Joint modeling of multiple longitudinal responses enables us to account for the association between them and is thus more efficient than seperate analyses. Most existing techniques to handle this problem are based on the assumptions of normality of the responses and linearity of the mean functions. However, non-normality of responses and non-linear shape of their mean functions often arise from medical and population growth studies. For example, it is desirable to investigate the nonlinear mean structures in the analysis of the effect of different drug formulations while accounting for their association in Pharmaco-dynamics (the study of what the drug does to the body). We propose to model data of mixed types jointly by incorporating both subject-specific and time-specific random effects into Tweedie nonlinear models. An optimal estimation procedure for our model has been developed using the orthodox best linear unbiased predictors of the random effects. This approach allows us to model multiple non-normal longitudinal responses with interpretable parameters.
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