idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k β | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 β | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
53,801 | Why do the 95% confidence limits in ARIMA models widen at the forecasts? | In short, because in time series, the observations depend on previous observations/errors.
Consider just a simple AR(1), for example. The next observation depends on the previous one.
When you're predicting time $t+1$ from time $t$, you know $y_t$, but you have an uncertain prediction because of variation in the proce... | Why do the 95% confidence limits in ARIMA models widen at the forecasts? | In short, because in time series, the observations depend on previous observations/errors.
Consider just a simple AR(1), for example. The next observation depends on the previous one.
When you're pre | Why do the 95% confidence limits in ARIMA models widen at the forecasts?
In short, because in time series, the observations depend on previous observations/errors.
Consider just a simple AR(1), for example. The next observation depends on the previous one.
When you're predicting time $t+1$ from time $t$, you know $y_t... | Why do the 95% confidence limits in ARIMA models widen at the forecasts?
In short, because in time series, the observations depend on previous observations/errors.
Consider just a simple AR(1), for example. The next observation depends on the previous one.
When you're pre |
53,802 | Building the connection between cosine similarity and correlation in R | The answer is really right there in your linked articles. From the first, here are the formulae for cosine and correlation (lightly edited for brevity and clarity):
\begin{align}
{\rm CosSim}(x,y) &= \frac{\sum_i x_i y_i}{ \sqrt{ \sum_i x_i^2} \sqrt{ \sum_i y_i^2 } } \\
\ \\
\ \\
{\rm Corr}(x,y) &= \frac{ \sum_i (x... | Building the connection between cosine similarity and correlation in R | The answer is really right there in your linked articles. From the first, here are the formulae for cosine and correlation (lightly edited for brevity and clarity):
\begin{align}
{\rm CosSim}(x,y) | Building the connection between cosine similarity and correlation in R
The answer is really right there in your linked articles. From the first, here are the formulae for cosine and correlation (lightly edited for brevity and clarity):
\begin{align}
{\rm CosSim}(x,y) &= \frac{\sum_i x_i y_i}{ \sqrt{ \sum_i x_i^2} \s... | Building the connection between cosine similarity and correlation in R
The answer is really right there in your linked articles. From the first, here are the formulae for cosine and correlation (lightly edited for brevity and clarity):
\begin{align}
{\rm CosSim}(x,y) |
53,803 | Building the connection between cosine similarity and correlation in R | The only line that has to be added is X <- apply(X, 2, function(x){ x-mean(x) }) which just subtracts the mean column-wise:
X <- apply(X, 2, function(x){ x-mean(x) })
cos.sim <- function(ix)
{
A = X[,ix[1]]
B = X[,ix[2]]
return(t(A)%*%B/sqrt(sum(A^2)*sum(B^2)))
}
n <- ncol(X)
cmb <- expand.grid(i=1:n, j... | Building the connection between cosine similarity and correlation in R | The only line that has to be added is X <- apply(X, 2, function(x){ x-mean(x) }) which just subtracts the mean column-wise:
X <- apply(X, 2, function(x){ x-mean(x) })
cos.sim <- function(ix)
{
| Building the connection between cosine similarity and correlation in R
The only line that has to be added is X <- apply(X, 2, function(x){ x-mean(x) }) which just subtracts the mean column-wise:
X <- apply(X, 2, function(x){ x-mean(x) })
cos.sim <- function(ix)
{
A = X[,ix[1]]
B = X[,ix[2]]
return(t(A)%*%B/... | Building the connection between cosine similarity and correlation in R
The only line that has to be added is X <- apply(X, 2, function(x){ x-mean(x) }) which just subtracts the mean column-wise:
X <- apply(X, 2, function(x){ x-mean(x) })
cos.sim <- function(ix)
{
|
53,804 | Neural network packages which allow shared weights and parallel training | It sounds like Pylearn2 may do what you want. It has two implementations for convolutional networks which requires some amount of weight sharing. Furthermore one of these implementations is optimized for use on a GPU via CUDA using Theano. See the documentation for more information. I believe the associated code is pyl... | Neural network packages which allow shared weights and parallel training | It sounds like Pylearn2 may do what you want. It has two implementations for convolutional networks which requires some amount of weight sharing. Furthermore one of these implementations is optimized | Neural network packages which allow shared weights and parallel training
It sounds like Pylearn2 may do what you want. It has two implementations for convolutional networks which requires some amount of weight sharing. Furthermore one of these implementations is optimized for use on a GPU via CUDA using Theano. See the... | Neural network packages which allow shared weights and parallel training
It sounds like Pylearn2 may do what you want. It has two implementations for convolutional networks which requires some amount of weight sharing. Furthermore one of these implementations is optimized |
53,805 | Neural network packages which allow shared weights and parallel training | I can't add a comment to @Emre's answer because I don't have enough points.
You can train shared-weight networks in torch, be that using CUDA or not. The weight-sharing is supported for any tensor type.
Training is done in parallel when you wrap the two shared modules in a nn.Parallel container
We use this in torch qu... | Neural network packages which allow shared weights and parallel training | I can't add a comment to @Emre's answer because I don't have enough points.
You can train shared-weight networks in torch, be that using CUDA or not. The weight-sharing is supported for any tensor typ | Neural network packages which allow shared weights and parallel training
I can't add a comment to @Emre's answer because I don't have enough points.
You can train shared-weight networks in torch, be that using CUDA or not. The weight-sharing is supported for any tensor type.
Training is done in parallel when you wrap ... | Neural network packages which allow shared weights and parallel training
I can't add a comment to @Emre's answer because I don't have enough points.
You can train shared-weight networks in torch, be that using CUDA or not. The weight-sharing is supported for any tensor typ |
53,806 | Neural network packages which allow shared weights and parallel training | I don't have practical experience with torch7, but I think the idea is to do the parallelization on the GPU, cf. cunn and cutorch.
There's also https://github.com/clementfarabet/lua---parallel | Neural network packages which allow shared weights and parallel training | I don't have practical experience with torch7, but I think the idea is to do the parallelization on the GPU, cf. cunn and cutorch.
There's also https://github.com/clementfarabet/lua---parallel | Neural network packages which allow shared weights and parallel training
I don't have practical experience with torch7, but I think the idea is to do the parallelization on the GPU, cf. cunn and cutorch.
There's also https://github.com/clementfarabet/lua---parallel | Neural network packages which allow shared weights and parallel training
I don't have practical experience with torch7, but I think the idea is to do the parallelization on the GPU, cf. cunn and cutorch.
There's also https://github.com/clementfarabet/lua---parallel |
53,807 | Permutation tests and multiple testing | You'll have to either (a) increase the number of permutations so the p-values won't have a lower bound as high as 0.01 (even with a single measure I'd use at least 1000 permutations!) or (b) incorporate multiple testing correction within the permutation testing. This can be achieved by the Max-T method: in each permuta... | Permutation tests and multiple testing | You'll have to either (a) increase the number of permutations so the p-values won't have a lower bound as high as 0.01 (even with a single measure I'd use at least 1000 permutations!) or (b) incorpora | Permutation tests and multiple testing
You'll have to either (a) increase the number of permutations so the p-values won't have a lower bound as high as 0.01 (even with a single measure I'd use at least 1000 permutations!) or (b) incorporate multiple testing correction within the permutation testing. This can be achiev... | Permutation tests and multiple testing
You'll have to either (a) increase the number of permutations so the p-values won't have a lower bound as high as 0.01 (even with a single measure I'd use at least 1000 permutations!) or (b) incorpora |
53,808 | Dummies instead of the Chow test | Let's first create a fake data with a break-point at 3.
> x=seq(1,5,length=100)
> y=numeric(100)
> y[1:50]=2*x[1:50]
> y[51:100]=rep(2*x[51],50)
> z=rnorm(100,0,.15)
> y=y+z
> plot(x,y)
Now I am gonna perform a Chow test using package strucchange in R to test if 3 is a break-point or not.
> require(strucchange)
> sct... | Dummies instead of the Chow test | Let's first create a fake data with a break-point at 3.
> x=seq(1,5,length=100)
> y=numeric(100)
> y[1:50]=2*x[1:50]
> y[51:100]=rep(2*x[51],50)
> z=rnorm(100,0,.15)
> y=y+z
> plot(x,y)
Now I am gon | Dummies instead of the Chow test
Let's first create a fake data with a break-point at 3.
> x=seq(1,5,length=100)
> y=numeric(100)
> y[1:50]=2*x[1:50]
> y[51:100]=rep(2*x[51],50)
> z=rnorm(100,0,.15)
> y=y+z
> plot(x,y)
Now I am gonna perform a Chow test using package strucchange in R to test if 3 is a break-point or ... | Dummies instead of the Chow test
Let's first create a fake data with a break-point at 3.
> x=seq(1,5,length=100)
> y=numeric(100)
> y[1:50]=2*x[1:50]
> y[51:100]=rep(2*x[51],50)
> z=rnorm(100,0,.15)
> y=y+z
> plot(x,y)
Now I am gon |
53,809 | What is the minimum viable cell size for 2x2 ANOVA? | There isn't really any absolute minimum except in a trivial sense (if you won't try to test for the interaction, the minimum $n_{ij}$ will be $1$, if you do want to test for interactions, the minimum cell size might be $2$). Instead, there are two issues here:
The first is the question of the robustness of the ANOV... | What is the minimum viable cell size for 2x2 ANOVA? | There isn't really any absolute minimum except in a trivial sense (if you won't try to test for the interaction, the minimum $n_{ij}$ will be $1$, if you do want to test for interactions, the minimum | What is the minimum viable cell size for 2x2 ANOVA?
There isn't really any absolute minimum except in a trivial sense (if you won't try to test for the interaction, the minimum $n_{ij}$ will be $1$, if you do want to test for interactions, the minimum cell size might be $2$). Instead, there are two issues here:
The... | What is the minimum viable cell size for 2x2 ANOVA?
There isn't really any absolute minimum except in a trivial sense (if you won't try to test for the interaction, the minimum $n_{ij}$ will be $1$, if you do want to test for interactions, the minimum |
53,810 | E[g(Y)] proof question | 1. The fact that
$$ \sum_{i=1}^m g_i \left\{ \sum_{\substack{\text{all $y_j$ such that} \\
g(y_j)=g_i}} p(y_j) \right\} = \sum_{i=1}^m \sum_{\substack{\text{all
$y_j$ such that} \\ g(y_j)=g_i}} g_i p(y_j) $$
is just the distributive property of the sum. Here is a more transparent example:
\begin{align*}
& \sum_i \... | E[g(Y)] proof question | 1. The fact that
$$ \sum_{i=1}^m g_i \left\{ \sum_{\substack{\text{all $y_j$ such that} \\
g(y_j)=g_i}} p(y_j) \right\} = \sum_{i=1}^m \sum_{\substack{\text{all
$y_j$ such that} \\ g(y_j)=g_i}} g_i | E[g(Y)] proof question
1. The fact that
$$ \sum_{i=1}^m g_i \left\{ \sum_{\substack{\text{all $y_j$ such that} \\
g(y_j)=g_i}} p(y_j) \right\} = \sum_{i=1}^m \sum_{\substack{\text{all
$y_j$ such that} \\ g(y_j)=g_i}} g_i p(y_j) $$
is just the distributive property of the sum. Here is a more transparent example:
\be... | E[g(Y)] proof question
1. The fact that
$$ \sum_{i=1}^m g_i \left\{ \sum_{\substack{\text{all $y_j$ such that} \\
g(y_j)=g_i}} p(y_j) \right\} = \sum_{i=1}^m \sum_{\substack{\text{all
$y_j$ such that} \\ g(y_j)=g_i}} g_i |
53,811 | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size | There are analogous effect size measures to Cohen's for paired data, sometimes called the "standardized mean change" or "standardized mean gain". This is computed with $$d = \frac{\bar{x}_1 - \bar{x}_2}{SD_D} = \frac{\bar{x}_D}{SD_D},$$ where $\bar{x}_1$ is the mean at time 1 (or under condition 1), $\bar{x}_2$ is the ... | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size | There are analogous effect size measures to Cohen's for paired data, sometimes called the "standardized mean change" or "standardized mean gain". This is computed with $$d = \frac{\bar{x}_1 - \bar{x}_ | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size
There are analogous effect size measures to Cohen's for paired data, sometimes called the "standardized mean change" or "standardized mean gain". This is computed with $$d = \frac{\bar{x}_1 - \bar{x}_2}{SD_D} = \frac{\b... | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size
There are analogous effect size measures to Cohen's for paired data, sometimes called the "standardized mean change" or "standardized mean gain". This is computed with $$d = \frac{\bar{x}_1 - \bar{x}_ |
53,812 | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size | mes does not account for the paired-ness of the data, so, it is a different test; usually, paired tests are more powerful, so it is not surprising that the paired test was significant and the unpaired was not. | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size | mes does not account for the paired-ness of the data, so, it is a different test; usually, paired tests are more powerful, so it is not surprising that the paired test was significant and the unpaired | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size
mes does not account for the paired-ness of the data, so, it is a different test; usually, paired tests are more powerful, so it is not surprising that the paired test was significant and the unpaired was not. | Conflict in confidence intervals for mean difference and confidence interval for Cohen'd effect size
mes does not account for the paired-ness of the data, so, it is a different test; usually, paired tests are more powerful, so it is not surprising that the paired test was significant and the unpaired |
53,813 | What is the expectation of one random variable divided over another (both independent)? | Basically, if $X$ and $Y$ are independent, then also $f(X)$ and $g(Y)$ are independent if $f$ and $g$ are measurable functions:
$$\eqalign{
P(f(X) \in A,\ g(Y) \in B) &= P\left(X \in f^{-1}(A),\ Y \in g^{-1}(B)\right) \\
& = P\left(X \in f^{-1}(A)\right) \ P\left(Y \in g^{-1}(B)\right) \\
& = P\left(f(X) \in A\right) ... | What is the expectation of one random variable divided over another (both independent)? | Basically, if $X$ and $Y$ are independent, then also $f(X)$ and $g(Y)$ are independent if $f$ and $g$ are measurable functions:
$$\eqalign{
P(f(X) \in A,\ g(Y) \in B) &= P\left(X \in f^{-1}(A),\ Y \in | What is the expectation of one random variable divided over another (both independent)?
