must implement a dataset with at least 2 clusters with n-dimension vectors (for a test is better 2-dimesion). Your code must rea
Power martingales for change detection: M goes to zero? In my opinion you don't understand change concept. Try to do this: You must implement a dataset with at least 2 clusters with n-dimension vectors (for a test is better 2-dimesion). Your code must reads one-to-one all the dates from cluster #1. When your code star...
Power martingales for change detection: M goes to zero? In my opinion you don't understand change concept. Try to do this: You must implement a dataset with at least 2 clusters with n-dimension vectors (for a test is better 2-dimesion). Your code must rea
51,043
computing the posterior of two Gaussian probability distributions
If $\epsilon$ is a scalar (which it seems to be), then your integral is a 1D convolution of $p_\epsilon(\epsilon|g)$ with a Gaussian. If $p_\epsilon$ is fairly well behaved, you could evaluate it on a 1D grid and use any old signal processing toolbox to calculate the convolution (you could also quite easily code it by...
computing the posterior of two Gaussian probability distributions
If $\epsilon$ is a scalar (which it seems to be), then your integral is a 1D convolution of $p_\epsilon(\epsilon|g)$ with a Gaussian. If $p_\epsilon$ is fairly well behaved, you could evaluate it on
computing the posterior of two Gaussian probability distributions If $\epsilon$ is a scalar (which it seems to be), then your integral is a 1D convolution of $p_\epsilon(\epsilon|g)$ with a Gaussian. If $p_\epsilon$ is fairly well behaved, you could evaluate it on a 1D grid and use any old signal processing toolbox to...
computing the posterior of two Gaussian probability distributions If $\epsilon$ is a scalar (which it seems to be), then your integral is a 1D convolution of $p_\epsilon(\epsilon|g)$ with a Gaussian. If $p_\epsilon$ is fairly well behaved, you could evaluate it on
51,044
simulate GLM with square root link in R
I figured out some answers to my questions. Regarding the mathematical expressions of predict and simulate, these can be obtained by the following code (thanks to a tip from W. van der Elst): getS3method(c("predict"), class = "glm") getS3method(c("simulate"), class = "lm") . Regarding the predict function, I incorrec...
simulate GLM with square root link in R
I figured out some answers to my questions. Regarding the mathematical expressions of predict and simulate, these can be obtained by the following code (thanks to a tip from W. van der Elst): getS3me
simulate GLM with square root link in R I figured out some answers to my questions. Regarding the mathematical expressions of predict and simulate, these can be obtained by the following code (thanks to a tip from W. van der Elst): getS3method(c("predict"), class = "glm") getS3method(c("simulate"), class = "lm") . Re...
simulate GLM with square root link in R I figured out some answers to my questions. Regarding the mathematical expressions of predict and simulate, these can be obtained by the following code (thanks to a tip from W. van der Elst): getS3me
51,045
simulate GLM with square root link in R
What is the difference? This model m <- glm(formula=d[,1] ~ d[,2] + d[,3] + d[,4], family=gaussian(link="sqrt")) is $$ y_i \sim N(\mu_i,\sigma^2), \quad \sqrt{\mu_i} = \vec{\beta}^\top\vec{x}_i $$ It is estimated with iterative weighted least squares. Thus you will find that more iteration are used library(MASS) ...
simulate GLM with square root link in R
What is the difference? This model m <- glm(formula=d[,1] ~ d[,2] + d[,3] + d[,4], family=gaussian(link="sqrt")) is $$ y_i \sim N(\mu_i,\sigma^2), \quad \sqrt{\mu_i} = \vec{\beta}^\top\vec{x}_i $
simulate GLM with square root link in R What is the difference? This model m <- glm(formula=d[,1] ~ d[,2] + d[,3] + d[,4], family=gaussian(link="sqrt")) is $$ y_i \sim N(\mu_i,\sigma^2), \quad \sqrt{\mu_i} = \vec{\beta}^\top\vec{x}_i $$ It is estimated with iterative weighted least squares. Thus you will find that...
simulate GLM with square root link in R What is the difference? This model m <- glm(formula=d[,1] ~ d[,2] + d[,3] + d[,4], family=gaussian(link="sqrt")) is $$ y_i \sim N(\mu_i,\sigma^2), \quad \sqrt{\mu_i} = \vec{\beta}^\top\vec{x}_i $
51,046
Is the PLS-DA approach for categorical variables the same as that used for PLS regression?
Yes. PLS-DA is basically PLS regression where Y consists of categorical variables. Here is an example of Y matrix with 3 groups each consists of 2 samples (the first row is headers and is not involved in calculations). After applying PLS-DA you can obtain a BETA matrix (if you are using SIMPLS algorithm, for example) ...
Is the PLS-DA approach for categorical variables the same as that used for PLS regression?
Yes. PLS-DA is basically PLS regression where Y consists of categorical variables. Here is an example of Y matrix with 3 groups each consists of 2 samples (the first row is headers and is not involved
Is the PLS-DA approach for categorical variables the same as that used for PLS regression? Yes. PLS-DA is basically PLS regression where Y consists of categorical variables. Here is an example of Y matrix with 3 groups each consists of 2 samples (the first row is headers and is not involved in calculations). After app...
Is the PLS-DA approach for categorical variables the same as that used for PLS regression? Yes. PLS-DA is basically PLS regression where Y consists of categorical variables. Here is an example of Y matrix with 3 groups each consists of 2 samples (the first row is headers and is not involved
51,047
Confidence interval for differences in total sums
Yes, you could simply go down the t-test route, because those deviations from normality don't really matter with sample sizes like that. Obviously, bootstrapping is a perfect alternative and I may display how easy that is with the following commented R code: # examples raw wins in A and be raw_win_A <- abs(rnorm(100000...
Confidence interval for differences in total sums
Yes, you could simply go down the t-test route, because those deviations from normality don't really matter with sample sizes like that. Obviously, bootstrapping is a perfect alternative and I may dis
Confidence interval for differences in total sums Yes, you could simply go down the t-test route, because those deviations from normality don't really matter with sample sizes like that. Obviously, bootstrapping is a perfect alternative and I may display how easy that is with the following commented R code: # examples ...
Confidence interval for differences in total sums Yes, you could simply go down the t-test route, because those deviations from normality don't really matter with sample sizes like that. Obviously, bootstrapping is a perfect alternative and I may dis
51,048
Confidence interval for differences in total sums
A straightforward bootstrap approach would be to build a vector of samples (A -B) if A and B are your logs of sales of the different versions of the website. Given this vector you perform bootstrap resamples of this vector. You thus end up with a number of resamples that can approximate the true distribution of the dif...
Confidence interval for differences in total sums
A straightforward bootstrap approach would be to build a vector of samples (A -B) if A and B are your logs of sales of the different versions of the website. Given this vector you perform bootstrap re
Confidence interval for differences in total sums A straightforward bootstrap approach would be to build a vector of samples (A -B) if A and B are your logs of sales of the different versions of the website. Given this vector you perform bootstrap resamples of this vector. You thus end up with a number of resamples tha...
