and Sik-Yum Lee
The Chinese University of Hong Kong and 
Zhongshan University
Abstract: A latent variable model is proposed to analyze two-level data with hierarchical structure and mixed continuous and polytomous data that are very common in behavioral, biomedical and social research. On the basis of an EM algorithm associated with the maximum likelihood estimation of the model, a method is developed for assessing local influence of minor perturbation for the proposed latent variable model. The key idea of the development is to derive diagnostic measures on the basis of the conditional expectation of the complete-data log-likelihood function in the E-step of the EM algorithm. Building blocks in the diagnostic measures are computed via observations generated by the Gibbs sampler. It is shown that the proposed method is computationally efficient and feasible for a wide variety of perturbations that carry clear interpretation. The approach is illustrated by a two-level data set concerning the development and findings from an AIDS preventive intervention of Filipino commercial sex workers.
Key words and phrases: Benchmark, conditional expectation, Gibbs sampler, MCEM algorithm, perturbation.