Basically, if $X$ and $Y$ are independent, then also $f(X)$ and $g(Y)$ are independent if $f$ and $g$ are measurable functions:
$$\eqalign{
P(f(X) \in A,\ g(Y) \in B) &= P\left(X \in f^{-1}(A),\ Y \in g^{-1}(B)\right) \\
& = P\left... | What is the expectation of one random variable divided over another (both independent)?
Basically, if $X$ and $Y$ are independent, then also $f(X)$ and $g(Y)$ are independent if $f$ and $g$ are measurable functions:
$$\eqalign{
P(f(X) \in A,\ g(Y) \in B) &= P\left(X \in f^{-1}(A),\ Y \in |
53,814 | What is the expectation of one random variable divided over another (both independent)? | let $Z=\frac{1}{Y}$, then we have:
\begin{equation}
E(XZ) = \int \int XZ p(X,Z) \mathrm{d}x \mathrm{d}z
\end{equation}
but $X$ and $Z$ are independent, so $p(X,Z) = p(X)p(Z)$ we have
\begin{equation}
E(XZ) = \int \int x .z . p(X=x).p(Z=z) \mathrm{d}x \mathrm{d}z
\end{equation}
which can be arranged as:
\begin{equation}... | What is the expectation of one random variable divided over another (both independent)? | let $Z=\frac{1}{Y}$, then we have:
\begin{equation}
E(XZ) = \int \int XZ p(X,Z) \mathrm{d}x \mathrm{d}z
\end{equation}
but $X$ and $Z$ are independent, so $p(X,Z) = p(X)p(Z)$ we have
\begin{equation}
| What is the expectation of one random variable divided over another (both independent)?
let $Z=\frac{1}{Y}$, then we have:
\begin{equation}
E(XZ) = \int \int XZ p(X,Z) \mathrm{d}x \mathrm{d}z
\end{equation}
but $X$ and $Z$ are independent, so $p(X,Z) = p(X)p(Z)$ we have
\begin{equation}
E(XZ) = \int \int x .z . p(X=x).... | What is the expectation of one random variable divided over another (both independent)?
let $Z=\frac{1}{Y}$, then we have:
\begin{equation}
E(XZ) = \int \int XZ p(X,Z) \mathrm{d}x \mathrm{d}z
\end{equation}
but $X$ and $Z$ are independent, so $p(X,Z) = p(X)p(Z)$ we have
\begin{equation}
|
53,815 | ARIMA model identification [duplicate] | 1) A pure AR(p) will have a cut off at lag p in the PACF:
ACF and PACF of a long AR(3) process
$ $
2) A pure MA(q) will have a cut off at lag q in the ACF.
ACF and PACF of a long MA(3) process
$ $
3) ARMA(p,q) will (eventually) have a decay in both; you often can't immediately tell p and q from empirical ACF and PA... | ARIMA model identification [duplicate] | 1) A pure AR(p) will have a cut off at lag p in the PACF:
ACF and PACF of a long AR(3) process
$ $
2) A pure MA(q) will have a cut off at lag q in the ACF.
ACF and PACF of a long MA(3) process
$ $ | ARIMA model identification [duplicate]
1) A pure AR(p) will have a cut off at lag p in the PACF:
ACF and PACF of a long AR(3) process
$ $
2) A pure MA(q) will have a cut off at lag q in the ACF.
ACF and PACF of a long MA(3) process
$ $
3) ARMA(p,q) will (eventually) have a decay in both; you often can't immediately... | ARIMA model identification [duplicate]
1) A pure AR(p) will have a cut off at lag p in the PACF:
ACF and PACF of a long AR(3) process
$ $
2) A pure MA(q) will have a cut off at lag q in the ACF.
ACF and PACF of a long MA(3) process
$ $ |
53,816 | ARIMA model identification [duplicate] | About the ACF and PACF of ARMA(p,q) one can say: ACF tails off after lag (q-p) and PACF tails off after lag (p-q) [e.g. Wei (2005), S. 109], which makes it difficult to identify the orders p and q. Usually one uses the information criteria like the AIC, BIC, FPE, .... One estimates severeal models with different orders... | ARIMA model identification [duplicate] | About the ACF and PACF of ARMA(p,q) one can say: ACF tails off after lag (q-p) and PACF tails off after lag (p-q) [e.g. Wei (2005), S. 109], which makes it difficult to identify the orders p and q. Us | ARIMA model identification [duplicate]
About the ACF and PACF of ARMA(p,q) one can say: ACF tails off after lag (q-p) and PACF tails off after lag (p-q) [e.g. Wei (2005), S. 109], which makes it difficult to identify the orders p and q. Usually one uses the information criteria like the AIC, BIC, FPE, .... One estimate... | ARIMA model identification [duplicate]
About the ACF and PACF of ARMA(p,q) one can say: ACF tails off after lag (q-p) and PACF tails off after lag (p-q) [e.g. Wei (2005), S. 109], which makes it difficult to identify the orders p and q. Us |
53,817 | Which Distribution Does the Data Point Belong to? | (My answer looks like I am assuming univariate distributions, but the underlying ideas carry over to the case with more variates.)
If you had population distributions ($F$, $G$) rather than samples and a point $x_{new}$, you could compare the height of the density (or probability function in the case of discrete random... | Which Distribution Does the Data Point Belong to? | (My answer looks like I am assuming univariate distributions, but the underlying ideas carry over to the case with more variates.)
If you had population distributions ($F$, $G$) rather than samples an | Which Distribution Does the Data Point Belong to?
(My answer looks like I am assuming univariate distributions, but the underlying ideas carry over to the case with more variates.)
If you had population distributions ($F$, $G$) rather than samples and a point $x_{new}$, you could compare the height of the density (or p... | Which Distribution Does the Data Point Belong to?
(My answer looks like I am assuming univariate distributions, but the underlying ideas carry over to the case with more variates.)
If you had population distributions ($F$, $G$) rather than samples an |
53,818 | Which Distribution Does the Data Point Belong to? | Being not a professional statistician, I see situation as this. We have two (or more) overlapping distributions. The task often appears in spectroscopy.
So here you have approximately 0.25 probability belonging to one distribution and 0.1 to another respectively. | Which Distribution Does the Data Point Belong to? | Being not a professional statistician, I see situation as this. We have two (or more) overlapping distributions. The task often appears in spectroscopy.
So here you have approximately 0.25 probability | Which Distribution Does the Data Point Belong to?
Being not a professional statistician, I see situation as this. We have two (or more) overlapping distributions. The task often appears in spectroscopy.
So here you have approximately 0.25 probability belonging to one distribution and 0.1 to another respectively. | Which Distribution Does the Data Point Belong to?
Being not a professional statistician, I see situation as this. We have two (or more) overlapping distributions. The task often appears in spectroscopy.
So here you have approximately 0.25 probability |
53,819 | Which Distribution Does the Data Point Belong to? | I am trying to solve an completely analogous problem. What I have started using as a basic approach is hypothesis testing.
If both the distributions are fairly spaced out, then you can check if the data point lies outside the bottom 95 percentile of the data of disliked websites. If it does, you can conclude with an er... | Which Distribution Does the Data Point Belong to? | I am trying to solve an completely analogous problem. What I have started using as a basic approach is hypothesis testing.
If both the distributions are fairly spaced out, then you can check if the da | Which Distribution Does the Data Point Belong to?
I am trying to solve an completely analogous problem. What I have started using as a basic approach is hypothesis testing.
If both the distributions are fairly spaced out, then you can check if the data point lies outside the bottom 95 percentile of the data of disliked... | Which Distribution Does the Data Point Belong to?
I am trying to solve an completely analogous problem. What I have started using as a basic approach is hypothesis testing.
If both the distributions are fairly spaced out, then you can check if the da |
53,820 | Should normalization completely weed out correlation? | Instead of normalizing by the length, I would suggest to normalize by the maximum possible number of subsequences for the given length $\ell$.
The maximum is reached for a sequence made of the repetition of the alphabet. E.g., if the alphabet is {A,B,C}, the maximum for a sequence of length 6, would be the number of su... | Should normalization completely weed out correlation? | Instead of normalizing by the length, I would suggest to normalize by the maximum possible number of subsequences for the given length $\ell$.
The maximum is reached for a sequence made of the repetit | Should normalization completely weed out correlation?
Instead of normalizing by the length, I would suggest to normalize by the maximum possible number of subsequences for the given length $\ell$.
The maximum is reached for a sequence made of the repetition of the alphabet. E.g., if the alphabet is {A,B,C}, the maximum... | Should normalization completely weed out correlation?
Instead of normalizing by the length, I would suggest to normalize by the maximum possible number of subsequences for the given length $\ell$.
The maximum is reached for a sequence made of the repetit |
53,821 | Should normalization completely weed out correlation? | Admittedly, this is just an operationalization of @whuber's comment (thanks!), but I still find it helpful to document it.
normalization <- function(order, length){
data <- as.data.frame(cbind(order, length))
model <- lm(order ~ length, data)
order_normalized <- order-(model$coefficients[1]+(model$coefficients[2]... | Should normalization completely weed out correlation? | Admittedly, this is just an operationalization of @whuber's comment (thanks!), but I still find it helpful to document it.
normalization <- function(order, length){
data <- as.data.frame(cbind(order | Should normalization completely weed out correlation?
Admittedly, this is just an operationalization of @whuber's comment (thanks!), but I still find it helpful to document it.
normalization <- function(order, length){
data <- as.data.frame(cbind(order, length))
model <- lm(order ~ length, data)
order_normalized ... | Should normalization completely weed out correlation?
Admittedly, this is just an operationalization of @whuber's comment (thanks!), but I still find it helpful to document it.
normalization <- function(order, length){
data <- as.data.frame(cbind(order |
53,822 | Which one to use Splines / Interaction or both? | Without going into detail,
cubic splines have advantages over linear splines, namely more properly reflecting smooth underlying relationships and being less sensitive to knot placement
knots can be placed using subject matter knowledge or using the observed data density (e.g., put knots at fixed quantiles of a predic... | Which one to use Splines / Interaction or both? | Without going into detail,
cubic splines have advantages over linear splines, namely more properly reflecting smooth underlying relationships and being less sensitive to knot placement
knots can be | Which one to use Splines / Interaction or both?
Without going into detail,
cubic splines have advantages over linear splines, namely more properly reflecting smooth underlying relationships and being less sensitive to knot placement
knots can be placed using subject matter knowledge or using the observed data density... | Which one to use Splines / Interaction or both?
Without going into detail,
cubic splines have advantages over linear splines, namely more properly reflecting smooth underlying relationships and being less sensitive to knot placement
knots can be |
53,823 | Statistical significance in canonical correlation analysis | Let $p_x$ and $p_y$ be the number of variables in your sets $X$ and $Y$. $N$ is the sample size. You have obtained $m=\min(p_x,p_y)$ canonical correlations $\gamma_1, \gamma_2,...,\gamma_m$. Testing them usually goes as follows.
Given $\gamma_j$, its corresponding eigenvalue is $\lambda_j= \frac{1}{1-\gamma_j^2}-1$.
