statistical Significance of the variance of the slope

[Shir Caller]

Hello Statalisters,
I have a multi-level model with random intercept and random slope (I'm using Stata 13).
I am trying to understand how can I know if the variance of the slope is statistically significant.

the command is:

xi: xtmelogit racist i.academic_education || cntry_numeric: i.academic_education , var mle or

here is the output of the analysis.

the estimates is 0.1022796. how can know if it's has statistical significance?

Thank you very much,
Shir

[Bruce Weaver]

The 95% CI for the variance of the random slopes does not include a value of 0. Therefore, you know that the variance estimate is significantly different from 0 at the .05 level. If you really need the p-value for some reason, you can compute the z-test yourself, as follows:

local z = .1022796/.0381247 // estimate / SE
local p = (1-abs(normal(`z')))*2
display "z = " `z' "   p = " `p'

Given that this a test on a variance, you probably don't need the abs() part of that second line (because variance estimates ought to be positive). But in general (when the estimate could be negative), it's safer.

Finally, bear in mind that nowadays, some folks (including the American Statistical Association) reckon we ought to stop using terms like statistically significant. (I thought I should mention that to spare Clyde having to do it.) ;-)

[Jackson Monroe]

My perspective would be that the question is wrong. No effect (or maybe very few) is exactly uniform across groups, the variance is never (very rarely) zero. I think a model comparison a la AIC BIC LOO etc. might be more informative, because I'm pretty sure (more than 95% let's say) that your slope has positive variance.

[Erik Ruzek]

Agreed with Jackson. You can run a likelihood ratio test comparing a mixed model without the random slope to one with the random slope. If you request it as an option, the lrtest will give you AIC and BIC -

lrtest m1 m2, stats

.

Edit: Unless you have a strong reason not to, you should allow the random slope and random intercept to covary.

 xtmelogit racist i.academic_education || cntry_numeric: academic_education , cov(unstructured) var mle or