Confidence interval for differences in total sums A straightforward bootstrap approach would be to build a vector of samples (A -B) if A and B are your logs of sales of the different versions of the website. Given this vector you perform bootstrap re
51,049
Bootstrapping the data to set up a prior
Have you considered simply applying a scaling to the covariance matrix, as suggested by Andrew Gelman? See also this paper on the scaled inverse Wishart.
Bootstrapping the data to set up a prior
Have you considered simply applying a scaling to the covariance matrix, as suggested by Andrew Gelman? See also this paper on the scaled inverse Wishart.
Bootstrapping the data to set up a prior Have you considered simply applying a scaling to the covariance matrix, as suggested by Andrew Gelman? See also this paper on the scaled inverse Wishart.
Bootstrapping the data to set up a prior Have you considered simply applying a scaling to the covariance matrix, as suggested by Andrew Gelman? See also this paper on the scaled inverse Wishart.
51,050
Combining Posterior Distributions of Separate Models
One approach to combine results from multiple models in a manner that reflects how well each model works on the dataset under analysis is Bayesian model averaging. One simple way of approximating full Bayesian model averaging is to use weights proportional to $e^{-\text{BIC}_m/2}$ (or using the effective number of par...
Combining Posterior Distributions of Separate Models
One approach to combine results from multiple models in a manner that reflects how well each model works on the dataset under analysis is Bayesian model averaging. One simple way of approximating ful
Combining Posterior Distributions of Separate Models One approach to combine results from multiple models in a manner that reflects how well each model works on the dataset under analysis is Bayesian model averaging. One simple way of approximating full Bayesian model averaging is to use weights proportional to $e^{-\...
Combining Posterior Distributions of Separate Models One approach to combine results from multiple models in a manner that reflects how well each model works on the dataset under analysis is Bayesian model averaging. One simple way of approximating ful
51,051
R - how to get standard error for a breakpoint/parameter in a piecewise regression
Hmm, so I think I figured out the issues I was having with segmented. It had to do with the weight statement (it doesn't work to weight the lm and the segmented model). Segmented seems like the best bet for me. It does a good job estimating breakpoints, even with my short datasets. It isn't terribly difficult to cons...
R - how to get standard error for a breakpoint/parameter in a piecewise regression
Hmm, so I think I figured out the issues I was having with segmented. It had to do with the weight statement (it doesn't work to weight the lm and the segmented model). Segmented seems like the best
R - how to get standard error for a breakpoint/parameter in a piecewise regression Hmm, so I think I figured out the issues I was having with segmented. It had to do with the weight statement (it doesn't work to weight the lm and the segmented model). Segmented seems like the best bet for me. It does a good job estim...
R - how to get standard error for a breakpoint/parameter in a piecewise regression Hmm, so I think I figured out the issues I was having with segmented. It had to do with the weight statement (it doesn't work to weight the lm and the segmented model). Segmented seems like the best
51,052
R - how to get standard error for a breakpoint/parameter in a piecewise regression
The distribution of the breakpoint estimator is a complicated one, and you cannot use standard methods for that. Fortunately, package strucchange implements breakpoint tests and confidence intervals (see the references in strucchange::breakpoints), which you can use very simply: I rewrote a data-generating process in a...
R - how to get standard error for a breakpoint/parameter in a piecewise regression
The distribution of the breakpoint estimator is a complicated one, and you cannot use standard methods for that. Fortunately, package strucchange implements breakpoint tests and confidence intervals (
R - how to get standard error for a breakpoint/parameter in a piecewise regression The distribution of the breakpoint estimator is a complicated one, and you cannot use standard methods for that. Fortunately, package strucchange implements breakpoint tests and confidence intervals (see the references in strucchange::br...
R - how to get standard error for a breakpoint/parameter in a piecewise regression The distribution of the breakpoint estimator is a complicated one, and you cannot use standard methods for that. Fortunately, package strucchange implements breakpoint tests and confidence intervals (
51,053
Statistical test for power law samples
I do not believe there is a simple answer to your question without more details about the distribution. Power law distributions can have infinite variance, in which cases the large sample guarantees from the CLT will not apply. If you know the variance of the distribution is finite (which can be guaranteed for certain...
Statistical test for power law samples
I do not believe there is a simple answer to your question without more details about the distribution. Power law distributions can have infinite variance, in which cases the large sample guarantees f
Statistical test for power law samples I do not believe there is a simple answer to your question without more details about the distribution. Power law distributions can have infinite variance, in which cases the large sample guarantees from the CLT will not apply. If you know the variance of the distribution is fini...
Statistical test for power law samples I do not believe there is a simple answer to your question without more details about the distribution. Power law distributions can have infinite variance, in which cases the large sample guarantees f
51,054
Statistical test for power law samples
If your distribution is a Pareto distribution, you can apply $\log$ to the values and you will get an exponential distribution. Then you can perform a t-test
Statistical test for power law samples
If your distribution is a Pareto distribution, you can apply $\log$ to the values and you will get an exponential distribution. Then you can perform a t-test
Statistical test for power law samples If your distribution is a Pareto distribution, you can apply $\log$ to the values and you will get an exponential distribution. Then you can perform a t-test
Statistical test for power law samples If your distribution is a Pareto distribution, you can apply $\log$ to the values and you will get an exponential distribution. Then you can perform a t-test
51,055
Correct statistical test when people could appear in multiple groups
I presume that when users were asked to rate the ease of website use, it was their overall impression, and ease was asked only once per user rather than specifically for each task. Therefore, if I said I used the website to update my profile & post a blog and I rated my ease of use 1 (presumably difficult), you would n...
Correct statistical test when people could appear in multiple groups
I presume that when users were asked to rate the ease of website use, it was their overall impression, and ease was asked only once per user rather than specifically for each task. Therefore, if I sai
Correct statistical test when people could appear in multiple groups I presume that when users were asked to rate the ease of website use, it was their overall impression, and ease was asked only once per user rather than specifically for each task. Therefore, if I said I used the website to update my profile & post a ...
Correct statistical test when people could appear in multiple groups I presume that when users were asked to rate the ease of website use, it was their overall impression, and ease was asked only once per user rather than specifically for each task. Therefore, if I sai
51,056
MCMC sampling with noisy likelihood
Generalized Poisson estimator seems to be what I'm looking for http://www.maths.lancs.ac.uk/~rowlings/Chicas/Talks/LightningNov2011/Prangle.pdf
MCMC sampling with noisy likelihood
Generalized Poisson estimator seems to be what I'm looking for http://www.maths.lancs.ac.uk/~rowlings/Chicas/Talks/LightningNov2011/Prangle.pdf
MCMC sampling with noisy likelihood Generalized Poisson estimator seems to be what I'm looking for http://www.maths.lancs.ac.uk/~rowlings/Chicas/Talks/LightningNov2011/Prangle.pdf
MCMC sampling with noisy likelihood Generalized Poisson estimator seems to be what I'm looking for http://www.maths.lancs.ac.uk/~rowlings/Chicas/Talks/LightningNov2011/Prangle.pdf
51,057
Missing data which simply cannot exist
For sources, I'd suggest Missing Data Problem in Machine Learning, by Benjamin M. Merlin (Thesis), or Statistical Analysis with Missing Data, by Roderick and Rubin. What you are explaining in your answer is similar to the augmented model. There are multiple approaches to deal with missing data, and as a quick look into...