Wi... | Statistical significance in canonical correlation analysis | Let $p_x$ and $p_y$ be the number of variables in your sets $X$ and $Y$. $N$ is the sample size. You have obtained $m=\min(p_x,p_y)$ canonical correlations $\gamma_1, \gamma_2,...,\gamma_m$. Testing t | Statistical significance in canonical correlation analysis
Let $p_x$ and $p_y$ be the number of variables in your sets $X$ and $Y$. $N$ is the sample size. You have obtained $m=\min(p_x,p_y)$ canonical correlations $\gamma_1, \gamma_2,...,\gamma_m$. Testing them usually goes as follows.
Given $\gamma_j$, its correspond... | Statistical significance in canonical correlation analysis
Let $p_x$ and $p_y$ be the number of variables in your sets $X$ and $Y$. $N$ is the sample size. You have obtained $m=\min(p_x,p_y)$ canonical correlations $\gamma_1, \gamma_2,...,\gamma_m$. Testing t |
53,824 | KL-divergence between two categorical/multinomial distributions gives negative values? | Letβs remove the two categories with probability $0$ in both distributions. Your example is $P = (0.9, 0.1)$ and $Q = (1,0)$.
The KL divergence is $KL(P||Q) = \sum_i p_i \log\left( {p_i \over q_i }\right)$. It is not
$$ 0.9 \times \log\, 0.9 + 0 $$
but
$$ 0.9 \times \log\, 0.9 + 0.1 \times ( +\infty ) = + \infty.$$ | KL-divergence between two categorical/multinomial distributions gives negative values? | Letβs remove the two categories with probability $0$ in both distributions. Your example is $P = (0.9, 0.1)$ and $Q = (1,0)$.
The KL divergence is $KL(P||Q) = \sum_i p_i \log\left( {p_i \over q_i }\r | KL-divergence between two categorical/multinomial distributions gives negative values?
Letβs remove the two categories with probability $0$ in both distributions. Your example is $P = (0.9, 0.1)$ and $Q = (1,0)$.
The KL divergence is $KL(P||Q) = \sum_i p_i \log\left( {p_i \over q_i }\right)$. It is not
$$ 0.9 \times ... | KL-divergence between two categorical/multinomial distributions gives negative values?
Letβs remove the two categories with probability $0$ in both distributions. Your example is $P = (0.9, 0.1)$ and $Q = (1,0)$.
The KL divergence is $KL(P||Q) = \sum_i p_i \log\left( {p_i \over q_i }\r |
53,825 | Implementing a Metropolis Hastings Algorithm in R | It is indeed a very poor idea to start learning a topic just from an on-line code with no explanation. Better read a book (like our Introduction to Monte Carlo methods with R!) or an introductory paper and write your own code.
As written, this code proposes a random walk on the parameter $(a,b)$ which in your case coul... | Implementing a Metropolis Hastings Algorithm in R | It is indeed a very poor idea to start learning a topic just from an on-line code with no explanation. Better read a book (like our Introduction to Monte Carlo methods with R!) or an introductory pape | Implementing a Metropolis Hastings Algorithm in R
It is indeed a very poor idea to start learning a topic just from an on-line code with no explanation. Better read a book (like our Introduction to Monte Carlo methods with R!) or an introductory paper and write your own code.
As written, this code proposes a random wal... | Implementing a Metropolis Hastings Algorithm in R
It is indeed a very poor idea to start learning a topic just from an on-line code with no explanation. Better read a book (like our Introduction to Monte Carlo methods with R!) or an introductory pape |
53,826 | LIBSVM "Warning: using -h 0 may be faster" | This means, that optimization algorithm detected that with high probability (not in the strict, mathematical sense) you can speed up your training by turning the -h 0 flag in your options. Basically, -h is the shrinking heuristics, implemented in the libsvm package which for some data significantly reduces number of re... | LIBSVM "Warning: using -h 0 may be faster" | This means, that optimization algorithm detected that with high probability (not in the strict, mathematical sense) you can speed up your training by turning the -h 0 flag in your options. Basically, | LIBSVM "Warning: using -h 0 may be faster"
This means, that optimization algorithm detected that with high probability (not in the strict, mathematical sense) you can speed up your training by turning the -h 0 flag in your options. Basically, -h is the shrinking heuristics, implemented in the libsvm package which for s... | LIBSVM "Warning: using -h 0 may be faster"
This means, that optimization algorithm detected that with high probability (not in the strict, mathematical sense) you can speed up your training by turning the -h 0 flag in your options. Basically, |
53,827 | Linear regression best polynomial (or better approach to use)? | Because brightness is a response with independent random error and it is expected to taper off with distance from the optimal point according to a Gaussian function, a quick nonlinear regression ought to do a good job.
The model is
$$y = b + a \exp\left(-\frac{1}{2}\left(\frac{x-m}{s}\right)^2\right) + \varepsilon$$
wh... | Linear regression best polynomial (or better approach to use)? | Because brightness is a response with independent random error and it is expected to taper off with distance from the optimal point according to a Gaussian function, a quick nonlinear regression ought | Linear regression best polynomial (or better approach to use)?
Because brightness is a response with independent random error and it is expected to taper off with distance from the optimal point according to a Gaussian function, a quick nonlinear regression ought to do a good job.
The model is
$$y = b + a \exp\left(-\f... | Linear regression best polynomial (or better approach to use)?
Because brightness is a response with independent random error and it is expected to taper off with distance from the optimal point according to a Gaussian function, a quick nonlinear regression ought |
53,828 | Linear regression best polynomial (or better approach to use)? | I assume the column of values you gave correspond to some kind of time series, and there is an implicit "time" column with evenly spaced values that you've not mentioned.
Given that, the question remains if you intend to fit a polynomial curve for prediction or forecasting. If the former, then the use of splines can be... | Linear regression best polynomial (or better approach to use)? | I assume the column of values you gave correspond to some kind of time series, and there is an implicit "time" column with evenly spaced values that you've not mentioned.
Given that, the question rema | Linear regression best polynomial (or better approach to use)?
I assume the column of values you gave correspond to some kind of time series, and there is an implicit "time" column with evenly spaced values that you've not mentioned.
Given that, the question remains if you intend to fit a polynomial curve for predictio... | Linear regression best polynomial (or better approach to use)?
I assume the column of values you gave correspond to some kind of time series, and there is an implicit "time" column with evenly spaced values that you've not mentioned.
Given that, the question rema |
53,829 | Linear regression best polynomial (or better approach to use)? | If your data should be a bell curve, you should fit that instead of the quadratic you have in the question. However, you can play with "other polynomials", for example in Python using mean squared error minimization with numpy.polyfit:
import numpy as np
import pylab as pl
# generate bell curve data
X = np.sort((10... | Linear regression best polynomial (or better approach to use)? | If your data should be a bell curve, you should fit that instead of the quadratic you have in the question. However, you can play with "other polynomials", for example in Python using mean squared | Linear regression best polynomial (or better approach to use)?
If your data should be a bell curve, you should fit that instead of the quadratic you have in the question. However, you can play with "other polynomials", for example in Python using mean squared error minimization with numpy.polyfit:
import numpy as n... | Linear regression best polynomial (or better approach to use)?
If your data should be a bell curve, you should fit that instead of the quadratic you have in the question. However, you can play with "other polynomials", for example in Python using mean squared |
53,830 | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate] | Each of the principal components projects the whole original feature space onto several dimensions, which I will call the latent features. The more an original feature contributes to a latent feature, the more important it is for that feature.
Thus, look at the absolute values of the Eigenvectors' components correspond... | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from t | Each of the principal components projects the whole original feature space onto several dimensions, which I will call the latent features. The more an original feature contributes to a latent feature, | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate]
Each of the principal components projects the whole original feature space onto several dimensions, which I will call the latent features. The more an original feature contributes to a latent feature,... | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from t
Each of the principal components projects the whole original feature space onto several dimensions, which I will call the latent features. The more an original feature contributes to a latent feature, |
53,831 | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate] | You can answer the last question by looking at the loadings of that PC. You could also do this for each of the other 5 PCs. I am not sure what you could do about the overall importance of particular variables. | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from t | You can answer the last question by looking at the loadings of that PC. You could also do this for each of the other 5 PCs. I am not sure what you could do about the overall importance of particular v | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate]
You can answer the last question by looking at the loadings of that PC. You could also do this for each of the other 5 PCs. I am not sure what you could do about the overall importance of particular v... | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from t
You can answer the last question by looking at the loadings of that PC. You could also do this for each of the other 5 PCs. I am not sure what you could do about the overall importance of particular v |
53,832 | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate] | Since eigen vectors are from the linear combination of the original variables, I don't think you can safely determine which of the original variables you can do away with from PCA. I felt this is more like a Factor Analysis question (related to latent variables). | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from t | Since eigen vectors are from the linear combination of the original variables, I don't think you can safely determine which of the original variables you can do away with from PCA. I felt this is mor | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from the PCs? [duplicate]
Since eigen vectors are from the linear combination of the original variables, I don't think you can safely determine which of the original variables you can do away with from PCA. I felt this is mor... | Perform PCA. Extract PCs. Can one then tell what the most important _original_ features were, from t
Since eigen vectors are from the linear combination of the original variables, I don't think you can safely determine which of the original variables you can do away with from PCA. I felt this is mor |
53,833 | degrees of freedom in ARIMA model | Let's say you have an $ARIMA(2,0,0)$, and the length $n=100$, then you have $98$ degrees of freedom. Then the first two values of the variable you are modelling are "used", and you will have $98$ fitted values, and $98$ degrees of freedom. | degrees of freedom in ARIMA model | Let's say you have an $ARIMA(2,0,0)$, and the length $n=100$, then you have $98$ degrees of freedom. Then the first two values of the variable you are modelling are "used", and you will have $98$ fitt | degrees of freedom in ARIMA model
Let's say you have an $ARIMA(2,0,0)$, and the length $n=100$, then you have $98$ degrees of freedom. Then the first two values of the variable you are modelling are "used", and you will have $98$ fitted values, and $98$ degrees of freedom. | degrees of freedom in ARIMA model
Let's say you have an $ARIMA(2,0,0)$, and the length $n=100$, then you have $98$ degrees of freedom. Then the first two values of the variable you are modelling are "used", and you will have $98$ fitt |
53,834 | degrees of freedom in ARIMA model | Working with AR in R:
for an ARIMA(2,0,0) the df = N - 2
including an intercept df = N - 3
including both an intercept and a time trend (i.e. xreg = 1:N)
the df = N - 4.
in the below code, an AR(2) is done using maximum likelihood to estimate the coefficients. In other languages (such as SAS) the sum of squared... | degrees of freedom in ARIMA model | Working with AR in R:
for an ARIMA(2,0,0) the df = N - 2
including an intercept df = N - 3
including both an intercept and a time trend (i.e. xreg = 1:N)
the df = N - 4.
in the below code, an | degrees of freedom in ARIMA model
Working with AR in R:
for an ARIMA(2,0,0) the df = N - 2
including an intercept df = N - 3
including both an intercept and a time trend (i.e. xreg = 1:N)
the df = N - 4.
in the below code, an AR(2) is done using maximum likelihood to estimate the coefficients. In other language... | degrees of freedom in ARIMA model
Working with AR in R:
for an ARIMA(2,0,0) the df = N - 2
including an intercept df = N - 3
including both an intercept and a time trend (i.e. xreg = 1:N)
the df = N - 4.
in the below code, an |
53,835 | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large? | There are a couple of good answers here already, but none which directly implement the problem as suggested in the question. The steps to do this are:
Sample 9 out of the 109 numbers from 0.01 to 1.09: sample(seq(0.01, 1.09, by=0.01), 9)
Find the differences between them:
Sort them: sort
Place them in a vector betwe... | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large? | There are a couple of good answers here already, but none which directly implement the problem as suggested in the question. The steps to do this are:
Sample 9 out of the 109 numbers from 0.01 to 1.0 | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large?
There are a couple of good answers here already, but none which directly implement the problem as suggested in the question. The steps to do this are:
Sample 9 out of the 109 numbers from 0.01 to 1.09: sample(seq(0.01, 1.09, by=0.01), ... | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large?
There are a couple of good answers here already, but none which directly implement the problem as suggested in the question. The steps to do this are:
Sample 9 out of the 109 numbers from 0.01 to 1.0 |
53,836 | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large? | Based on the edit it sounds like what is desired is to generate, independently and uniformly at random, a partition of the $N=100$-vector $(1/100, 1/100, \ldots, 1/100)$ into $k=10$ pieces and to output the sums of elements in each piece.
More generally we might ask how to do this for an arbitrary vector $x$. For exam... | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large? | Based on the edit it sounds like what is desired is to generate, independently and uniformly at random, a partition of the $N=100$-vector $(1/100, 1/100, \ldots, 1/100)$ into $k=10$ pieces and to outp | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large?
Based on the edit it sounds like what is desired is to generate, independently and uniformly at random, a partition of the $N=100$-vector $(1/100, 1/100, \ldots, 1/100)$ into $k=10$ pieces and to output the sums of elements in each piec... | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large?
