An Expert Model Selection Approach to Determine the “Best” Pattern Structure in Factor Analysis Models

This paper introduces and develops an expert data-analytic model selection approach based on Akaike’s Information Criterion (AIC) and asymptotically Consistent Akaike’s Information Criterion (CAIC), to choose the number of factors, m, and to determine the “best” factor pattern structure among all possible patterns under the orthogonal factor model using Mallows’ Cp Criterion.A subset selection procedure is carried out using a “leaps and bounds” algorithm to interpret the complex interrelationships between the best fitting number of factors and the original variables.The new approach presented in this paper tries to unify both the exploratory and confirmatory factor analysis to find “the best fitting simple structure for the best m-factor model” in one expert statistical system.Numerical examples are provided to show how to achieve flexibility in modeling and to demonstrate the efficiency of this procedure.