obtaining standard errors (and confidence intervals) for predicted probabilities from a multilevel logistic model

[Ariel Beccia]

Hello,

I am trying to obtain standard errors (to be used in calculating 95% CIs) for group-level predicted probabilities generated from a multilevel logistic model. For context, I have individuals at level 1 nested within groups at level 2, and I am using the "xtmelogit" command. I first fit the model and use "predict" to get the level 2 residuals for each group and their standard errors:

xtmelogit outcome cov1 cov2 || group:, variance 
predict u0, reffects
predict u0se, reses
egen pickone = tag(iig)

I then use "predict" to get the predicted probabilities. Specifically, I am calculating the predicted probability for each group first based on the fixed effects and random effects:

p_total = logit^-1(beta0 + beta1(cov1) + beta2(cov2) + u)

And then looking to "decompose" this into the part due to just the fixed effects:

p_fixed = logit^-1(beta0 + beta1(cov1) + beta2(cov2))

And obtaining the part due to the random effects through subtraction:

p_random = p_total - p_fixed

predict p_total, mu 
predict p_fixed, mu fixedonly
generate p_random = p_total - p_fixed
list group p_total p_fixed p_random if pickone==1

I know that predict [newvar] stdp calculates the standard error of the linear prediction; however, is it possible to calculate the standard error for my three predicted values (p_total, p_fixed, and p_random)? Thank you very much!

[Jen He]

Hi Ariel,

I am wondering if you have figured this out. I am doing a similar computation.