Bayesian Analysis for Parameters of Multivariate tFA model with Simulation

Abstract

In many kinds of pollution, such as economic and environmental pollution, the researchers use the normal linear model to present their data studies. That selection may be inaccurate because the data of those studies do not vacate from outlier observations, which have great effect on the estimation problem even if they are processed or removed from the sample study. These processes lead to facts defacement to the decision maker. For that reason, the non-normal linear models has been found out to combat that matter. That error term in these models belongs to the family of probability distributions which resist outliers, for example, the multivariate distributions. The factor analysis model belongs to the family of linear models and because the multivariate data sets do not vacate outliers .For this reason this paper is concerned with studying the t factor analysis model. The model analyzed by Bayesian technique in which the common factors are treated as fixed and random variables . We supposed that all parameters of both two models were unknown and their prior distributions belong to conjugate families. The number of extracted factors in factor analysis models cannot be determined a prior .On this foundation, in Bayesian analysis, these factors are treated as random variables. We obtained a posterior probability criterion to choose the number of extracted factors for the two models. We choose the number of factors in which they must be entered, and the model which they have maximum posterior probability. All results that we concluded were applied to empirical data sets which are generated by simulation in two different sample sizes (n=50,100) at different values of the degrees of freedom for the distribution of the error term. Also, we selected different forms of factor loading matrix and variance matrix of error term. Matlab (7.9) language is used in data generation and analysis.