Based on the edit it sounds like what is desired is to generate, independently and uniformly at random, a partition of the $N=100$-vector $(1/100, 1/100, \ldots, 1/100)$ into $k=10$ pieces and to outp |
53,837 | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large? | To hold the set of vectors that combn(109,9) would return if it could, by my estimate you would need upward of 32 petabytes of memory, which exceeds how much R can allocate.
Are the stated criteria the only ones that matter to you? Or do the elements of each vector also have to be unique? I went ahead and assumed yes.
... | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large? | To hold the set of vectors that combn(109,9) would return if it could, by my estimate you would need upward of 32 petabytes of memory, which exceeds how much R can allocate.
Are the stated criteria th | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large?
To hold the set of vectors that combn(109,9) would return if it could, by my estimate you would need upward of 32 petabytes of memory, which exceeds how much R can allocate.
Are the stated criteria the only ones that matter to you? Or d... | In R, how to sample from the output of combn(a,b) if the "a choose b" is too large?
To hold the set of vectors that combn(109,9) would return if it could, by my estimate you would need upward of 32 petabytes of memory, which exceeds how much R can allocate.
Are the stated criteria th |
53,838 | Interpreting plot of PCA results (from 3 to 2 dimensions) | The previous answer correctly explains what you see, but I would like to add that one of the properties of PCA is that it makes all variables uncorrelated. So after doing PCA each component is guaranteed to be uncorrelated with any other component, and you should not be surprised.
If you are a bit familiar with mathema... | Interpreting plot of PCA results (from 3 to 2 dimensions) | The previous answer correctly explains what you see, but I would like to add that one of the properties of PCA is that it makes all variables uncorrelated. So after doing PCA each component is guarant | Interpreting plot of PCA results (from 3 to 2 dimensions)
The previous answer correctly explains what you see, but I would like to add that one of the properties of PCA is that it makes all variables uncorrelated. So after doing PCA each component is guaranteed to be uncorrelated with any other component, and you shoul... | Interpreting plot of PCA results (from 3 to 2 dimensions)
The previous answer correctly explains what you see, but I would like to add that one of the properties of PCA is that it makes all variables uncorrelated. So after doing PCA each component is guarant |
53,839 | Interpreting plot of PCA results (from 3 to 2 dimensions) | Your initial data was rotated in the existing three dimensions such that the bulk of the variance was along the X axis, then rotated again such that the remaining variance was predominantly along the Y axis. Then the Z axis was flattened so only the new X and Y axes remained.
This article goes into a really good and a... | Interpreting plot of PCA results (from 3 to 2 dimensions) | Your initial data was rotated in the existing three dimensions such that the bulk of the variance was along the X axis, then rotated again such that the remaining variance was predominantly along the | Interpreting plot of PCA results (from 3 to 2 dimensions)
Your initial data was rotated in the existing three dimensions such that the bulk of the variance was along the X axis, then rotated again such that the remaining variance was predominantly along the Y axis. Then the Z axis was flattened so only the new X and Y ... | Interpreting plot of PCA results (from 3 to 2 dimensions)
Your initial data was rotated in the existing three dimensions such that the bulk of the variance was along the X axis, then rotated again such that the remaining variance was predominantly along the |
53,840 | Location, scale, and shape parameters of the lognormal (with notation ambiguity) | Naturally I can't speak authoritatively about any unreferenced papers you (don't) cite, but you appear to be encountering common conventions, apart from one mistake.
You are being given location and scale on the back-transformed (logged) scale; things are simplest on that scale as the equivalent normal has
Mean, med... | Location, scale, and shape parameters of the lognormal (with notation ambiguity) | Naturally I can't speak authoritatively about any unreferenced papers you (don't) cite, but you appear to be encountering common conventions, apart from one mistake.
You are being given location and | Location, scale, and shape parameters of the lognormal (with notation ambiguity)
Naturally I can't speak authoritatively about any unreferenced papers you (don't) cite, but you appear to be encountering common conventions, apart from one mistake.
You are being given location and scale on the back-transformed (logged) ... | Location, scale, and shape parameters of the lognormal (with notation ambiguity)
Naturally I can't speak authoritatively about any unreferenced papers you (don't) cite, but you appear to be encountering common conventions, apart from one mistake.
You are being given location and |
53,841 | Does the Holt-Winters algorithm for exponential smoothing in time series modelling require the normality assumption in residuals? | There is no normality assumption in fitting an exponential smoothing model. Even if maximum likelihood estimation is used with a Gaussian likelihood, the estimates will still be good under almost all residual distributions.
There is also no normality assumption when producing point forecasts from an exponential smoothi... | Does the Holt-Winters algorithm for exponential smoothing in time series modelling require the norma | There is no normality assumption in fitting an exponential smoothing model. Even if maximum likelihood estimation is used with a Gaussian likelihood, the estimates will still be good under almost all | Does the Holt-Winters algorithm for exponential smoothing in time series modelling require the normality assumption in residuals?
There is no normality assumption in fitting an exponential smoothing model. Even if maximum likelihood estimation is used with a Gaussian likelihood, the estimates will still be good under a... | Does the Holt-Winters algorithm for exponential smoothing in time series modelling require the norma
There is no normality assumption in fitting an exponential smoothing model. Even if maximum likelihood estimation is used with a Gaussian likelihood, the estimates will still be good under almost all |
53,842 | Negative inner fence value in a box and whiskers plot? | You just calculated the limits on where the whiskers can go, not the whisker ends themselves (which are limited to the range of the data).
The actual whiskers go out to the furthest-out data value inside the (inner) fences. The fences can go outside the data, but aren't actually plotted.
(for more details see this im... | Negative inner fence value in a box and whiskers plot? | You just calculated the limits on where the whiskers can go, not the whisker ends themselves (which are limited to the range of the data).
The actual whiskers go out to the furthest-out data value in | Negative inner fence value in a box and whiskers plot?
You just calculated the limits on where the whiskers can go, not the whisker ends themselves (which are limited to the range of the data).
The actual whiskers go out to the furthest-out data value inside the (inner) fences. The fences can go outside the data, but ... | Negative inner fence value in a box and whiskers plot?
You just calculated the limits on where the whiskers can go, not the whisker ends themselves (which are limited to the range of the data).
The actual whiskers go out to the furthest-out data value in |
53,843 | Given the below dependent variable description, should I choose either Ordered or Multinomial logistic regressions? | Lets start with the good news: The proportional odds assumptions does not require that the distances between categories are the same.
So what does the proportional odds assumption imply? Say we have three ordered outcomes (1, 2, 3), then we could model the choice of 1 versus 2 or 3 and the choice of 2 versus 3. The pr... | Given the below dependent variable description, should I choose either Ordered or Multinomial logist | Lets start with the good news: The proportional odds assumptions does not require that the distances between categories are the same.
So what does the proportional odds assumption imply? Say we have | Given the below dependent variable description, should I choose either Ordered or Multinomial logistic regressions?
Lets start with the good news: The proportional odds assumptions does not require that the distances between categories are the same.
So what does the proportional odds assumption imply? Say we have thre... | Given the below dependent variable description, should I choose either Ordered or Multinomial logist
Lets start with the good news: The proportional odds assumptions does not require that the distances between categories are the same.
So what does the proportional odds assumption imply? Say we have |
53,844 | is this interpretation of the p-value legit? | The null hypothesis in this case is that the proportions are equal. One alternative hypothesis that the two are not equal. The statement "there is a 79.76% chance that that the proportions are different" is a statement about the probability of the alternative hypothesis. This is not the correct interpretation of the p-... | is this interpretation of the p-value legit? | The null hypothesis in this case is that the proportions are equal. One alternative hypothesis that the two are not equal. The statement "there is a 79.76% chance that that the proportions are differe | is this interpretation of the p-value legit?
The null hypothesis in this case is that the proportions are equal. One alternative hypothesis that the two are not equal. The statement "there is a 79.76% chance that that the proportions are different" is a statement about the probability of the alternative hypothesis. Thi... | is this interpretation of the p-value legit?
The null hypothesis in this case is that the proportions are equal. One alternative hypothesis that the two are not equal. The statement "there is a 79.76% chance that that the proportions are differe |
53,845 | Purpose of ScheffΓ©'s confidence intervals | This is a classic case of simultaneous inference used for selective inference (see [1]). I will explain.
"Selective (marginal) inference" is when you want to make inference on a data-driven subset of parameters. In the ANOVA case, the subset would be several contrasts.
"Simultaneous inference" is when you want to make ... | Purpose of ScheffΓ©'s confidence intervals | This is a classic case of simultaneous inference used for selective inference (see [1]). I will explain.
"Selective (marginal) inference" is when you want to make inference on a data-driven subset of | Purpose of ScheffΓ©'s confidence intervals
This is a classic case of simultaneous inference used for selective inference (see [1]). I will explain.
"Selective (marginal) inference" is when you want to make inference on a data-driven subset of parameters. In the ANOVA case, the subset would be several contrasts.
"Simulta... | Purpose of ScheffΓ©'s confidence intervals
This is a classic case of simultaneous inference used for selective inference (see [1]). I will explain.
"Selective (marginal) inference" is when you want to make inference on a data-driven subset of |
53,846 | Purpose of ScheffΓ©'s confidence intervals | "A test of contrasts will only have the correct distribution under the null when the set of contrasts that might be tested is specified before you see the data." would have been a better way of putting it. ScheffΓ©'s method then specifies all possible contrasts between the means of pre-defined groups & I doubt there's a... | Purpose of ScheffΓ©'s confidence intervals | "A test of contrasts will only have the correct distribution under the null when the set of contrasts that might be tested is specified before you see the data." would have been a better way of puttin | Purpose of ScheffΓ©'s confidence intervals
"A test of contrasts will only have the correct distribution under the null when the set of contrasts that might be tested is specified before you see the data." would have been a better way of putting it. ScheffΓ©'s method then specifies all possible contrasts between the means... | Purpose of ScheffΓ©'s confidence intervals
"A test of contrasts will only have the correct distribution under the null when the set of contrasts that might be tested is specified before you see the data." would have been a better way of puttin |
53,847 | Can time series data have both unit root and structural break? | Others have already answered about the wrong idea of hypothesis testing. Regarding your question : yes it is possible.
Take for example this time series. It is the price series of a stock of the S&P 500 (therefore, real data) in a time span of more than 10 years. As you can see the series presents what seems to be a s... | Can time series data have both unit root and structural break? | Others have already answered about the wrong idea of hypothesis testing. Regarding your question : yes it is possible.
Take for example this time series. It is the price series of a stock of the S&P | Can time series data have both unit root and structural break?
Others have already answered about the wrong idea of hypothesis testing. Regarding your question : yes it is possible.
Take for example this time series. It is the price series of a stock of the S&P 500 (therefore, real data) in a time span of more than 10... | Can time series data have both unit root and structural break?
Others have already answered about the wrong idea of hypothesis testing. Regarding your question : yes it is possible.
Take for example this time series. It is the price series of a stock of the S&P |
53,848 | Can time series data have both unit root and structural break? | The two older answers already give you a good sense, yet I would like to add some points about the nature of unit-roots and unit root testing.
Please refer to the following question in order
What is the difference between a stationary test and a unit root test?
Here is the part of my answer which matters for you:
How... | Can time series data have both unit root and structural break? | The two older answers already give you a good sense, yet I would like to add some points about the nature of unit-roots and unit root testing.
Please refer to the following question in order
What is | Can time series data have both unit root and structural break?
The two older answers already give you a good sense, yet I would like to add some points about the nature of unit-roots and unit root testing.
Please refer to the following question in order
What is the difference between a stationary test and a unit root ... | Can time series data have both unit root and structural break?
The two older answers already give you a good sense, yet I would like to add some points about the nature of unit-roots and unit root testing.
Please refer to the following question in order
What is |
53,849 | Can time series data have both unit root and structural break? | Yes, it can. Nothing restricts the following DGP to exist:
$$ y_t =
\begin{cases}
c,& \text{if } t = 0 \\
y_{t-1} + e_t,& \text{if } 0 < t < t_1\\
-y_{t-1} + e_t,& \text{if } t_1 \leq t
\end{cases}
$$
where $e_t \sim N(0,\sigma^2)$.
An implementation in R:
remove(list = ls())
set.seed(1)
i <- 1
n1 <- 50
n... | Can time series data have both unit root and structural break? | Yes, it can. Nothing restricts the following DGP to exist:
$$ y_t =
\begin{cases}
c,& \text{if } t = 0 \\
y_{t-1} + e_t,& \text{if } 0 < t < t_1\\
-y_{t-1} + e_t,& \text{if } t_1 \leq t
\ | Can time series data have both unit root and structural break?
