Testing variance components across equations

[philipplersch]

Hi everyone,

We want to compare the random components across equations in a multi-equation model for observations nested within persons. We estimate the multilevel model with several equations using runmlwin with MLwiN 2.36 in Stata 14.1. The code is:

runmlwin (y1 x cons , eq(1)) ///
(y2 x cons , eq(2)) ///
(y3 x cons , eq(3)) , ///
level1(observation_id: (cons, eq(1)) (cons, eq(2)) (cons, eq(3)) ,diagonal) ///
level2(person_id: (cons x, eq(1)) (cons x, eq(2)) (cons x, eq(3)) ,diagonal) ///
nopause

We are interested in comparing the variances in slopes and intercepts across the three equations. We use Stata's test command to do so. For example, after estimating above model we run:

test [RP2]var(cons_1)=[RP2]var(cons_2)

Now the question is whether this is appropriate? Can we use a Wald test to examine whether the variances differ significantly? If not, what would be an approporiate approach?

Thank you!
Philipp

[GeorgeLeckie]

Hi Phillipe,

Wald tests are frowned upon when testing whether variance components are significant as variances do not have normal sampling distributions. For this reason, likelihood ratio tests are generally preferred in this setting.

In your case you are interested in testing whether the difference between two variances is significant. This will in general be less problematic and so the Wald test showed in general perform better than the first scenario. However, it would be prudent to still compare the resulting p-value with that resulting from a likelihood ratio test to compare the current model to one where you have constrained the two variances to be equal.

Best wishes

George

[philipplersch]

Thanks, George. That is helpful.