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# How to show degrees of feedom for random components of a mixed model

How do I show the degrees of freedom for random components of a mixed model in proc mixed?

Is there a way to show them in the table of the output of the covariance parameter estimates? Does anyone know????

Thanks a lot

Antoine

Here is my syntax:

proc mixed data = work.import method=reml;
class ID A B C D E;
model outcome = A B C D A*B /s ddfm = kr;
random intercept A B E  / subject = ID v = 1;

run;
repeated / subject = ID r = 1;
run;

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‎12-22-2015 05:07 PM
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Posts: 684

## Re: How to show degrees of feedom for random components of a mixed model

There are no degrees of freedom for an estimated variance or covariance based on likelihood (restricted likelihood) analysis. That's the short answer. It can be more complicated (for different purposes). An estimated variance asymptotically has a normal distribution (i.e., a t distribution with infinite df). But asymptotic results kick in here only for VERY large sample size. It is rare that one can rely on large-sample theory to use the normal approximation (although you can request this with a COVTEST statement in GLIMMIX). One can also test an estimated variance based on a likelihood ratio test. This still relies on asymptotic theory, but simulations generally show that one can use this approach at much smaller and more reasonable sample sizes. If you have one variance term (in addition to a residual), you can use:

COVTEST 0;

to test for the equality of the variance to 0. The df nominally is 1 for this (basically 1 for the numerator df and infinity for the denominator df), and a chi-squared test statistic (with 1 df) is used. However, for certain common situations, other work shows that the test statistic is more complicated than that, being a mixture of two chi-squared distributions (with 1 df and 0 df for the two components). The COVTEST statement figures this out automatically.

Anyway, I go back to the start of the message. I would not report any df for your estimated variances.

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Solution
‎12-22-2015 05:07 PM
Valued Guide
Posts: 684

## Re: How to show degrees of feedom for random components of a mixed model

There are no degrees of freedom for an estimated variance or covariance based on likelihood (restricted likelihood) analysis. That's the short answer. It can be more complicated (for different purposes). An estimated variance asymptotically has a normal distribution (i.e., a t distribution with infinite df). But asymptotic results kick in here only for VERY large sample size. It is rare that one can rely on large-sample theory to use the normal approximation (although you can request this with a COVTEST statement in GLIMMIX). One can also test an estimated variance based on a likelihood ratio test. This still relies on asymptotic theory, but simulations generally show that one can use this approach at much smaller and more reasonable sample sizes. If you have one variance term (in addition to a residual), you can use:

COVTEST 0;

to test for the equality of the variance to 0. The df nominally is 1 for this (basically 1 for the numerator df and infinity for the denominator df), and a chi-squared test statistic (with 1 df) is used. However, for certain common situations, other work shows that the test statistic is more complicated than that, being a mixture of two chi-squared distributions (with 1 df and 0 df for the two components). The COVTEST statement figures this out automatically.

Anyway, I go back to the start of the message. I would not report any df for your estimated variances.

New Contributor
Posts: 2

## Re: How to show degrees of feedom for random components of a mixed model

Thank you very much for your support in helping me. I think your answer is very clear !

Regards

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