Can someone please help me with a multilevel modeling question? I've gotten conflicting advice from colleagues, so I thought I'd ask the experts here...

I'm estimating a mixed effects logit model with several variables, trying to determine which should have random slopes. The command I'm using has the form:

melogit Y X1 X2 || group: X1 X2

X1 appears to have a significant effect on Y, but X2 does not.

The random effects portion of my output looks like this:


| Coef. Std. Err. [95% Conf. Interval]
-----------------+----------------------------------------------------------------
group |
var(X1) | .031886 .0129037 .0144256 .07048
var(X2) | 1.981478 1.375139 .5084618 7.721827
var(_cons) | 1.588888 .6971545 .6723764 3.754689
----------------------------------------------------------------------------------
LR test vs. logistic model: chi2(3) = 461.64 Prob > chi2 = 0.0000

One colleague tells me that the random slope on X2 is not necessary, since the variance looks insignificant (and the variable's effect on Y is insignificant). Another colleague tells me a likelihood ratio test is actually necessary for random slopes. So I tested the model with X1 and X2 random slopes against a smaller model with a random slope on X1 only. (FWIW, X2's effect on Y is insignificant in the simpler model too.)

The LR test result (Prob > chi2 = 0.0003) suggests that the random slope on X2 is preferred, even though the variance LOOKED insignificant based on the larger model's output shown above.

Whose advice do I believe? Do I report the model with random slopes on X1 and X2 or the model with a random slope on X1 only? (And is there a source I can cite to explain this decision to reviewers?)

Thanks!

Joe