A problem on generalized mixed linear model

[milanxiaoyao]

Hi all. 

Recently I've got a tricky problem on estimating the generalized mixed linear model. I hope I could get some suggestions here. Since the problem involves many mathematical formulas, I have put them in the word docomument in the attachment. Please check it. 

Many thanks

[milanxiaoyao]

I think such model can be called as mixed outcome data models.  Looking forward to your answer~~~~~~~~