The Extensions Of Two Multivariate Statistical Models And The Local Influence

Multinomial probit and multivariate probit model are two important statistical models that have been applied in many fields, such as in econometrics, biostatistics, transportaion studies, psychics, medicine and behavior science. In the past decades, many authors have studied the two models, and made them advanced. For example, MNPFA and MPCFA models were extended models by incorporating factor analysis.This paper is devoted to extending the two multivariate statistical models and implementing local influence analysis of them, and the EM algorithm is used to estimate parameters of the two models based on maximum likelihood estimates. In chapter 2, we consider local influence analysis, which is well-recognized important step of data analysis, of MNPFA model based on the theory of statistical diagnosis. Then we can obtain assessment of local influence in minor perturbations of the statistical model. The assessment of local influence of MNPFA models is illustrated by numerical simulations, and the results show that the proposed method is feasible and stable. For fitting samples with long tails, in chapter 3 we extend MNPFA model by assuming t-distribution error in probit factor analysis. The MCECM algorithm is used to estimate parameters of the proposed models. The methodology is illustrated with numerical simulations. In chapter 4, we propose MPCFA with t-distribution error and make MPCFA model applied more widely.