Missing data which simply cannot exist
For sources, I'd suggest Missing Data Problem in Machine Learning, by Benjamin M. Merlin (Thesis), or Statistical Analysis with Missing Data, by Roderick and Rubin. What you are explaining in your ans
Missing data which simply cannot exist For sources, I'd suggest Missing Data Problem in Machine Learning, by Benjamin M. Merlin (Thesis), or Statistical Analysis with Missing Data, by Roderick and Rubin. What you are explaining in your answer is similar to the augmented model. There are multiple approaches to deal with...
Missing data which simply cannot exist For sources, I'd suggest Missing Data Problem in Machine Learning, by Benjamin M. Merlin (Thesis), or Statistical Analysis with Missing Data, by Roderick and Rubin. What you are explaining in your ans
51,058
Missing data which simply cannot exist
So I sat down and worked this through. I thought I would share the answer - I struggled to find a source which worked this through and the couple of upvotes suggest interest in the solution. Firstly, lets set up a scenario: 1 dependent variable: Y 2 variables: X1 & X2 X1 & X2 are correlated Both have a subset of observ...
Missing data which simply cannot exist
So I sat down and worked this through. I thought I would share the answer - I struggled to find a source which worked this through and the couple of upvotes suggest interest in the solution. Firstly,
Missing data which simply cannot exist So I sat down and worked this through. I thought I would share the answer - I struggled to find a source which worked this through and the couple of upvotes suggest interest in the solution. Firstly, lets set up a scenario: 1 dependent variable: Y 2 variables: X1 & X2 X1 & X2 are ...
Missing data which simply cannot exist So I sat down and worked this through. I thought I would share the answer - I struggled to find a source which worked this through and the couple of upvotes suggest interest in the solution. Firstly,
51,059
Significance test for entropy?
I agree with @Nir Friedman that a Bayesian approach would be a good fit here, so I went ahead and implemented it in Python. Since the uniform prior is conjugate to the multinomial distribution, we can implement it without any fancy MCMC/HMC stuff. First things first, I imported a few libraries and defined a function to...
Significance test for entropy?
I agree with @Nir Friedman that a Bayesian approach would be a good fit here, so I went ahead and implemented it in Python. Since the uniform prior is conjugate to the multinomial distribution, we can
Significance test for entropy? I agree with @Nir Friedman that a Bayesian approach would be a good fit here, so I went ahead and implemented it in Python. Since the uniform prior is conjugate to the multinomial distribution, we can implement it without any fancy MCMC/HMC stuff. First things first, I imported a few libr...
Significance test for entropy? I agree with @Nir Friedman that a Bayesian approach would be a good fit here, so I went ahead and implemented it in Python. Since the uniform prior is conjugate to the multinomial distribution, we can
51,060
Significance test for entropy?
I think what's a little tricky is this: in a Student T test for comparing whether two populations have the same sample mean, you have a null hypothesis that the two populations have the same sample mean. Notice that this is as far as you have to specify the null hypothesis, you don't need to specify what both means are...
Significance test for entropy?
I think what's a little tricky is this: in a Student T test for comparing whether two populations have the same sample mean, you have a null hypothesis that the two populations have the same sample me
Significance test for entropy? I think what's a little tricky is this: in a Student T test for comparing whether two populations have the same sample mean, you have a null hypothesis that the two populations have the same sample mean. Notice that this is as far as you have to specify the null hypothesis, you don't need...
Significance test for entropy? I think what's a little tricky is this: in a Student T test for comparing whether two populations have the same sample mean, you have a null hypothesis that the two populations have the same sample me
51,061
Significance test for entropy?
For each distribution, compute the maximum possible entropy as log2N, then divide by the actual entropy. Test this ratio using a Z-test for proportions.
Significance test for entropy?
For each distribution, compute the maximum possible entropy as log2N, then divide by the actual entropy. Test this ratio using a Z-test for proportions.
Significance test for entropy? For each distribution, compute the maximum possible entropy as log2N, then divide by the actual entropy. Test this ratio using a Z-test for proportions.
Significance test for entropy? For each distribution, compute the maximum possible entropy as log2N, then divide by the actual entropy. Test this ratio using a Z-test for proportions.
51,062
What is an appropriate statistical test to identify significantly different time-points in two time-courses?
Obviously super late with an answer here, but in case you haven't yet solved the issue, or you are working in the field and will face similar issues again... I would suggest adopting your first strategy and adjusting for multiple comparisons using a threshold-free cluster-enhancement technique followed by a maximum per...
What is an appropriate statistical test to identify significantly different time-points in two time-
Obviously super late with an answer here, but in case you haven't yet solved the issue, or you are working in the field and will face similar issues again... I would suggest adopting your first strate
What is an appropriate statistical test to identify significantly different time-points in two time-courses? Obviously super late with an answer here, but in case you haven't yet solved the issue, or you are working in the field and will face similar issues again... I would suggest adopting your first strategy and adju...
What is an appropriate statistical test to identify significantly different time-points in two time- Obviously super late with an answer here, but in case you haven't yet solved the issue, or you are working in the field and will face similar issues again... I would suggest adopting your first strate
51,063
Confidence interval for a constrained fit to Gaussian-like data
Jeff, Two comments. 1) The steps you described correspond to fitting the model: \begin{equation} G_i = AG_0(x_i) + \epsilon_i \end{equation} with {epsilon_i} iid, normally distributed, with mean 0 and variance sigma, which is a standard linear model (linear in the way the observations are assumed to depend on the un-kn...
Confidence interval for a constrained fit to Gaussian-like data
Jeff, Two comments. 1) The steps you described correspond to fitting the model: \begin{equation} G_i = AG_0(x_i) + \epsilon_i \end{equation} with {epsilon_i} iid, normally distributed, with mean 0 and
Confidence interval for a constrained fit to Gaussian-like data Jeff, Two comments. 1) The steps you described correspond to fitting the model: \begin{equation} G_i = AG_0(x_i) + \epsilon_i \end{equation} with {epsilon_i} iid, normally distributed, with mean 0 and variance sigma, which is a standard linear model (linea...
Confidence interval for a constrained fit to Gaussian-like data Jeff, Two comments. 1) The steps you described correspond to fitting the model: \begin{equation} G_i = AG_0(x_i) + \epsilon_i \end{equation} with {epsilon_i} iid, normally distributed, with mean 0 and
51,064
Restoring original distribution from noisy observations
If the $\sigma_i$ are a known constant then this is just a variation on kernel density estimation. If they are not constant (but known at least up to a constant) then it would be a form of weighted kernel density estimation. If the $\sigma_i$ are not known, but believed to be related to $x_i$ then it becomes more compl...
Restoring original distribution from noisy observations
If the $\sigma_i$ are a known constant then this is just a variation on kernel density estimation. If they are not constant (but known at least up to a constant) then it would be a form of weighted ke
Restoring original distribution from noisy observations If the $\sigma_i$ are a known constant then this is just a variation on kernel density estimation. If they are not constant (but known at least up to a constant) then it would be a form of weighted kernel density estimation. If the $\sigma_i$ are not known, but be...
Restoring original distribution from noisy observations If the $\sigma_i$ are a known constant then this is just a variation on kernel density estimation. If they are not constant (but known at least up to a constant) then it would be a form of weighted ke
51,065
Detecting outliers in circular data?