Yes, it can. Nothing restricts the following DGP to exist:
$$ y_t =
\begin{cases}
c,& \text{if } t = 0 \\
y_{t-1} + e_t,& \text{if } 0 < t < t_1\\
-y_{t-1} + e_t,& \text{if } t_1 \leq t
\end{cases}
$$
where $e_t \sim N(0,\sigma^2)$.
An implemen... | Can time series data have both unit root and structural break?
Yes, it can. Nothing restricts the following DGP to exist:
$$ y_t =
\begin{cases}
c,& \text{if } t = 0 \\
y_{t-1} + e_t,& \text{if } 0 < t < t_1\\
-y_{t-1} + e_t,& \text{if } t_1 \leq t
\ |
53,850 | Can time series data have both unit root and structural break? | Partially answered in comments:
Your data doesn't reject anything, it's just numbers. I assume you applied some test. Wouldn't a structural break invalidate the test assumptions? But yes, you can write models that have a unit root and a structural break, so data could have both. β Glen_b | Can time series data have both unit root and structural break? | Partially answered in comments:
Your data doesn't reject anything, it's just numbers. I assume you applied some test. Wouldn't a structural break invalidate the test assumptions? But yes, you can wri | Can time series data have both unit root and structural break?
Partially answered in comments:
Your data doesn't reject anything, it's just numbers. I assume you applied some test. Wouldn't a structural break invalidate the test assumptions? But yes, you can write models that have a unit root and a structural break, s... | Can time series data have both unit root and structural break?
Partially answered in comments:
Your data doesn't reject anything, it's just numbers. I assume you applied some test. Wouldn't a structural break invalidate the test assumptions? But yes, you can wri |
53,851 | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable? | Whatever software you used was evidently reporting coefficients to 3 d.p. So 0.000 just meant <0.0005.
It makes perfect sense to use units of measurement that yield coefficients that aren't inconveniently large or small. No statistical principle is violated thereby. You don't need a reference or authority to back this... | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable? | Whatever software you used was evidently reporting coefficients to 3 d.p. So 0.000 just meant <0.0005.
It makes perfect sense to use units of measurement that yield coefficients that aren't inconveni | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable?
Whatever software you used was evidently reporting coefficients to 3 d.p. So 0.000 just meant <0.0005.
It makes perfect sense to use units of measurement that yield coefficients that aren't inconveniently large or small. N... | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable?
Whatever software you used was evidently reporting coefficients to 3 d.p. So 0.000 just meant <0.0005.
It makes perfect sense to use units of measurement that yield coefficients that aren't inconveni |
53,852 | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable? | One way to look at it is this. If you change the units of all independent variables (while keeping the same units for the dependent variable) then you should expect the regression coefficients to change. The smaller the units, implying larger values, the smaller the coefficients. No academic paper would make such a ... | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable? | One way to look at it is this. If you change the units of all independent variables (while keeping the same units for the dependent variable) then you should expect the regression coefficients to cha | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable?
One way to look at it is this. If you change the units of all independent variables (while keeping the same units for the dependent variable) then you should expect the regression coefficients to change. The smaller the u... | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable?
One way to look at it is this. If you change the units of all independent variables (while keeping the same units for the dependent variable) then you should expect the regression coefficients to cha |
53,853 | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable? | I like to think of this as a problem in choosing representative or otherwise sensible values of x1 and x2 for a predictor X, and getting predicted Y when X=x2 minus predicted Y when X=x1. It is easy to get a confidence intervals for such a difference (in R this is a feature of the rms package). This handles nonlinear... | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable? | I like to think of this as a problem in choosing representative or otherwise sensible values of x1 and x2 for a predictor X, and getting predicted Y when X=x2 minus predicted Y when X=x1. It is easy | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable?
I like to think of this as a problem in choosing representative or otherwise sensible values of x1 and x2 for a predictor X, and getting predicted Y when X=x2 minus predicted Y when X=x1. It is easy to get a confidence int... | Is it valid to divide data by a constant to make the estimated beta larger / more interpretable?
I like to think of this as a problem in choosing representative or otherwise sensible values of x1 and x2 for a predictor X, and getting predicted Y when X=x2 minus predicted Y when X=x1. It is easy |
53,854 | Monotonic and non-monotonic patterns of missing values: how do they look like? | The definition of monotonic missing is that, once the subject dropped out he will drop out forever, while for non-monotonic missing the subject may come back or be missing again.
For example, if we follow one subject for five years and he dropped out in the third year, monotonic missing is like o o m m m, and one kind ... | Monotonic and non-monotonic patterns of missing values: how do they look like? | The definition of monotonic missing is that, once the subject dropped out he will drop out forever, while for non-monotonic missing the subject may come back or be missing again.
For example, if we fo | Monotonic and non-monotonic patterns of missing values: how do they look like?
The definition of monotonic missing is that, once the subject dropped out he will drop out forever, while for non-monotonic missing the subject may come back or be missing again.
For example, if we follow one subject for five years and he dr... | Monotonic and non-monotonic patterns of missing values: how do they look like?
The definition of monotonic missing is that, once the subject dropped out he will drop out forever, while for non-monotonic missing the subject may come back or be missing again.
For example, if we fo |
53,855 | Monotonic and non-monotonic patterns of missing values: how do they look like? | Actually the accepted answer is not completely correct.
According to the Statistical Analysis with Missing Data book a monotone pattern is:
monotone missing data: where the variables can be arranged so that all
Y(j+1) ... Y(K) are missing for cases where Y(j) is missing, for
all J = 1 ... K-1.
So for ANY order o... | Monotonic and non-monotonic patterns of missing values: how do they look like? | Actually the accepted answer is not completely correct.
According to the Statistical Analysis with Missing Data book a monotone pattern is:
monotone missing data: where the variables can be arranged | Monotonic and non-monotonic patterns of missing values: how do they look like?
Actually the accepted answer is not completely correct.
According to the Statistical Analysis with Missing Data book a monotone pattern is:
monotone missing data: where the variables can be arranged so that all
Y(j+1) ... Y(K) are missing... | Monotonic and non-monotonic patterns of missing values: how do they look like?
Actually the accepted answer is not completely correct.
According to the Statistical Analysis with Missing Data book a monotone pattern is:
monotone missing data: where the variables can be arranged |
53,856 | Proof of normal equation in regression using tensor notation | A "modern" (post-1900) view of tensors is a geometric one. Perhaps the clearest notation would therefore be a figure, because the "normal equations" are nothing more than a familiar, ages-old theorem of plane geometry!
As a point of departure, let's begin with an expression from your previous question. The setting is... | Proof of normal equation in regression using tensor notation | A "modern" (post-1900) view of tensors is a geometric one. Perhaps the clearest notation would therefore be a figure, because the "normal equations" are nothing more than a familiar, ages-old theorem | Proof of normal equation in regression using tensor notation
A "modern" (post-1900) view of tensors is a geometric one. Perhaps the clearest notation would therefore be a figure, because the "normal equations" are nothing more than a familiar, ages-old theorem of plane geometry!
As a point of departure, let's begin wi... | Proof of normal equation in regression using tensor notation
A "modern" (post-1900) view of tensors is a geometric one. Perhaps the clearest notation would therefore be a figure, because the "normal equations" are nothing more than a familiar, ages-old theorem |
53,857 | Proof of normal equation in regression using tensor notation | The proof for the normal equation (in matrix notation):
Let $J$ be the cost function for the linear regression given by
$$
\begin{aligned}
J &= \vert\vert {\bf X}{\bf w} - {\bf t}\vert\vert^2\\
&= \left({\bf X}{\bf w} - {\bf t}\right)^T\left({\bf X}{\bf w} - {\bf t}\right)\\
&= \left({\bf w}^T{\bf X}^T - {\bf t}^T\r... | Proof of normal equation in regression using tensor notation | The proof for the normal equation (in matrix notation):
Let $J$ be the cost function for the linear regression given by
$$
\begin{aligned}
J &= \vert\vert {\bf X}{\bf w} - {\bf t}\vert\vert^2\\
&= \ | Proof of normal equation in regression using tensor notation
The proof for the normal equation (in matrix notation):
Let $J$ be the cost function for the linear regression given by
$$
\begin{aligned}
J &= \vert\vert {\bf X}{\bf w} - {\bf t}\vert\vert^2\\
&= \left({\bf X}{\bf w} - {\bf t}\right)^T\left({\bf X}{\bf w} ... | Proof of normal equation in regression using tensor notation
The proof for the normal equation (in matrix notation):
Let $J$ be the cost function for the linear regression given by
$$
\begin{aligned}
J &= \vert\vert {\bf X}{\bf w} - {\bf t}\vert\vert^2\\
&= \ |
53,858 | additive and non-additive(multiplicative) interactions - soft question - | we use models with multiplicative interaction effects when relationship between independent variable and dependent variable are non-additive.
My question is, Are all models with multiplicative interaction effects non-linear? and all models with additive interaction effects linear?
The answer to such a question depend... | additive and non-additive(multiplicative) interactions - soft question - | we use models with multiplicative interaction effects when relationship between independent variable and dependent variable are non-additive.
My question is, Are all models with multiplicative intera | additive and non-additive(multiplicative) interactions - soft question -
we use models with multiplicative interaction effects when relationship between independent variable and dependent variable are non-additive.
My question is, Are all models with multiplicative interaction effects non-linear? and all models with a... | additive and non-additive(multiplicative) interactions - soft question -
we use models with multiplicative interaction effects when relationship between independent variable and dependent variable are non-additive.
My question is, Are all models with multiplicative intera |
53,859 | additive and non-additive(multiplicative) interactions - soft question - | To understand this, you must first be clear about the disctinction between features and parameters.
Features - this is basically the input columns of your training data.
Parameters - these are basically the weights of your model that you want to learn
For example, for a linear regression model with two features, you ma... | additive and non-additive(multiplicative) interactions - soft question - | To understand this, you must first be clear about the disctinction between features and parameters.
Features - this is basically the input columns of your training data.
Parameters - these are basical | additive and non-additive(multiplicative) interactions - soft question -
To understand this, you must first be clear about the disctinction between features and parameters.
Features - this is basically the input columns of your training data.
Parameters - these are basically the weights of your model that you want to l... | additive and non-additive(multiplicative) interactions - soft question -
To understand this, you must first be clear about the disctinction between features and parameters.
Features - this is basically the input columns of your training data.
Parameters - these are basical |
53,860 | What does a confidence interval around a p-value mean when using a permutation test? | The theory of permutation tests (and bootstraping) is based on the idea of looking at every possible permutation. If you can look at every possible permutation then you have an exact p-value.
For most cases it is impractical to compute every possible permutation so instead we sample from the "population" of possible p... | What does a confidence interval around a p-value mean when using a permutation test? | The theory of permutation tests (and bootstraping) is based on the idea of looking at every possible permutation. If you can look at every possible permutation then you have an exact p-value.
For mos | What does a confidence interval around a p-value mean when using a permutation test?
The theory of permutation tests (and bootstraping) is based on the idea of looking at every possible permutation. If you can look at every possible permutation then you have an exact p-value.
For most cases it is impractical to comput... | What does a confidence interval around a p-value mean when using a permutation test?
The theory of permutation tests (and bootstraping) is based on the idea of looking at every possible permutation. If you can look at every possible permutation then you have an exact p-value.
For mos |
53,861 | What does a confidence interval around a p-value mean when using a permutation test? | The pure frequentist interpretation: If your were to do this experiment $N$ times, you should expect $X$ percent of the time (99% in your case) or $N * X$ times, that the true $p$ value falls inside the range provided by this 99% confidence interval that percentage or number of times. | What does a confidence interval around a p-value mean when using a permutation test? | The pure frequentist interpretation: If your were to do this experiment $N$ times, you should expect $X$ percent of the time (99% in your case) or $N * X$ times, that the true $p$ value falls inside t | What does a confidence interval around a p-value mean when using a permutation test?
The pure frequentist interpretation: If your were to do this experiment $N$ times, you should expect $X$ percent of the time (99% in your case) or $N * X$ times, that the true $p$ value falls inside the range provided by this 99% confi... | What does a confidence interval around a p-value mean when using a permutation test?
