Standard Errors in MixedModels

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Standard Errors in MixedModels

Thomas Covert
I have become a huge fan of MixedModels - its much faster than STATA's xtreg, which is great.  However, I can't figure out how to get it to show me the standard error of the estimate of the variance of the random effects  Is this intentional?  As far as I can tell, this is a well defined object, and STATA's xtreg does report it when the maximum likelihood routine is chosen.

-thom

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Re: Standard Errors in MixedModels

Douglas Bates
On Tuesday, August 26, 2014 8:44:30 PM UTC-5, Thomas Covert wrote:
I have become a huge fan of MixedModels - its much faster than STATA's xtreg, which is great.  

I'm glad you are enjoying using it.  I'm open to receiving suggestions or success stories, either as issues in the repository or by email, as I am writing a follow up paper to arxiv.org/abs/1406.5823 to describe the methods in the MixedModels package.  
 
However, I can't figure out how to get it to show me the standard error of the estimate of the variance of the random effects  Is this intentional?

Yes.
 
As far as I can tell, this is a well defined object, and STATA's xtreg does report it when the maximum likelihood routine is chosen.

Well-defined, perhaps but also misleading at best and totally meaningless at worst.  A standard error is the estimated standard deviation of the estimator and represents an interesting quantity if the distribution of the estimator is close to Gaussian or at least symmetric.  The distribution of a variance estimator is not symmetric - it is highly skewed.  In the simplest case, estimating the variance given an i.i.d. sample from a Gaussian distribution, the distribution of the estimator is a chi-square, which can be very skew.

This is also the reason that the desirability of REML estimates, which are touted as being unbiased estimators of variance components or at least less biased than ML estimates, is questionable.  Bias is related to the mean of the estimator yet the mean of a skewed distribution is not a good way of summarizing a typical value.

I have a couple of presentations related to this that I will post a link to when I get to the office.

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Re: Standard Errors in MixedModels

Thomas Covert
gotcha.  I assume the answer to this is no, but would it matter if I were estimating the log standard deviation of the random effect as opposed to the variance itself?  Wouldn't this at least be symmetric (I have no idea if it would be unbiased or not)?

-thom

On Wednesday, August 27, 2014 9:04:03 AM UTC-5, Douglas Bates wrote:
On Tuesday, August 26, 2014 8:44:30 PM UTC-5, Thomas Covert wrote:
I have become a huge fan of MixedModels - its much faster than STATA's xtreg, which is great.  

I'm glad you are enjoying using it.  I'm open to receiving suggestions or success stories, either as issues in the repository or by email, as I am writing a follow up paper to <a href="http://arxiv.org/abs/1406.5823" target="_blank" onmousedown="this.href='http://www.google.com/url?q\75http%3A%2F%2Farxiv.org%2Fabs%2F1406.5823\46sa\75D\46sntz\0751\46usg\75AFQjCNHg4YiNxmH9hRn8TcL5ch6RaGYCkA';return true;" onclick="this.href='http://www.google.com/url?q\75http%3A%2F%2Farxiv.org%2Fabs%2F1406.5823\46sa\75D\46sntz\0751\46usg\75AFQjCNHg4YiNxmH9hRn8TcL5ch6RaGYCkA';return true;">arxiv.org/abs/1406.5823 to describe the methods in the MixedModels package.  
 
However, I can't figure out how to get it to show me the standard error of the estimate of the variance of the random effects  Is this intentional?

Yes.
 
As far as I can tell, this is a well defined object, and STATA's xtreg does report it when the maximum likelihood routine is chosen.

Well-defined, perhaps but also misleading at best and totally meaningless at worst.  A standard error is the estimated standard deviation of the estimator and represents an interesting quantity if the distribution of the estimator is close to Gaussian or at least symmetric.  The distribution of a variance estimator is not symmetric - it is highly skewed.  In the simplest case, estimating the variance given an i.i.d. sample from a Gaussian distribution, the distribution of the estimator is a chi-square, which can be very skew.

This is also the reason that the desirability of REML estimates, which are touted as being unbiased estimators of variance components or at least less biased than ML estimates, is questionable.  Bias is related to the mean of the estimator yet the mean of a skewed distribution is not a good way of summarizing a typical value.

I have a couple of presentations related to this that I will post a link to when I get to the office.

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Re: Standard Errors in MixedModels

Douglas Bates
On Wednesday, August 27, 2014 9:13:17 AM UTC-5, Thomas Covert wrote:
gotcha.  I assume the answer to this is no, but would it matter if I were estimating the log standard deviation of the random effect as opposed to the variance itself?  Wouldn't this at least be symmetric (I have no idea if it would be unbiased or not)?

The log standard deviation is a good scale on which to work, except in cases where estimates of variance components can reasonably be zero.

I may not be able to post a link to the slides I mentioned today but will do so tomorrow at the latest.
 
On Wednesday, August 27, 2014 9:04:03 AM UTC-5, Douglas Bates wrote:
On Tuesday, August 26, 2014 8:44:30 PM UTC-5, Thomas Covert wrote:
I have become a huge fan of MixedModels - its much faster than STATA's xtreg, which is great.  

I'm glad you are enjoying using it.  I'm open to receiving suggestions or success stories, either as issues in the repository or by email, as I am writing a follow up paper to <a href="http://arxiv.org/abs/1406.5823" target="_blank" onmousedown="this.href='http://www.google.com/url?q\75http%3A%2F%2Farxiv.org%2Fabs%2F1406.5823\46sa\75D\46sntz\0751\46usg\75AFQjCNHg4YiNxmH9hRn8TcL5ch6RaGYCkA';return true;" onclick="this.href='http://www.google.com/url?q\75http%3A%2F%2Farxiv.org%2Fabs%2F1406.5823\46sa\75D\46sntz\0751\46usg\75AFQjCNHg4YiNxmH9hRn8TcL5ch6RaGYCkA';return true;">arxiv.org/abs/1406.5823 to describe the methods in the MixedModels package.  
 
However, I can't figure out how to get it to show me the standard error of the estimate of the variance of the random effects  Is this intentional?

Yes.
 
As far as I can tell, this is a well defined object, and STATA's xtreg does report it when the maximum likelihood routine is chosen.

Well-defined, perhaps but also misleading at best and totally meaningless at worst.  A standard error is the estimated standard deviation of the estimator and represents an interesting quantity if the distribution of the estimator is close to Gaussian or at least symmetric.  The distribution of a variance estimator is not symmetric - it is highly skewed.  In the simplest case, estimating the variance given an i.i.d. sample from a Gaussian distribution, the distribution of the estimator is a chi-square, which can be very skew.

This is also the reason that the desirability of REML estimates, which are touted as being unbiased estimators of variance components or at least less biased than ML estimates, is questionable.  Bias is related to the mean of the estimator yet the mean of a skewed distribution is not a good way of summarizing a typical value.

I have a couple of presentations related to this that I will post a link to when I get to the office.

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