I am battling similar problems at the moment and found some literature that help you. Abuzaid, Mohamed, Hussin have designed and proposed circular boxplots, see: Boxplot for circular variables (2012), doi 10.1007/s00180-011-0261-5 http://dl.acm.org/citation.cfm?id=2347773 Outlier labeling via circular boxplot http://...
Detecting outliers in circular data?
I am battling similar problems at the moment and found some literature that help you. Abuzaid, Mohamed, Hussin have designed and proposed circular boxplots, see: Boxplot for circular variables (2012),
Detecting outliers in circular data? I am battling similar problems at the moment and found some literature that help you. Abuzaid, Mohamed, Hussin have designed and proposed circular boxplots, see: Boxplot for circular variables (2012), doi 10.1007/s00180-011-0261-5 http://dl.acm.org/citation.cfm?id=2347773 Outlier l...
Detecting outliers in circular data? I am battling similar problems at the moment and found some literature that help you. Abuzaid, Mohamed, Hussin have designed and proposed circular boxplots, see: Boxplot for circular variables (2012),
51,066
Detecting outliers in circular data?
One way to go about this would be to calculate the circular dispersion as in this answer. If you set the constant $c$ fairly high, ie. 2 or 3, you may view all observations outside the interval $ \left[\hat\mu - c \hat\delta, \hat\mu + c \hat\delta \right]$ as outliers. In that answer, you may also find some code...
Detecting outliers in circular data?
One way to go about this would be to calculate the circular dispersion as in this answer. If you set the constant $c$ fairly high, ie. 2 or 3, you may view all observations outside the interval $
Detecting outliers in circular data? One way to go about this would be to calculate the circular dispersion as in this answer. If you set the constant $c$ fairly high, ie. 2 or 3, you may view all observations outside the interval $ \left[\hat\mu - c \hat\delta, \hat\mu + c \hat\delta \right]$ as outliers. In tha...
Detecting outliers in circular data? One way to go about this would be to calculate the circular dispersion as in this answer. If you set the constant $c$ fairly high, ie. 2 or 3, you may view all observations outside the interval $
51,067
Bootstrap Confidence Intervals for Weir & Cockerham's Fst
The method you outlined of computing the Studentized bootstrap confidence intervals looks fine to me. As long as you have data from multiple loci and are using that to estimate one value of $F_{st}$, bootstrapping over loci using a Studentized bootstrap confidence interval should be the way to go. The first paper you c...
Bootstrap Confidence Intervals for Weir & Cockerham's Fst
The method you outlined of computing the Studentized bootstrap confidence intervals looks fine to me. As long as you have data from multiple loci and are using that to estimate one value of $F_{st}$,
Bootstrap Confidence Intervals for Weir & Cockerham's Fst The method you outlined of computing the Studentized bootstrap confidence intervals looks fine to me. As long as you have data from multiple loci and are using that to estimate one value of $F_{st}$, bootstrapping over loci using a Studentized bootstrap confiden...
Bootstrap Confidence Intervals for Weir & Cockerham's Fst The method you outlined of computing the Studentized bootstrap confidence intervals looks fine to me. As long as you have data from multiple loci and are using that to estimate one value of $F_{st}$,
51,068
How to apply hurdle models to panel data (using Stata)?
You can estimate double hurdle models to panel data with random effects using the module called dhreg. The Stata module is described on the following article (paywall until 2017): http://www.stata-journal.com/article.html?article=st0359 You can find and install the software by typing findit dhreg on Stata.
How to apply hurdle models to panel data (using Stata)?
You can estimate double hurdle models to panel data with random effects using the module called dhreg. The Stata module is described on the following article (paywall until 2017): http://www.stata-jou
How to apply hurdle models to panel data (using Stata)? You can estimate double hurdle models to panel data with random effects using the module called dhreg. The Stata module is described on the following article (paywall until 2017): http://www.stata-journal.com/article.html?article=st0359 You can find and install th...
How to apply hurdle models to panel data (using Stata)? You can estimate double hurdle models to panel data with random effects using the module called dhreg. The Stata module is described on the following article (paywall until 2017): http://www.stata-jou
51,069
Interpretation of Spearman's rank correlation coefficient - beyond its significance
The Spearman's rank c. c. is the Pearson' c.c. of the ranked variables; in its turn the Pearson's c.c. is defined as the mean of the product of the paired standardized scores $z(X_i)$, $z(Y_i)$. \begin{equation} r(X,Y) = \Sigma_i[z(X_i) z(Y_i)]/(n-1) \end{equation} in which $n$ is the sample size and the standard scor...
Interpretation of Spearman's rank correlation coefficient - beyond its significance
The Spearman's rank c. c. is the Pearson' c.c. of the ranked variables; in its turn the Pearson's c.c. is defined as the mean of the product of the paired standardized scores $z(X_i)$, $z(Y_i)$. \beg
Interpretation of Spearman's rank correlation coefficient - beyond its significance The Spearman's rank c. c. is the Pearson' c.c. of the ranked variables; in its turn the Pearson's c.c. is defined as the mean of the product of the paired standardized scores $z(X_i)$, $z(Y_i)$. \begin{equation} r(X,Y) = \Sigma_i[z(X_i...
Interpretation of Spearman's rank correlation coefficient - beyond its significance The Spearman's rank c. c. is the Pearson' c.c. of the ranked variables; in its turn the Pearson's c.c. is defined as the mean of the product of the paired standardized scores $z(X_i)$, $z(Y_i)$. \beg
51,070
Zero inflated negative binomial with selection
Not an answer, but more of a comment. I once spent time looking for this with no luck. This particular model is not even in the Winkelmann or Cameron and Trivedi's count data books. Some possible solutions: Ask this on Statalist. Jeff Wooldridge may know the answer. Do note the SL policy on cross-posting. etpoisson w...
Zero inflated negative binomial with selection
Not an answer, but more of a comment. I once spent time looking for this with no luck. This particular model is not even in the Winkelmann or Cameron and Trivedi's count data books. Some possible solu
Zero inflated negative binomial with selection Not an answer, but more of a comment. I once spent time looking for this with no luck. This particular model is not even in the Winkelmann or Cameron and Trivedi's count data books. Some possible solutions: Ask this on Statalist. Jeff Wooldridge may know the answer. Do n...
Zero inflated negative binomial with selection Not an answer, but more of a comment. I once spent time looking for this with no luck. This particular model is not even in the Winkelmann or Cameron and Trivedi's count data books. Some possible solu
51,071
Generalized linear model with lasso regularization for continuous non-negative response
Check out the machine learning application H2O (http://www.h2o.ai/), which can be run from within R. This allows you to fit penalised glms (e.g. ridge and lasso models) with a gamma error and log link (as well as several other error structures).
Generalized linear model with lasso regularization for continuous non-negative response
Check out the machine learning application H2O (http://www.h2o.ai/), which can be run from within R. This allows you to fit penalised glms (e.g. ridge and lasso models) with a gamma error and log lin
Generalized linear model with lasso regularization for continuous non-negative response Check out the machine learning application H2O (http://www.h2o.ai/), which can be run from within R. This allows you to fit penalised glms (e.g. ridge and lasso models) with a gamma error and log link (as well as several other erro...