The pure frequentist interpretation: If your were to do this experiment $N$ times, you should expect $X$ percent of the time (99% in your case) or $N * X$ times, that the true $p$ value falls inside t |
53,862 | Constrained least squares estimation | One way to accomplish this task is to alter your model slightly. Rather than fitting the typical model of $$Y=\beta_0+\sum_{i=1}^{p}\beta_iX_i+\varepsilon$$ instead fit the model $$Y=e^{\beta_0}+\sum_{i=1}^{p}e^{\beta_i}X_i+\varepsilon$$ This can still be fit by least squares fairly easily in R and it has the effect of... | Constrained least squares estimation | One way to accomplish this task is to alter your model slightly. Rather than fitting the typical model of $$Y=\beta_0+\sum_{i=1}^{p}\beta_iX_i+\varepsilon$$ instead fit the model $$Y=e^{\beta_0}+\sum_ | Constrained least squares estimation
One way to accomplish this task is to alter your model slightly. Rather than fitting the typical model of $$Y=\beta_0+\sum_{i=1}^{p}\beta_iX_i+\varepsilon$$ instead fit the model $$Y=e^{\beta_0}+\sum_{i=1}^{p}e^{\beta_i}X_i+\varepsilon$$ This can still be fit by least squares fairly... | Constrained least squares estimation
One way to accomplish this task is to alter your model slightly. Rather than fitting the typical model of $$Y=\beta_0+\sum_{i=1}^{p}\beta_iX_i+\varepsilon$$ instead fit the model $$Y=e^{\beta_0}+\sum_ |
53,863 | Constrained least squares estimation | 1) You could fit it by putting box-type constraints to an optimizer that can deal with them - see ?optim and ?nlminb, for example.
2) You could use code like this: http://www.stat.colostate.edu/~meyer/constrparam.R
3) You could use a package designed to have positivity-constrained models, such as the package penalized
... | Constrained least squares estimation | 1) You could fit it by putting box-type constraints to an optimizer that can deal with them - see ?optim and ?nlminb, for example.
2) You could use code like this: http://www.stat.colostate.edu/~meyer | Constrained least squares estimation
1) You could fit it by putting box-type constraints to an optimizer that can deal with them - see ?optim and ?nlminb, for example.
2) You could use code like this: http://www.stat.colostate.edu/~meyer/constrparam.R
3) You could use a package designed to have positivity-constrained m... | Constrained least squares estimation
1) You could fit it by putting box-type constraints to an optimizer that can deal with them - see ?optim and ?nlminb, for example.
2) You could use code like this: http://www.stat.colostate.edu/~meyer |
53,864 | Constrained least squares estimation | This is a quadratic programming problem:
Let $\mathbf I\in\mathbb R^{n\times 9}$, be your design matrix ($n$ is the number of measurements, so each row contains one measurement with the investments $I_1,\ldots, I_9$), and $\boldsymbol \beta\in\mathbb R^9$ your linear coefficients, which you want to be nonnegative (at l... | Constrained least squares estimation | This is a quadratic programming problem:
Let $\mathbf I\in\mathbb R^{n\times 9}$, be your design matrix ($n$ is the number of measurements, so each row contains one measurement with the investments $I | Constrained least squares estimation
This is a quadratic programming problem:
Let $\mathbf I\in\mathbb R^{n\times 9}$, be your design matrix ($n$ is the number of measurements, so each row contains one measurement with the investments $I_1,\ldots, I_9$), and $\boldsymbol \beta\in\mathbb R^9$ your linear coefficients, w... | Constrained least squares estimation
This is a quadratic programming problem:
Let $\mathbf I\in\mathbb R^{n\times 9}$, be your design matrix ($n$ is the number of measurements, so each row contains one measurement with the investments $I |
53,865 | Constrained least squares estimation | The pcls() function in the mgcv package does partially constrained least squares. You can include equality and/or inequality constraints on some or all of the parameter estimates, and in fact on linear combinations of them. (It also allows for quadratic penalties, which are probably not relevant in your case.) | Constrained least squares estimation | The pcls() function in the mgcv package does partially constrained least squares. You can include equality and/or inequality constraints on some or all of the parameter estimates, and in fact on linea | Constrained least squares estimation
The pcls() function in the mgcv package does partially constrained least squares. You can include equality and/or inequality constraints on some or all of the parameter estimates, and in fact on linear combinations of them. (It also allows for quadratic penalties, which are probably... | Constrained least squares estimation
The pcls() function in the mgcv package does partially constrained least squares. You can include equality and/or inequality constraints on some or all of the parameter estimates, and in fact on linea |
53,866 | Probability of picking a biased coin | Your answer is right. The solution can be derived using Bayes' Theorem:
$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
You want to know the probability of $P(\text{biased coin}|\text{three heads})$.
What do we know?
There are $100$ coins. $99$ are fair, $1$ is biased with both sides as heads.
With a fair coin, the probability of t... | Probability of picking a biased coin | Your answer is right. The solution can be derived using Bayes' Theorem:
$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
You want to know the probability of $P(\text{biased coin}|\text{three heads})$.
What do we kn | Probability of picking a biased coin
Your answer is right. The solution can be derived using Bayes' Theorem:
$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
You want to know the probability of $P(\text{biased coin}|\text{three heads})$.
What do we know?
There are $100$ coins. $99$ are fair, $1$ is biased with both sides as heads.
W... | Probability of picking a biased coin
Your answer is right. The solution can be derived using Bayes' Theorem:
$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$
You want to know the probability of $P(\text{biased coin}|\text{three heads})$.
What do we kn |
53,867 | Probability of picking a biased coin | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Here is a write that describes something very similar ... | Probability of picking a biased coin | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| Probability of picking a biased coin
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
Here is a write t... | Probability of picking a biased coin
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
53,868 | Probability of picking a biased coin | In general,
P(biased coin|k heads) = (2^k)/[(2^k) + 99]
Where k is no of consective heads
so if the trick coin was tossed 3 times
(2^3)/[(2^3) + 99] = 8/(8+99) = 8/107 = 0.07 | Probability of picking a biased coin | In general,
P(biased coin|k heads) = (2^k)/[(2^k) + 99]
Where k is no of consective heads
so if the trick coin was tossed 3 times
(2^3)/[(2^3) + 99] = 8/(8+99) = 8/107 = 0.07 | Probability of picking a biased coin
In general,
P(biased coin|k heads) = (2^k)/[(2^k) + 99]
Where k is no of consective heads
so if the trick coin was tossed 3 times
(2^3)/[(2^3) + 99] = 8/(8+99) = 8/107 = 0.07 | Probability of picking a biased coin
In general,
P(biased coin|k heads) = (2^k)/[(2^k) + 99]
Where k is no of consective heads
so if the trick coin was tossed 3 times
(2^3)/[(2^3) + 99] = 8/(8+99) = 8/107 = 0.07 |
53,869 | Time series forecast in R with yearly frequency | Try using the tbats() function in the forecast package for R:
x <- ts(myts, frequency=365)
fit <- tbats(x)
plot(forecast(fit))
TBATS is a generalization of ETS models designed to deal with high frequency data. See http://robjhyndman.com/papers/complex-seasonality/ for the JASA paper behind it. | Time series forecast in R with yearly frequency | Try using the tbats() function in the forecast package for R:
x <- ts(myts, frequency=365)
fit <- tbats(x)
plot(forecast(fit))
TBATS is a generalization of ETS models designed to deal with high frequ | Time series forecast in R with yearly frequency
Try using the tbats() function in the forecast package for R:
x <- ts(myts, frequency=365)
fit <- tbats(x)
plot(forecast(fit))
TBATS is a generalization of ETS models designed to deal with high frequency data. See http://robjhyndman.com/papers/complex-seasonality/ for th... | Time series forecast in R with yearly frequency
Try using the tbats() function in the forecast package for R:
x <- ts(myts, frequency=365)
fit <- tbats(x)
plot(forecast(fit))
TBATS is a generalization of ETS models designed to deal with high frequ |
53,870 | Time series forecast in R with yearly frequency | R may be of little use to you due to the complexity of your problem. We recently developed forecasts for a daily series that looks "similar" but "different" to yours.
.
It required combining Intervention Detection , Causal Variables (Holidays , Promotions etc.) and ARIMA structure. We used AUTOBOX ( a product that I... | Time series forecast in R with yearly frequency | R may be of little use to you due to the complexity of your problem. We recently developed forecasts for a daily series that looks "similar" but "different" to yours.
.
It required combining Interve | Time series forecast in R with yearly frequency
R may be of little use to you due to the complexity of your problem. We recently developed forecasts for a daily series that looks "similar" but "different" to yours.
.
It required combining Intervention Detection , Causal Variables (Holidays , Promotions etc.) and ARI... | Time series forecast in R with yearly frequency
R may be of little use to you due to the complexity of your problem. We recently developed forecasts for a daily series that looks "similar" but "different" to yours.
.
It required combining Interve |
53,871 | Mixed model specification with nlme in R | If I understand your question correctly, you can specify your model with nested random effects like this:
fit.1 <- lme(Change ~ Dose*Time, random=~1|ID/Dose, data=mydata)
To specify the covariance structure, e.g. a simple compound symmetry form, try this:
fit.2 <- lme(Change ~ Dose*Time, random=~1|ID/Dose, data=mydata... | Mixed model specification with nlme in R | If I understand your question correctly, you can specify your model with nested random effects like this:
fit.1 <- lme(Change ~ Dose*Time, random=~1|ID/Dose, data=mydata)
To specify the covariance st | Mixed model specification with nlme in R
If I understand your question correctly, you can specify your model with nested random effects like this:
fit.1 <- lme(Change ~ Dose*Time, random=~1|ID/Dose, data=mydata)
To specify the covariance structure, e.g. a simple compound symmetry form, try this:
fit.2 <- lme(Change ~ ... | Mixed model specification with nlme in R
If I understand your question correctly, you can specify your model with nested random effects like this:
fit.1 <- lme(Change ~ Dose*Time, random=~1|ID/Dose, data=mydata)
To specify the covariance st |
53,872 | Mixed model specification with nlme in R | Looks like you want to fit a mixed effects model with Dose-Time interaction with random intercepts for each animale (ID) e.g.
lmer(Change ~ Dose*Time + ( 1 | ID ), data=data)
A model that allows for random slopes (over Time) in addition to random intercepts would look like this:
lmer(Change ~ Dose*Time + ( Time | ID )... | Mixed model specification with nlme in R | Looks like you want to fit a mixed effects model with Dose-Time interaction with random intercepts for each animale (ID) e.g.
lmer(Change ~ Dose*Time + ( 1 | ID ), data=data)
A model that allows for | Mixed model specification with nlme in R
Looks like you want to fit a mixed effects model with Dose-Time interaction with random intercepts for each animale (ID) e.g.
lmer(Change ~ Dose*Time + ( 1 | ID ), data=data)
A model that allows for random slopes (over Time) in addition to random intercepts would look like this... | Mixed model specification with nlme in R
Looks like you want to fit a mixed effects model with Dose-Time interaction with random intercepts for each animale (ID) e.g.
lmer(Change ~ Dose*Time + ( 1 | ID ), data=data)
A model that allows for |
53,873 | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature selection? | You write
From what I understand, if the p-values are above a certain threshold
for a given variable (e.g. p-value > 0.05) as is the case with
variable x1's pvalue=0.975, then one can say that this particular
regression doesn't gain any additional information from having this
variable in there.
This is not co... | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature se | You write
From what I understand, if the p-values are above a certain threshold
for a given variable (e.g. p-value > 0.05) as is the case with
variable x1's pvalue=0.975, then one can say that th | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature selection?
You write
From what I understand, if the p-values are above a certain threshold
for a given variable (e.g. p-value > 0.05) as is the case with
variable x1's pvalue=0.975, then one can say that this particul... | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature se
You write
From what I understand, if the p-values are above a certain threshold
for a given variable (e.g. p-value > 0.05) as is the case with
variable x1's pvalue=0.975, then one can say that th |
53,874 | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature selection? | I would interpret those t statistics with caution. The beta coefficients in the regression model are calculated by taking all of the variables into account, and the t statistics are based on all of the variables, so it can be misleading to interpret them individually. Each variable's estimate is influenced by the prese... | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature se | I would interpret those t statistics with caution. The beta coefficients in the regression model are calculated by taking all of the variables into account, and the t statistics are based on all of th | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature selection?
I would interpret those t statistics with caution. The beta coefficients in the regression model are calculated by taking all of the variables into account, and the t statistics are based on all of the variables... | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature se
I would interpret those t statistics with caution. The beta coefficients in the regression model are calculated by taking all of the variables into account, and the t statistics are based on all of th |
53,875 | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature selection? | Regarding feature selection: I would personally argue not to be based on p-values regarding feature selection. Use back-wards elimination; start with fitting a model with all the variables of interest and calculate your "favourite" information criterion (eg. AIC), then sequentially exclude one of your feature and recal... | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature se | Regarding feature selection: I would personally argue not to be based on p-values regarding feature selection. Use back-wards elimination; start with fitting a model with all the variables of interest | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature selection?
Regarding feature selection: I would personally argue not to be based on p-values regarding feature selection. Use back-wards elimination; start with fitting a model with all the variables of interest and calcul... | How should I interpret the p-values (i.e. t-tests) in regressions, and can I use them for feature se
Regarding feature selection: I would personally argue not to be based on p-values regarding feature selection. Use back-wards elimination; start with fitting a model with all the variables of interest |
53,876 | Ordinal regression vs. summated score | Ordinal regression is appropriate whenever the dependent variable is ordinal: That is, when you can assume that the levels are in order, but not that the gaps between the levels are equal.
