st: predicted probabilities for three-way interaction in xtmelogit

[Ola Sjöberg <Ola.Sjoberg@sofi.su.se>]

Dear Members,

I am trying to calculate predicted probabilities that include random effects in xtmelogit. 
I am estimating a simple random intercepts model. In this model I have a three-way cross-level interaction term, education*GDP*Generosity, where:
Education=level-one variable (separating between low- and high educated)
GDP=level-2 variable (continuous)
Generosity=level-2 variable (continuous)
Dependent variable is health (1=good health, 0=bad health)

So, I am trying to estimate the model: xtmelogit health i.education##c.GDP##c.Generosity

I would like to get predicted probabilities for having good health for low- and high educated, along the observed values for Generosity, and for three levels of GDP (low, medium and high)

Thanks to the excellent Stata FAQ "How can I estimate probabilities that include the random effects in xtmelogit". I can get predicted probabilities that include random effects, but only for two-way interaction effects, and not my three-way interaction effect. 

I am using the following syntax, which is working fine for  estimating probabilities along the variable generosity (values=100, 120, 140 etc). But now I would like to see how these selected probabilities vary for three values of GDP (=50, 100, 150)
Basically, as I understand I would like to get  second variable in there (j=50(50)100, but I can't get it to work:

xtmelogit health i.education##c.GDP##generosity || group:

predict mu1, mu

predict re*, reffects  


forvalues i=100(20)220 {
   quietly replace generosity = `i'
   quietly replace education = 1  
   predict xbm`i' , xb
   gen mum`i' = 1 /(1+exp(-1*(xbm`i' + re1))) 
   quietly replace education = 2  
   predict xbf`i' , xb
   gen muf`i' = 1 /(1+exp(-1*(xbf`i' + re1))) 
   }

sum mum* muf*



Thanks!
Ola, Stockholm university




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