| Latent variable models (LVMs) have been applied extensively to the behavioral, medical and social sciences for studying inter-relationships among manifest and latent variables. To cope with the strong demand for models to deal with more complex data in various fields, more sophisticated models have been developed recently. So far, the statistical developments of these LVMs are mainly on estimation. The key idea in the estimation is to treat the latent variables in the model as hypothetical missing data and reformulate the problem as a missing data problem, then the powerful EM algorithm can be applied to obtain the maximum likelihood estimates of the parameters in the model.;An important statistical analysis beyond estimation is on detecting outliers and influential observations of the data set. Since the pioneer work of Cook (1977, 1986), this topic has attracted much attention in applied statistics. However, due to the intractable integrals involved in the observed-data likelihood function associated with the complex LVMs, Cook's approaches cannot be directly applied to obtain the diagnostic measures. The main objective of this thesis is to develop efficient procedures for solving this problem. In the context of the EM algorithm in estimation, we will develop the diagnostic measures on the basis of the conditional expectation of the complete-data likelihood function at the E-step with the latent variables in the LVMs treated as hypothetical missing data. Formulas for achieving the diagnostic measures and the bench mark are derived. The Gibbs sampler and the Metropolis-Hastings (MH) algorithm are implemented to simulate observations from the conditional distributions for evaluating the building blocks of the diagnostic measures. Several complex LVMs will be considered, these include the factor analysis with continuous and ordinal categorical variables, full item factor analysis model, and nonlinear mixed models. The newly developed methodology is illustrated with simulations and real examples. |