If you analyze individual Likert items (each scored 1-5 or 1-7 or whatever) then this could be a very reasonable assumption. But o... | Ordinal regression vs. summated score | Ordinal regression is appropriate whenever the dependent variable is ordinal: That is, when you can assume that the levels are in order, but not that the gaps between the levels are equal.
If you ana | Ordinal regression vs. summated score
Ordinal regression is appropriate whenever the dependent variable is ordinal: That is, when you can assume that the levels are in order, but not that the gaps between the levels are equal.
If you analyze individual Likert items (each scored 1-5 or 1-7 or whatever) then this could ... | Ordinal regression vs. summated score
Ordinal regression is appropriate whenever the dependent variable is ordinal: That is, when you can assume that the levels are in order, but not that the gaps between the levels are equal.
If you ana |
53,877 | Plotting logistic regression interaction (categorical) in R | You could plot fitted probabilities by placement, separately for each level of ethnic. Create some dummy data and fit your model:
set.seed(1)
nn <- 100
placements <- seq(0,10)
foo <- data.frame(disorder=sample(c(0,1),size=nn,replace=TRUE),
placement=sample(placements,size=nn,replace=TRUE),
ethnic=sample(c("White","Blac... | Plotting logistic regression interaction (categorical) in R | You could plot fitted probabilities by placement, separately for each level of ethnic. Create some dummy data and fit your model:
set.seed(1)
nn <- 100
placements <- seq(0,10)
foo <- data.frame(disord | Plotting logistic regression interaction (categorical) in R
You could plot fitted probabilities by placement, separately for each level of ethnic. Create some dummy data and fit your model:
set.seed(1)
nn <- 100
placements <- seq(0,10)
foo <- data.frame(disorder=sample(c(0,1),size=nn,replace=TRUE),
placement=sample(pla... | Plotting logistic regression interaction (categorical) in R
You could plot fitted probabilities by placement, separately for each level of ethnic. Create some dummy data and fit your model:
set.seed(1)
nn <- 100
placements <- seq(0,10)
foo <- data.frame(disord |
53,878 | Plotting logistic regression interaction (categorical) in R | I suggest a mosaic plot, available in the vcd package.
There is a vignette and a few papers; typing ??mosaic will show them. A very simple example is
library(vcd)
data(HairEyeColor)
HairEye <- margin.table(HairEyeColor, c(1,2))
mosaic(HairEye, main = "Basic Mosaic Display of Hair Eye Color data")
Another option is ... | Plotting logistic regression interaction (categorical) in R | I suggest a mosaic plot, available in the vcd package.
There is a vignette and a few papers; typing ??mosaic will show them. A very simple example is
library(vcd)
data(HairEyeColor)
HairEye <- margi | Plotting logistic regression interaction (categorical) in R
I suggest a mosaic plot, available in the vcd package.
There is a vignette and a few papers; typing ??mosaic will show them. A very simple example is
library(vcd)
data(HairEyeColor)
HairEye <- margin.table(HairEyeColor, c(1,2))
mosaic(HairEye, main = "Basic... | Plotting logistic regression interaction (categorical) in R
I suggest a mosaic plot, available in the vcd package.
There is a vignette and a few papers; typing ??mosaic will show them. A very simple example is
library(vcd)
data(HairEyeColor)
HairEye <- margi |
53,879 | Plotting logistic regression interaction (categorical) in R | @Stephan Kolassa's answer was very good. Here I build in two other plotting ideas:
It's helpful to see the relative N sizes at each level of the x-variable, Placements. These sizes can be indicated using hash marks.
It can be convenient to show group (here, Ethnicity) labels alongside their lines, rather than in a ... | Plotting logistic regression interaction (categorical) in R | @Stephan Kolassa's answer was very good. Here I build in two other plotting ideas:
It's helpful to see the relative N sizes at each level of the x-variable, Placements. These sizes can be indicated | Plotting logistic regression interaction (categorical) in R
@Stephan Kolassa's answer was very good. Here I build in two other plotting ideas:
It's helpful to see the relative N sizes at each level of the x-variable, Placements. These sizes can be indicated using hash marks.
It can be convenient to show group (here... | Plotting logistic regression interaction (categorical) in R
@Stephan Kolassa's answer was very good. Here I build in two other plotting ideas:
It's helpful to see the relative N sizes at each level of the x-variable, Placements. These sizes can be indicated |
53,880 | What is a WISARD Neural Network? | IIRC WISARD was a RAM based neural network method developed by Igor Aleksander at Imperial College in the 1980s and early 1990s. RAM based neural networks essentially use look up tables to store the function computed by each neuron, and hence are easily implemented in digital hardware and have efficient training algor... | What is a WISARD Neural Network? | IIRC WISARD was a RAM based neural network method developed by Igor Aleksander at Imperial College in the 1980s and early 1990s. RAM based neural networks essentially use look up tables to store the | What is a WISARD Neural Network?
IIRC WISARD was a RAM based neural network method developed by Igor Aleksander at Imperial College in the 1980s and early 1990s. RAM based neural networks essentially use look up tables to store the function computed by each neuron, and hence are easily implemented in digital hardware ... | What is a WISARD Neural Network?
IIRC WISARD was a RAM based neural network method developed by Igor Aleksander at Imperial College in the 1980s and early 1990s. RAM based neural networks essentially use look up tables to store the |
53,881 | What is a WISARD Neural Network? | A major working development to date (1985) in this area however is the N-tuple classifier: "WISARD" (WIlkie, Stoneham and Aleksander, Recognition Device), which has been developed at Brunel University and is produced commercially by Computer Recognition Systems Limited.
The WISARD system acts upon images from standard... | What is a WISARD Neural Network? | A major working development to date (1985) in this area however is the N-tuple classifier: "WISARD" (WIlkie, Stoneham and Aleksander, Recognition Device), which has been developed at Brunel University | What is a WISARD Neural Network?
A major working development to date (1985) in this area however is the N-tuple classifier: "WISARD" (WIlkie, Stoneham and Aleksander, Recognition Device), which has been developed at Brunel University and is produced commercially by Computer Recognition Systems Limited.
The WISARD syst... | What is a WISARD Neural Network?
A major working development to date (1985) in this area however is the N-tuple classifier: "WISARD" (WIlkie, Stoneham and Aleksander, Recognition Device), which has been developed at Brunel University |
53,882 | What is a WISARD Neural Network? | WISARD was actually built by Bruce Wilkie , Sonham asreader , Alexandre getting the funding . Eric Conan being one of technicians building it .
It was presented at Royal Institution , Maggie had a look
Wi Wilkie
S Stonham
A Alexandre
R recognition
D discriminator -
two 19 inc... | What is a WISARD Neural Network? | WISARD was actually built by Bruce Wilkie , Sonham asreader , Alexandre getting the funding . Eric Conan being one of technicians building it .
It was presented at Royal Institution , | What is a WISARD Neural Network?
WISARD was actually built by Bruce Wilkie , Sonham asreader , Alexandre getting the funding . Eric Conan being one of technicians building it .
It was presented at Royal Institution , Maggie had a look
Wi Wilkie
S Stonham
A Alexandre
R recognition
D... | What is a WISARD Neural Network?
WISARD was actually built by Bruce Wilkie , Sonham asreader , Alexandre getting the funding . Eric Conan being one of technicians building it .
It was presented at Royal Institution , |
53,883 | What is a WISARD Neural Network? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
WISARD stamds for WILKIE STONHAM AND ALEXANDER. A Neural network based on hardware RAMs hardwired to be a perc... | What is a WISARD Neural Network? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
| What is a WISARD Neural Network?
Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
WISARD stamds for WILKIE STONHAM AND ALEXANDER. A Neural network based on har... | What is a WISARD Neural Network?
Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
|
53,884 | Strict Exogeneity and Seasonal Dummy Variables | Strict exogeneity means that the error $u_t$ is uncorrelated with all past and future values of the seasonal dummies. This means that such variables cannot react to shocks to $y$ in the past or the future. Suppose consumers feel worried about the economy in December and such sentiments are unobserved. This means there ... | Strict Exogeneity and Seasonal Dummy Variables | Strict exogeneity means that the error $u_t$ is uncorrelated with all past and future values of the seasonal dummies. This means that such variables cannot react to shocks to $y$ in the past or the fu | Strict Exogeneity and Seasonal Dummy Variables
Strict exogeneity means that the error $u_t$ is uncorrelated with all past and future values of the seasonal dummies. This means that such variables cannot react to shocks to $y$ in the past or the future. Suppose consumers feel worried about the economy in December and su... | Strict Exogeneity and Seasonal Dummy Variables
Strict exogeneity means that the error $u_t$ is uncorrelated with all past and future values of the seasonal dummies. This means that such variables cannot react to shocks to $y$ in the past or the fu |
53,885 | Strict Exogeneity and Seasonal Dummy Variables | A seasonal dummy is nonrandom: Whatever sample you draw, winter is winter, never summer. The covariance of a random variable and a constant is zero. | Strict Exogeneity and Seasonal Dummy Variables | A seasonal dummy is nonrandom: Whatever sample you draw, winter is winter, never summer. The covariance of a random variable and a constant is zero. | Strict Exogeneity and Seasonal Dummy Variables
A seasonal dummy is nonrandom: Whatever sample you draw, winter is winter, never summer. The covariance of a random variable and a constant is zero. | Strict Exogeneity and Seasonal Dummy Variables
A seasonal dummy is nonrandom: Whatever sample you draw, winter is winter, never summer. The covariance of a random variable and a constant is zero. |
53,886 | Within model with plm package | The two estimators are computed differently, but are numerically identical, so essentially it doesn't matter. The within estimator is computationally easier since it keeps the size of the design matrix in check, and I would think that is how the within estimator is implemented. Here is some R code to demonstrate this
l... | Within model with plm package | The two estimators are computed differently, but are numerically identical, so essentially it doesn't matter. The within estimator is computationally easier since it keeps the size of the design matri | Within model with plm package
The two estimators are computed differently, but are numerically identical, so essentially it doesn't matter. The within estimator is computationally easier since it keeps the size of the design matrix in check, and I would think that is how the within estimator is implemented. Here is som... | Within model with plm package
The two estimators are computed differently, but are numerically identical, so essentially it doesn't matter. The within estimator is computationally easier since it keeps the size of the design matri |
53,887 | What are pure random sampling and orthogonal sampling? | Latin Hypercube (LHC) sampling is a sampling method than ensures that each sampling space dimension is roughly evenly sampled. Orthogonal sampling is basically an extension to latin hypercube sampling that ensures that each subspace is evenly sampled. This also ensures that correlation between sampling dimensions is mi... | What are pure random sampling and orthogonal sampling? | Latin Hypercube (LHC) sampling is a sampling method than ensures that each sampling space dimension is roughly evenly sampled. Orthogonal sampling is basically an extension to latin hypercube sampling | What are pure random sampling and orthogonal sampling?
Latin Hypercube (LHC) sampling is a sampling method than ensures that each sampling space dimension is roughly evenly sampled. Orthogonal sampling is basically an extension to latin hypercube sampling that ensures that each subspace is evenly sampled. This also ens... | What are pure random sampling and orthogonal sampling?
Latin Hypercube (LHC) sampling is a sampling method than ensures that each sampling space dimension is roughly evenly sampled. Orthogonal sampling is basically an extension to latin hypercube sampling |
53,888 | Can one have two random variables, perfectly correlated, but with different variances (as percent of their mean)? | Sure you can, e.g.
set.seed(38821010)
x <- rnorm(100)
y <- 5*x + 3
var(y)/mean(y)
var(x)/mean(x)
cor(x,y)
as an example. | Can one have two random variables, perfectly correlated, but with different variances (as percent of | Sure you can, e.g.
set.seed(38821010)
x <- rnorm(100)
y <- 5*x + 3
var(y)/mean(y)
var(x)/mean(x)
cor(x,y)
as an example. | Can one have two random variables, perfectly correlated, but with different variances (as percent of their mean)?
Sure you can, e.g.
set.seed(38821010)
x <- rnorm(100)
y <- 5*x + 3
var(y)/mean(y)
var(x)/mean(x)
cor(x,y)
as an example. | Can one have two random variables, perfectly correlated, but with different variances (as percent of
Sure you can, e.g.
set.seed(38821010)
x <- rnorm(100)
y <- 5*x + 3
var(y)/mean(y)
var(x)/mean(x)
cor(x,y)
as an example. |
53,889 | Can one have two random variables, perfectly correlated, but with different variances (as percent of their mean)? | I think to put what Peter said in simple terms. If Y is a linear function of X the absolute value of the Pearson correlation is 1. But the variances will differ unless the coefficient of X is 1. This is simply due to the fact that
Var(cX)=c$^2$Var(X) and Var(X+a)=Var(X) for any constants a and c.