Generalized linear model with lasso regularization for continuous non-negative response Check out the machine learning application H2O (http://www.h2o.ai/), which can be run from within R. This allows you to fit penalised glms (e.g. ridge and lasso models) with a gamma error and log lin
51,072
Are world cup predictions testable?
Yes, World Cup predictions are testable. In addition to the great comments above, here is one way to think about it: The 45% probability that Brazil wins (or won, since my answer is years late) is not drawn out of thin air. Instead, it comes out of simulations of the outcomes of individual matches, in which the model ...
Are world cup predictions testable?
Yes, World Cup predictions are testable. In addition to the great comments above, here is one way to think about it: The 45% probability that Brazil wins (or won, since my answer is years late) is no
Are world cup predictions testable? Yes, World Cup predictions are testable. In addition to the great comments above, here is one way to think about it: The 45% probability that Brazil wins (or won, since my answer is years late) is not drawn out of thin air. Instead, it comes out of simulations of the outcomes of ind...
Are world cup predictions testable? Yes, World Cup predictions are testable. In addition to the great comments above, here is one way to think about it: The 45% probability that Brazil wins (or won, since my answer is years late) is no
51,073
When forecasting sequential data is it best to use auto-regressive models or build a more traditional n x p dataset with features?
I've yet to find a satisfactory line of research in the literature that handles nonparametric time-series forecasting. What follows is my duct-tape approach. The pervasive question in performing nonparametric time-series analysis is: What do I really care about? Most problems are made more complex by requiring confiden...
When forecasting sequential data is it best to use auto-regressive models or build a more traditiona
I've yet to find a satisfactory line of research in the literature that handles nonparametric time-series forecasting. What follows is my duct-tape approach. The pervasive question in performing nonpa
When forecasting sequential data is it best to use auto-regressive models or build a more traditional n x p dataset with features? I've yet to find a satisfactory line of research in the literature that handles nonparametric time-series forecasting. What follows is my duct-tape approach. The pervasive question in perfo...
When forecasting sequential data is it best to use auto-regressive models or build a more traditiona I've yet to find a satisfactory line of research in the literature that handles nonparametric time-series forecasting. What follows is my duct-tape approach. The pervasive question in performing nonpa
51,074
find the point at which the curve significantly shoots up
You could use Outlier Detection from Time Series (Zhao - R and data mining). The first chart is the original time series, the second the seasonality , the third shows the trend and the last one plots the outliers on top of the remaining components after removing trend and seasonality. Reproducible example code: # use...
find the point at which the curve significantly shoots up
You could use Outlier Detection from Time Series (Zhao - R and data mining). The first chart is the original time series, the second the seasonality , the third shows the trend and the last one plot
find the point at which the curve significantly shoots up You could use Outlier Detection from Time Series (Zhao - R and data mining). The first chart is the original time series, the second the seasonality , the third shows the trend and the last one plots the outliers on top of the remaining components after removi...
find the point at which the curve significantly shoots up You could use Outlier Detection from Time Series (Zhao - R and data mining). The first chart is the original time series, the second the seasonality , the third shows the trend and the last one plot
51,075
find the point at which the curve significantly shoots up
This really depends on what the data looks like. Without a plot and from the description it sounds like the mean increases during the rainy season. If it is just a case of a baseline value of rainfall outside the rainy season and then this switches to another (higher) baseline during rainfall season then you are looki...
find the point at which the curve significantly shoots up
This really depends on what the data looks like. Without a plot and from the description it sounds like the mean increases during the rainy season. If it is just a case of a baseline value of rainfal
find the point at which the curve significantly shoots up This really depends on what the data looks like. Without a plot and from the description it sounds like the mean increases during the rainy season. If it is just a case of a baseline value of rainfall outside the rainy season and then this switches to another (...
find the point at which the curve significantly shoots up This really depends on what the data looks like. Without a plot and from the description it sounds like the mean increases during the rainy season. If it is just a case of a baseline value of rainfal
51,076
find the point at which the curve significantly shoots up
I would start with applying the kernel smoother, such as Gaussian. It'll give you a smooth curve $f(t)$, where you can play with the scale of the length $b$ to get it the curve as smooth as you wish. Now, you can apply analytical methods, such as the first derivative $\frac{df(t)}{dt}>a$, where $a$ is some threshold, t...
find the point at which the curve significantly shoots up
I would start with applying the kernel smoother, such as Gaussian. It'll give you a smooth curve $f(t)$, where you can play with the scale of the length $b$ to get it the curve as smooth as you wish.
find the point at which the curve significantly shoots up I would start with applying the kernel smoother, such as Gaussian. It'll give you a smooth curve $f(t)$, where you can play with the scale of the length $b$ to get it the curve as smooth as you wish. Now, you can apply analytical methods, such as the first deriv...
find the point at which the curve significantly shoots up I would start with applying the kernel smoother, such as Gaussian. It'll give you a smooth curve $f(t)$, where you can play with the scale of the length $b$ to get it the curve as smooth as you wish.
51,077
find the point at which the curve significantly shoots up
If you are just looking at modelling the seasonality in the data, you could use a (possibly non-linear) regression model to predict the rainfall as a function of the sine and cosine of the day of year. If you want to look for changes or trends, then you could include other variables, such as the number of days since t...
find the point at which the curve significantly shoots up
If you are just looking at modelling the seasonality in the data, you could use a (possibly non-linear) regression model to predict the rainfall as a function of the sine and cosine of the day of year
find the point at which the curve significantly shoots up If you are just looking at modelling the seasonality in the data, you could use a (possibly non-linear) regression model to predict the rainfall as a function of the sine and cosine of the day of year. If you want to look for changes or trends, then you could i...
find the point at which the curve significantly shoots up If you are just looking at modelling the seasonality in the data, you could use a (possibly non-linear) regression model to predict the rainfall as a function of the sine and cosine of the day of year
51,078
How to test the ARIMA coefficients?
You can use use the standard error of the coefficient to COMPUTE the t value . INTERPREATION of the t value i.e. converting the t value to a probability using the normal distribution REQUIRES that the errors from the model are Gaussian. To test the Gaussian assumption one must verify the following: There are no pulses...
How to test the ARIMA coefficients?
You can use use the standard error of the coefficient to COMPUTE the t value . INTERPREATION of the t value i.e. converting the t value to a probability using the normal distribution REQUIRES that the
How to test the ARIMA coefficients? You can use use the standard error of the coefficient to COMPUTE the t value . INTERPREATION of the t value i.e. converting the t value to a probability using the normal distribution REQUIRES that the errors from the model are Gaussian. To test the Gaussian assumption one must verify...
How to test the ARIMA coefficients? You can use use the standard error of the coefficient to COMPUTE the t value . INTERPREATION of the t value i.e. converting the t value to a probability using the normal distribution REQUIRES that the
51,079
Is there a negative impact from imbalance/skew in predictor variables?
Lack of balance is not bad for a saturated model. With two categorical variables this means having $ AB $ predictors ($ A $ is number of categories in the variable, $ B $ the second). If you include the interaction term $ x_1$ and $ x_2$ you should be fine. If this fit is too "noisy" then include it as a random effe...
Is there a negative impact from imbalance/skew in predictor variables?
