Using Predetermined Factor Structures to Simulate a Variety of Data Conditions

This paper presents a method through which data sets of varying characteristics can be simulated based on predetermined, uncorrelated factor structures. As demonstrated in a series of studies, this Monte Carlo method yields factor structures that are clear and simple. The process begins with the application of conceptual and actual factor loadings to the creation of correlation matrices; samples are then generated based on these correlation matrices. The method for generating correlation matrices allows the researcher to manipulate the number of observed variables, the communality among variables, and the number of common factors. The process for simulating samples of observations provides additional options for specifying sample size and level of measurement. This paper includes an example of the process for generating a correlation matrix and a distribution of simulated observations. This paper is intended for researchers that are interested in factor analytic designs and are familiar with PROC IML.