Now adding the idea... | Can one have two random variables, perfectly correlated, but with different variances (as percent of | I think to put what Peter said in simple terms. If Y is a linear function of X the absolute value of the Pearson correlation is 1. But the variances will differ unless the coefficient of X is 1. Thi | Can one have two random variables, perfectly correlated, but with different variances (as percent of their mean)?
I think to put what Peter said in simple terms. If Y is a linear function of X the absolute value of the Pearson correlation is 1. But the variances will differ unless the coefficient of X is 1. This is s... | Can one have two random variables, perfectly correlated, but with different variances (as percent of
I think to put what Peter said in simple terms. If Y is a linear function of X the absolute value of the Pearson correlation is 1. But the variances will differ unless the coefficient of X is 1. Thi |
53,890 | Contradiction between significant effect in multiple regression, but non-significant t-test on its own | The multiple regression model controls for other sources of variability in the DV, whereas in the t-test, all of that variability is lumped into the error term. Thus, the t-test has lower statistical power to detect the effect. Under the assumption that the effect is real, however, the t-test would show 'significance... | Contradiction between significant effect in multiple regression, but non-significant t-test on its o | The multiple regression model controls for other sources of variability in the DV, whereas in the t-test, all of that variability is lumped into the error term. Thus, the t-test has lower statistical | Contradiction between significant effect in multiple regression, but non-significant t-test on its own
The multiple regression model controls for other sources of variability in the DV, whereas in the t-test, all of that variability is lumped into the error term. Thus, the t-test has lower statistical power to detect ... | Contradiction between significant effect in multiple regression, but non-significant t-test on its o
The multiple regression model controls for other sources of variability in the DV, whereas in the t-test, all of that variability is lumped into the error term. Thus, the t-test has lower statistical |
53,891 | Contradiction between significant effect in multiple regression, but non-significant t-test on its own | Gung already gave a good answer. I would also add that in a model with 10 covariates, it's very easy to obtain small, sometimes spurious, effects, just because your other variables are absorbing so much variance. I would examine some effect size metrics (such as delta R^2) for your gender effect to help you determine... | Contradiction between significant effect in multiple regression, but non-significant t-test on its o | Gung already gave a good answer. I would also add that in a model with 10 covariates, it's very easy to obtain small, sometimes spurious, effects, just because your other variables are absorbing so m | Contradiction between significant effect in multiple regression, but non-significant t-test on its own
Gung already gave a good answer. I would also add that in a model with 10 covariates, it's very easy to obtain small, sometimes spurious, effects, just because your other variables are absorbing so much variance. I ... | Contradiction between significant effect in multiple regression, but non-significant t-test on its o
Gung already gave a good answer. I would also add that in a model with 10 covariates, it's very easy to obtain small, sometimes spurious, effects, just because your other variables are absorbing so m |
53,892 | Contradiction between significant effect in multiple regression, but non-significant t-test on its own | In the model gender is one of 10 covariates. It has some influence on the response complaining in conjunction with the other covariates. But by itself it makes less of a difference and is not a statistically significant difference. | Contradiction between significant effect in multiple regression, but non-significant t-test on its o | In the model gender is one of 10 covariates. It has some influence on the response complaining in conjunction with the other covariates. But by itself it makes less of a difference and is not a stat | Contradiction between significant effect in multiple regression, but non-significant t-test on its own
In the model gender is one of 10 covariates. It has some influence on the response complaining in conjunction with the other covariates. But by itself it makes less of a difference and is not a statistically signifi... | Contradiction between significant effect in multiple regression, but non-significant t-test on its o
In the model gender is one of 10 covariates. It has some influence on the response complaining in conjunction with the other covariates. But by itself it makes less of a difference and is not a stat |
53,893 | Two-sided permutation test vs. two one-sided [duplicate] | Here is an R example of permutation testing.
## dummy data
set.seed(1)
x <- runif(20)
y <- 0.5 * x
y <- y + rnorm(20)
## set up for the permutation, compute observed R
nullR <- numeric(length = 1000)
nullR[1] <- cor(x, y) ## obsered R in [1]
N <- length(x)
## permutation test
for(i in seq_len(999) + 1) {
nullR[i]... | Two-sided permutation test vs. two one-sided [duplicate] | Here is an R example of permutation testing.
## dummy data
set.seed(1)
x <- runif(20)
y <- 0.5 * x
y <- y + rnorm(20)
## set up for the permutation, compute observed R
nullR <- numeric(length = 1000) | Two-sided permutation test vs. two one-sided [duplicate]
Here is an R example of permutation testing.
## dummy data
set.seed(1)
x <- runif(20)
y <- 0.5 * x
y <- y + rnorm(20)
## set up for the permutation, compute observed R
nullR <- numeric(length = 1000)
nullR[1] <- cor(x, y) ## obsered R in [1]
N <- length(x)
## p... | Two-sided permutation test vs. two one-sided [duplicate]
Here is an R example of permutation testing.
## dummy data
set.seed(1)
x <- runif(20)
y <- 0.5 * x
y <- y + rnorm(20)
## set up for the permutation, compute observed R
nullR <- numeric(length = 1000) |
53,894 | Two-sided permutation test vs. two one-sided [duplicate] | Your formula for $p_2$ only works if you have distribution symmetric around $0$, which at least your illustration do not seem to have.
A better estimate is given by $p_2(t) = {\rm min}(2p_{+}, 2p_{-})$. using your definitions of $p_{+}$ and $p_{-}$. | Two-sided permutation test vs. two one-sided [duplicate] | Your formula for $p_2$ only works if you have distribution symmetric around $0$, which at least your illustration do not seem to have.
A better estimate is given by $p_2(t) = {\rm min}(2p_{+}, 2p_{-} | Two-sided permutation test vs. two one-sided [duplicate]
Your formula for $p_2$ only works if you have distribution symmetric around $0$, which at least your illustration do not seem to have.
A better estimate is given by $p_2(t) = {\rm min}(2p_{+}, 2p_{-})$. using your definitions of $p_{+}$ and $p_{-}$. | Two-sided permutation test vs. two one-sided [duplicate]
Your formula for $p_2$ only works if you have distribution symmetric around $0$, which at least your illustration do not seem to have.
A better estimate is given by $p_2(t) = {\rm min}(2p_{+}, 2p_{-} |
53,895 | Why does my naive Bayes classifier only give me probabilities near 0? | Naive Bayes generally uses a decision rule like
$$
\text{argmax}_{C_i} P(C_i)P(D|C_i),
$$
which comes from the fact we can write
$$
P(C_i|D) = \frac{P(C_i)P(D|C_i)}{P(D)}.
$$
and drop the denominator $P(D)$ since it does not depend on the class. However, since $P(D) << 1$ (i.e. there are many possible documents), negl... | Why does my naive Bayes classifier only give me probabilities near 0? | Naive Bayes generally uses a decision rule like
$$
\text{argmax}_{C_i} P(C_i)P(D|C_i),
$$
which comes from the fact we can write
$$
P(C_i|D) = \frac{P(C_i)P(D|C_i)}{P(D)}.
$$
and drop the denominator | Why does my naive Bayes classifier only give me probabilities near 0?
Naive Bayes generally uses a decision rule like
$$
\text{argmax}_{C_i} P(C_i)P(D|C_i),
$$
which comes from the fact we can write
$$
P(C_i|D) = \frac{P(C_i)P(D|C_i)}{P(D)}.
$$
and drop the denominator $P(D)$ since it does not depend on the class. How... | Why does my naive Bayes classifier only give me probabilities near 0?
Naive Bayes generally uses a decision rule like
$$
\text{argmax}_{C_i} P(C_i)P(D|C_i),
$$
which comes from the fact we can write
$$
P(C_i|D) = \frac{P(C_i)P(D|C_i)}{P(D)}.
$$
and drop the denominator |
53,896 | Likert scale question divided into different group. How to calculate mean of different group? | See this question: Analyzing Likert scales
Agresti does a lot of this ordinal data analysis (e.g., "Analysis of Ordinal Categorical Data").
For your particular problem, I would suggest looking at three methods: multiple hypothesis testing http://en.wikipedia.org/wiki/Multiple_comparisons, mixed effects models http://en... | Likert scale question divided into different group. How to calculate mean of different group? | See this question: Analyzing Likert scales
Agresti does a lot of this ordinal data analysis (e.g., "Analysis of Ordinal Categorical Data").
For your particular problem, I would suggest looking at thre | Likert scale question divided into different group. How to calculate mean of different group?
See this question: Analyzing Likert scales
Agresti does a lot of this ordinal data analysis (e.g., "Analysis of Ordinal Categorical Data").
For your particular problem, I would suggest looking at three methods: multiple hypoth... | Likert scale question divided into different group. How to calculate mean of different group?
See this question: Analyzing Likert scales
Agresti does a lot of this ordinal data analysis (e.g., "Analysis of Ordinal Categorical Data").
For your particular problem, I would suggest looking at thre |
53,897 | Likert scale question divided into different group. How to calculate mean of different group? | Often questions are grouped according to domains (your groups are like domains) and comparisons are made on the domains by summing the individual question scores (equivalent to averaging). This makes sense if the scoring is consistent from one question to another. | Likert scale question divided into different group. How to calculate mean of different group? | Often questions are grouped according to domains (your groups are like domains) and comparisons are made on the domains by summing the individual question scores (equivalent to averaging). This makes | Likert scale question divided into different group. How to calculate mean of different group?
Often questions are grouped according to domains (your groups are like domains) and comparisons are made on the domains by summing the individual question scores (equivalent to averaging). This makes sense if the scoring is c... | Likert scale question divided into different group. How to calculate mean of different group?
Often questions are grouped according to domains (your groups are like domains) and comparisons are made on the domains by summing the individual question scores (equivalent to averaging). This makes |
53,898 | Likert scale question divided into different group. How to calculate mean of different group? | The mean would be totally acceptable. Some people like to think that it doesn't make sense because the distance between two values (e.g. 2 - 3 vs. 4 - 5) are not necessarily homogeneous. Those aren't the kinds of issues that keep me awake at night. Another option is to consider proportions of top-box responses. In surv... | Likert scale question divided into different group. How to calculate mean of different group? | The mean would be totally acceptable. Some people like to think that it doesn't make sense because the distance between two values (e.g. 2 - 3 vs. 4 - 5) are not necessarily homogeneous. Those aren't | Likert scale question divided into different group. How to calculate mean of different group?
The mean would be totally acceptable. Some people like to think that it doesn't make sense because the distance between two values (e.g. 2 - 3 vs. 4 - 5) are not necessarily homogeneous. Those aren't the kinds of issues that k... | Likert scale question divided into different group. How to calculate mean of different group?
The mean would be totally acceptable. Some people like to think that it doesn't make sense because the distance between two values (e.g. 2 - 3 vs. 4 - 5) are not necessarily homogeneous. Those aren't |
53,899 | Likert scale question divided into different group. How to calculate mean of different group? | With 16 respondents, you may be better served just by reading each person's survey responses individually, and following up with them to understand any particularly high or low scores :-) But, since this is a statistical Q&A site, I'll discuss the statistical approach.
Ideally, the survey would ask an overall question ... | Likert scale question divided into different group. How to calculate mean of different group? | With 16 respondents, you may be better served just by reading each person's survey responses individually, and following up with them to understand any particularly high or low scores :-) But, since t | Likert scale question divided into different group. How to calculate mean of different group?
With 16 respondents, you may be better served just by reading each person's survey responses individually, and following up with them to understand any particularly high or low scores :-) But, since this is a statistical Q&A s... | Likert scale question divided into different group. How to calculate mean of different group?
With 16 respondents, you may be better served just by reading each person's survey responses individually, and following up with them to understand any particularly high or low scores :-) But, since t |
53,900 | Likert scale question divided into different group. How to calculate mean of different group? | You are getting some good responses here. I will see if I can organize some of this information and add some other bits to create a fuller picture for you. Your project appears to be entirely descriptive rather than inferential, so I think you don't have to worry about as much. For the most part, as several others s... | Likert scale question divided into different group. How to calculate mean of different group? | You are getting some good responses here. I will see if I can organize some of this information and add some other bits to create a fuller picture for you. Your project appears to be entirely descri | Likert scale question divided into different group. How to calculate mean of different group?
You are getting some good responses here. I will see if I can organize some of this information and add some other bits to create a fuller picture for you. Your project appears to be entirely descriptive rather than inferent... | Likert scale question divided into different group. How to calculate mean of different group?
You are getting some good responses here. I will see if I can organize some of this information and add some other bits to create a fuller picture for you. Your project appears to be entirely descri |
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