Lack of balance is not bad for a saturated model. With two categorical variables this means having $ AB $ predictors ($ A $ is number of categories in the variable, $ B $ the second). If you include
Is there a negative impact from imbalance/skew in predictor variables? Lack of balance is not bad for a saturated model. With two categorical variables this means having $ AB $ predictors ($ A $ is number of categories in the variable, $ B $ the second). If you include the interaction term $ x_1$ and $ x_2$ you shoul...
Is there a negative impact from imbalance/skew in predictor variables? Lack of balance is not bad for a saturated model. With two categorical variables this means having $ AB $ predictors ($ A $ is number of categories in the variable, $ B $ the second). If you include
51,080
Is there a negative impact from imbalance/skew in predictor variables?
$y = B0 + B1*x1 + B2*x2$? Does it even make sense for categorical variables? If you look at continuous variables, for example most values of $x$ are clustered together, and there's a couple of outliers, these outliers is going to have high leverage and have a large impact on the regression coefficients. I imagine the s...
Is there a negative impact from imbalance/skew in predictor variables?
$y = B0 + B1*x1 + B2*x2$? Does it even make sense for categorical variables? If you look at continuous variables, for example most values of $x$ are clustered together, and there's a couple of outlier
Is there a negative impact from imbalance/skew in predictor variables? $y = B0 + B1*x1 + B2*x2$? Does it even make sense for categorical variables? If you look at continuous variables, for example most values of $x$ are clustered together, and there's a couple of outliers, these outliers is going to have high leverage ...
Is there a negative impact from imbalance/skew in predictor variables? $y = B0 + B1*x1 + B2*x2$? Does it even make sense for categorical variables? If you look at continuous variables, for example most values of $x$ are clustered together, and there's a couple of outlier
51,081
Best way to generate Gaussian Field
Yes this is too big for Cholesky! If you generate on a regular grid, then the spectral methods are the best. They are kind of hard to set up. Fortunately, there are several R packages, for example, RandomFields.
Best way to generate Gaussian Field
Yes this is too big for Cholesky! If you generate on a regular grid, then the spectral methods are the best. They are kind of hard to set up. Fortunately, there are several R packages, for example, R
Best way to generate Gaussian Field Yes this is too big for Cholesky! If you generate on a regular grid, then the spectral methods are the best. They are kind of hard to set up. Fortunately, there are several R packages, for example, RandomFields.
Best way to generate Gaussian Field Yes this is too big for Cholesky! If you generate on a regular grid, then the spectral methods are the best. They are kind of hard to set up. Fortunately, there are several R packages, for example, R
51,082
DNA: The number of 'AAAAA'-s in a randomly generated DNA sequence that's 1000 base pairs long
Well, there is a way to get an asymptotic probability that gets closer as the size of the sequence gets bigger. For a 1000-lenght sequence I think it can give you a good approximation. Call $L_{i}$ the letter in the position $i$. Consider the Markov Chain $X_{i} = \max(n|L_{i-j}, 0\leq j < n). $ The transition probab...
DNA: The number of 'AAAAA'-s in a randomly generated DNA sequence that's 1000 base pairs long
Well, there is a way to get an asymptotic probability that gets closer as the size of the sequence gets bigger. For a 1000-lenght sequence I think it can give you a good approximation. Call $L_{i}$ t
DNA: The number of 'AAAAA'-s in a randomly generated DNA sequence that's 1000 base pairs long Well, there is a way to get an asymptotic probability that gets closer as the size of the sequence gets bigger. For a 1000-lenght sequence I think it can give you a good approximation. Call $L_{i}$ the letter in the position ...
DNA: The number of 'AAAAA'-s in a randomly generated DNA sequence that's 1000 base pairs long Well, there is a way to get an asymptotic probability that gets closer as the size of the sequence gets bigger. For a 1000-lenght sequence I think it can give you a good approximation. Call $L_{i}$ t
51,083
Conditional density and variance of Nadaraya-Watson model
Here you have well described the conditional density (with $y$ in the place of your $t$): http://en.wikipedia.org/wiki/Kernel_regression#Derivation The conditional density is the $f(y|x) = \frac{f(x,y)}{f(x)}$. The conditional mean would be the mean for that density $E(Y|X)$ and the same thing for variance $E(Y-E(Y|X)...
Conditional density and variance of Nadaraya-Watson model
Here you have well described the conditional density (with $y$ in the place of your $t$): http://en.wikipedia.org/wiki/Kernel_regression#Derivation The conditional density is the $f(y|x) = \frac{f(x,y
Conditional density and variance of Nadaraya-Watson model Here you have well described the conditional density (with $y$ in the place of your $t$): http://en.wikipedia.org/wiki/Kernel_regression#Derivation The conditional density is the $f(y|x) = \frac{f(x,y)}{f(x)}$. The conditional mean would be the mean for that de...
Conditional density and variance of Nadaraya-Watson model Here you have well described the conditional density (with $y$ in the place of your $t$): http://en.wikipedia.org/wiki/Kernel_regression#Derivation The conditional density is the $f(y|x) = \frac{f(x,y
51,084
Significance of overlap between multiple lists
I'm dealing with similar problems, and haven't found a straightforward function. So I wrote a function myself. Although it's not very concise, it does the work. Hope it also helps you. hyper_matrix <- function(gene.list, background){ # generate every combinations of two gene lists combination <- expand.grid(names(g...
Significance of overlap between multiple lists
I'm dealing with similar problems, and haven't found a straightforward function. So I wrote a function myself. Although it's not very concise, it does the work. Hope it also helps you. hyper_matrix <-
Significance of overlap between multiple lists I'm dealing with similar problems, and haven't found a straightforward function. So I wrote a function myself. Although it's not very concise, it does the work. Hope it also helps you. hyper_matrix <- function(gene.list, background){ # generate every combinations of two ...
Significance of overlap between multiple lists I'm dealing with similar problems, and haven't found a straightforward function. So I wrote a function myself. Although it's not very concise, it does the work. Hope it also helps you. hyper_matrix <-
51,085
Item-based collaborative filtering – Can you add demographic information to initial user×item matrix?
I had a similar question/problem and got an answer here - How to integrate users' profile information into a recommender system . The simplest solution is to use kNN method - find the closest neighbors using your demographic data and infer recommendations from their ratings A somewhat more profound technique is to use...
Item-based collaborative filtering – Can you add demographic information to initial user×item matrix
I had a similar question/problem and got an answer here - How to integrate users' profile information into a recommender system . The simplest solution is to use kNN method - find the closest neighbo
Item-based collaborative filtering – Can you add demographic information to initial user×item matrix? I had a similar question/problem and got an answer here - How to integrate users' profile information into a recommender system . The simplest solution is to use kNN method - find the closest neighbors using your demo...
Item-based collaborative filtering – Can you add demographic information to initial user×item matrix I had a similar question/problem and got an answer here - How to integrate users' profile information into a recommender system . The simplest solution is to use kNN method - find the closest neighbo
51,086
Meta-analysis of prevalence at the country level
I see your question is quite old, but still it might be worthwhile to try to answer, very humbly though. First, I think you extracted correctly the weights from metaprop. Second, my impression (but I am not the ultimate expert) is that you built both your models correctly. Third, I would consider reporting results from...
