Robust Likelihood Inference for Correlated Mixed Type Data(2/2)

Amongst various methods for analyzing mixed correlated data, latent variables, location model, and Copula are frequently adopted. However, once model assumptions are incorrect, Copula not only faces the problems of giving inconsistent maximum likelihood parameter estimates, the estimation of the association parameter in Copula can be very much unstable. This makes application of Copula in real data analysis quite questionable. The performance of latent variables method and location model in terms of robustness under model misspecification are rarely studied. That is, how sensitive is the validity of inference derived from latent variables method and location model, when, in fact, data distributions do not conform to the model assumptions? There are several univariate distributions, including gamma, Poisson, normal, negative binomial and binomials that can be robustified under model misspecification. The objectives of this research project includes 1.When any of the above univariate distributions that can be robustified are adopted as part of the latent variables method/location model, will the property of robustness be reserved?2.If that is the case, can the latent variables/location model be robustified to deliver legitimate likelihood inference? How do the adjusted robust likelihood derived from the latent variables/location model compare to the robust likelihood derived from the independence working model approach that my researches in recently years are most devoted to?3.If that is not the case, what contributes to the problem and any possible remedies?We will focus our research on data of mixing types, such as correlated (count, continuous), (nominal, continuous), (count, nominal) data. These data types are certainly the scenarios that latent variables method, location model and Copula are most popular.