p-values for standard deviation of the random coefficients in a mixed logic model missing

[Peter Tsigaris]

Hi all

I ran the following mixed logic model

cmmixlogit OS3 North Central South Mod Maj ASC0 ASC0Concern ASC0R ASC0U ASC0MI ASC0HI, ///
rand(A1 Biol TG) noconstant vce(robust)

I get results but for the sd(A1), sd(Biol) and sd(TG) the output provides their coefficient, their standard error and the 95% CI but does not report the p-values. Also the standard errors are greater than the coefficient, but the 95% CI does not include zero.....
See below. Any help would be appreciated.

[Peter Tsigaris]

sorry logit!

[Clyde Schechter]

There is no p-value provided because the null hypothesis that this would test, that the variance component is zero, cannot be tested for in that way (and is basically not meaningful anyway).

Variance components are, by definition, non-negative. Zero is an edge case, and one which rarely, if ever, occurs in real life. As such testing a hypothesis that a variance component equals 0 is rarely sensible--in almost every situation we know a priori that it is not zero. Moreover, even where it might make sense to do that, you cannot do it with the usual Wald z = b/se test, because the estimates do not have anything like a normal sampling distribution. Rather, the sampling distribution is a mixture of chi square distributions, and it is not characterized by a simple statistic like z (or t). If you want to test that hypothesis, you must instead run the model both with and without the variance component included and then perform a likelihood ratio test contrasting the two models.

The confidence intervals, similarly, do not include zero even though the standard error is larger than the estimate because, again due to the non-normal sampling distribution of estimated variance components, the usual normal-theory confidence interval calculation is not applicable here. A different method, the details of which I don't know off hand, is used, one that provides the nominal coverage level.

[Peter Tsigaris]

Thanks a million Clyde! So resourceful! Thank you thank you thank you thank you thank you thank you!