Meta-analysis of prevalence at the country level
I see your question is quite old, but still it might be worthwhile to try to answer, very humbly though. First, I think you extracted correctly the weights from metaprop. Second, my impression (but I
Meta-analysis of prevalence at the country level I see your question is quite old, but still it might be worthwhile to try to answer, very humbly though. First, I think you extracted correctly the weights from metaprop. Second, my impression (but I am not the ultimate expert) is that you built both your models correctl...
Meta-analysis of prevalence at the country level I see your question is quite old, but still it might be worthwhile to try to answer, very humbly though. First, I think you extracted correctly the weights from metaprop. Second, my impression (but I
51,087
"Robust" normalization of features from multiple groups and unknown distributions prior to learning
I agree with gaborous in that you maybe seeking standardization, and a quick search for a visualization reveals lectures on why standardization is useful. TLDW version is that this is all to avoid squashed (elliptical or canoe) shaped input space, because such shapes will cause linear regression to wander. Credit to ...
"Robust" normalization of features from multiple groups and unknown distributions prior to learning
I agree with gaborous in that you maybe seeking standardization, and a quick search for a visualization reveals lectures on why standardization is useful. TLDW version is that this is all to avoid squ
"Robust" normalization of features from multiple groups and unknown distributions prior to learning I agree with gaborous in that you maybe seeking standardization, and a quick search for a visualization reveals lectures on why standardization is useful. TLDW version is that this is all to avoid squashed (elliptical or...
"Robust" normalization of features from multiple groups and unknown distributions prior to learning I agree with gaborous in that you maybe seeking standardization, and a quick search for a visualization reveals lectures on why standardization is useful. TLDW version is that this is all to avoid squ
51,088
How to perform parameters tuning for machine learning?
Given that you trust your validation setup option 2 is the way to go. You have performed the CV to identify the most general parameter setup (or model selection or whatever you're trying to optimize). These findings should be applied to the entire trainingset and tested (once) on the test set. The picture below illustr...
How to perform parameters tuning for machine learning?
Given that you trust your validation setup option 2 is the way to go. You have performed the CV to identify the most general parameter setup (or model selection or whatever you're trying to optimize).
How to perform parameters tuning for machine learning? Given that you trust your validation setup option 2 is the way to go. You have performed the CV to identify the most general parameter setup (or model selection or whatever you're trying to optimize). These findings should be applied to the entire trainingset and t...
How to perform parameters tuning for machine learning? Given that you trust your validation setup option 2 is the way to go. You have performed the CV to identify the most general parameter setup (or model selection or whatever you're trying to optimize).
51,089
Time varying predictors at higher aggregation levels in multilevel survival analysis
I think I found a solution. I read two book chapters about multilevel event history models (Courgeau, 2007; Goldstein, 2011), which discuss similar cases and suggest using a three-level structure such as time (level-1) nested within households (level-2), which are in turn nested within municipalities (level-3). Goldste...
Time varying predictors at higher aggregation levels in multilevel survival analysis
I think I found a solution. I read two book chapters about multilevel event history models (Courgeau, 2007; Goldstein, 2011), which discuss similar cases and suggest using a three-level structure such
Time varying predictors at higher aggregation levels in multilevel survival analysis I think I found a solution. I read two book chapters about multilevel event history models (Courgeau, 2007; Goldstein, 2011), which discuss similar cases and suggest using a three-level structure such as time (level-1) nested within ho...
Time varying predictors at higher aggregation levels in multilevel survival analysis I think I found a solution. I read two book chapters about multilevel event history models (Courgeau, 2007; Goldstein, 2011), which discuss similar cases and suggest using a three-level structure such
51,090
Statistical comparison of two signals
Time series analysis incorporating both ARIMA structure and empirically identifiable deterministic structure (level shifts/local time trends.seasonal pulses and pulses) might be of some use to you http://www.unc.edu/~jbhill/tsay.pdf. Good analytics/software should/could identify 2 level shifts ( 3 regimes) which would ...
Statistical comparison of two signals
Time series analysis incorporating both ARIMA structure and empirically identifiable deterministic structure (level shifts/local time trends.seasonal pulses and pulses) might be of some use to you htt
Statistical comparison of two signals Time series analysis incorporating both ARIMA structure and empirically identifiable deterministic structure (level shifts/local time trends.seasonal pulses and pulses) might be of some use to you http://www.unc.edu/~jbhill/tsay.pdf. Good analytics/software should/could identify 2 ...
Statistical comparison of two signals Time series analysis incorporating both ARIMA structure and empirically identifiable deterministic structure (level shifts/local time trends.seasonal pulses and pulses) might be of some use to you htt
51,091
Statistical comparison of two signals
There is no one single algorithm that will yield what you want. If your desire is to compare two signals then from the signal procesing point of view you can do the following. If the signal is stationary use multitaper magnitude-squared coherence from multitaper package using Harmonic F Statistic against a null hypot...
Statistical comparison of two signals
There is no one single algorithm that will yield what you want. If your desire is to compare two signals then from the signal procesing point of view you can do the following. If the signal is stati
Statistical comparison of two signals There is no one single algorithm that will yield what you want. If your desire is to compare two signals then from the signal procesing point of view you can do the following. If the signal is stationary use multitaper magnitude-squared coherence from multitaper package using Har...
Statistical comparison of two signals There is no one single algorithm that will yield what you want. If your desire is to compare two signals then from the signal procesing point of view you can do the following. If the signal is stati
51,092
Multi-output decision tree
If I understand your problem right, maybe the best way about is not multi output. You are trying to predict which segmentation to use. So it seems like you can do this in two ways. Give each tumor a class - the class is the segmentation that got the best accuracy score - and do class prediction. This is, I think, wh...
Multi-output decision tree
If I understand your problem right, maybe the best way about is not multi output. You are trying to predict which segmentation to use. So it seems like you can do this in two ways. Give each tumor
Multi-output decision tree If I understand your problem right, maybe the best way about is not multi output. You are trying to predict which segmentation to use. So it seems like you can do this in two ways. Give each tumor a class - the class is the segmentation that got the best accuracy score - and do class predi...
Multi-output decision tree If I understand your problem right, maybe the best way about is not multi output. You are trying to predict which segmentation to use. So it seems like you can do this in two ways. Give each tumor
51,093
Multi-output decision tree
For n-way outputs, I think you could build n decision (regression) trees. Tree i would take the m input variables (m=6 tumor parameters), and predict the rank of the accuracy of the i-th output (i in {1..n}, n=8, segmentation methods). The i-th tree would thus try to capture the range of parameter values in which the i...
Multi-output decision tree
For n-way outputs, I think you could build n decision (regression) trees. Tree i would take the m input variables (m=6 tumor parameters), and predict the rank of the accuracy of the i-th output (i in
Multi-output decision tree For n-way outputs, I think you could build n decision (regression) trees. Tree i would take the m input variables (m=6 tumor parameters), and predict the rank of the accuracy of the i-th output (i in {1..n}, n=8, segmentation methods). The i-th tree would thus try to capture the range of para...
Multi-output decision tree For n-way outputs, I think you could build n decision (regression) trees. Tree i would take the m input variables (m=6 tumor parameters), and predict the rank of the accuracy of the i-th output (i in
51,094
Multivariate data analyis of compositional data
Make sure you understand the algorithms before using them. E.g. k-means minimizes variance, and of course an attribute with a larger scale, with have a much larger variance, too. Therefore, standardizing data is often beneficial there. But with e.g. hierarchical clustering, you need to give a distance function. Euclide...
Multivariate data analyis of compositional data
Make sure you understand the algorithms before using them. E.g. k-means minimizes variance, and of course an attribute with a larger scale, with have a much larger variance, too. Therefore, standardiz
Multivariate data analyis of compositional data Make sure you understand the algorithms before using them. E.g. k-means minimizes variance, and of course an attribute with a larger scale, with have a much larger variance, too. Therefore, standardizing data is often beneficial there. But with e.g. hierarchical clusterin...
Multivariate data analyis of compositional data Make sure you understand the algorithms before using them. E.g. k-means minimizes variance, and of course an attribute with a larger scale, with have a much larger variance, too. Therefore, standardiz
51,095
How to correct for non-linearity of response in linear regression
I don't know details of your model, but in my opinion you need to deal with the large amount of "zero responses". Look into compound models with a mass point at zero. Something like the "Tweedie model".
How to correct for non-linearity of response in linear regression
I don't know details of your model, but in my opinion you need to deal with the large amount of "zero responses". Look into compound models with a mass point at zero. Something like the "Tweedie model
How to correct for non-linearity of response in linear regression I don't know details of your model, but in my opinion you need to deal with the large amount of "zero responses". Look into compound models with a mass point at zero. Something like the "Tweedie model".
How to correct for non-linearity of response in linear regression I don't know details of your model, but in my opinion you need to deal with the large amount of "zero responses". Look into compound models with a mass point at zero. Something like the "Tweedie model
51,096
Marginal distributions of off-diagonal terms in a Wishart-distributed random variable
I believe the answer to this can actually be found on the wikipedia article about the Wishart distribution, which indicates that it is variance-gamma distributed.
Marginal distributions of off-diagonal terms in a Wishart-distributed random variable
I believe the answer to this can actually be found on the wikipedia article about the Wishart distribution, which indicates that it is variance-gamma distributed.
Marginal distributions of off-diagonal terms in a Wishart-distributed random variable I believe the answer to this can actually be found on the wikipedia article about the Wishart distribution, which indicates that it is variance-gamma distributed.
Marginal distributions of off-diagonal terms in a Wishart-distributed random variable I believe the answer to this can actually be found on the wikipedia article about the Wishart distribution, which indicates that it is variance-gamma distributed.
51,097
Interpreting plm output in R - number of observations used with very unbalanced panel
Capital N gives you the total number of rows in your data which corresponds to the number of observations in the pooled model (option model="pooling" in the plm function). Lowercase n gives you the unique number of observations (let's say groups or individuals). This corresponds to the number of dummies you add if you...
Interpreting plm output in R - number of observations used with very unbalanced panel
Capital N gives you the total number of rows in your data which corresponds to the number of observations in the pooled model (option model="pooling" in the plm function). Lowercase n gives you the u
Interpreting plm output in R - number of observations used with very unbalanced panel Capital N gives you the total number of rows in your data which corresponds to the number of observations in the pooled model (option model="pooling" in the plm function). Lowercase n gives you the unique number of observations (let'...
Interpreting plm output in R - number of observations used with very unbalanced panel Capital N gives you the total number of rows in your data which corresponds to the number of observations in the pooled model (option model="pooling" in the plm function). Lowercase n gives you the u
51,098
How to select the best classification scheme in survival analysis (SurvivalROC, R2, Concordance, AIC)?
I figure the schemas' groups does not come with an absolute probability of an event in any given period. In that case, you care about the ranking which leads to focusing on AUC or concordance of the options you have given. The concordance measure is a generalization of AUC to time outcomes. So unless you really care ab...
How to select the best classification scheme in survival analysis (SurvivalROC, R2, Concordance, AIC
I figure the schemas' groups does not come with an absolute probability of an event in any given period. In that case, you care about the ranking which leads to focusing on AUC or concordance of the o
How to select the best classification scheme in survival analysis (SurvivalROC, R2, Concordance, AIC)? I figure the schemas' groups does not come with an absolute probability of an event in any given period. In that case, you care about the ranking which leads to focusing on AUC or concordance of the options you have g...
How to select the best classification scheme in survival analysis (SurvivalROC, R2, Concordance, AIC I figure the schemas' groups does not come with an absolute probability of an event in any given period. In that case, you care about the ranking which leads to focusing on AUC or concordance of the o
51,099
What are the 2nd derivatives of the log multivariate normal density?
Alright, the negative information matrix for $L(\mu,K)$ is $$\frac{\partial^2 L}{\partial\mu\,\partial\mu'} = -\left(\frac{1}{N}K\right)^{-1}$$ $$\frac{\partial^2 L}{\partial K\partial \mu} = 0$$ $\frac{\partial^2 L}{\partial K\, \partial K'}$, in a more general formulation, is given at http://en.wikipedia.org/wiki/Fis...
What are the 2nd derivatives of the log multivariate normal density?
Alright, the negative information matrix for $L(\mu,K)$ is $$\frac{\partial^2 L}{\partial\mu\,\partial\mu'} = -\left(\frac{1}{N}K\right)^{-1}$$ $$\frac{\partial^2 L}{\partial K\partial \mu} = 0$$ $\fr
What are the 2nd derivatives of the log multivariate normal density? Alright, the negative information matrix for $L(\mu,K)$ is $$\frac{\partial^2 L}{\partial\mu\,\partial\mu'} = -\left(\frac{1}{N}K\right)^{-1}$$ $$\frac{\partial^2 L}{\partial K\partial \mu} = 0$$ $\frac{\partial^2 L}{\partial K\, \partial K'}$, in a m...
What are the 2nd derivatives of the log multivariate normal density? Alright, the negative information matrix for $L(\mu,K)$ is $$\frac{\partial^2 L}{\partial\mu\,\partial\mu'} = -\left(\frac{1}{N}K\right)^{-1}$$ $$\frac{\partial^2 L}{\partial K\partial \mu} = 0$$ $\fr
51,100
Dealing with correlating fixed effects in a linear mixed-effects analysis
I'm not sure if this is what Baayen mean, but one advantage of the model comparison approach is that you get to see the effect of adding pupil size on the other parameters, model fit statistics and so on. This isn't specific to multi-level models; often people build up models, first using a simple model, then a more c...
Dealing with correlating fixed effects in a linear mixed-effects analysis
I'm not sure if this is what Baayen mean, but one advantage of the model comparison approach is that you get to see the effect of adding pupil size on the other parameters, model fit statistics and so
Dealing with correlating fixed effects in a linear mixed-effects analysis I'm not sure if this is what Baayen mean, but one advantage of the model comparison approach is that you get to see the effect of adding pupil size on the other parameters, model fit statistics and so on. This isn't specific to multi-level model...
Dealing with correlating fixed effects in a linear mixed-effects analysis I'm not sure if this is what Baayen mean, but one advantage of the model comparison approach is that you get to see the effect of adding pupil size on the other parameters, model fit statistics and so