An Analysis of Factor Extraction Strategies: A Comparison of the Relative Strengths of Principal Axis, Ordinary Least Squares, and Maximum Likelihood in Research Contexts that Include both Categorical and Continuous Variables

Abstract

This study is intended to provide researchers with empirically derived guidelines for conducting factor analytic studies in research contexts that include dichotomous and continuous levels of measurement. This study is based on the hypotheses that ordinary least squares (OLS) factor analysis will yield more accurate parameter estimates than maximum likelihood (ML) and principal axis factor anlaysis (PAF); the level of improvement in estimates will be related to the proportion of observed variables that are dichotomized and the strength of communalities within the data sets.\nTo achieve this study's objective, maximum likelihood, ordinary least squares, and principal axis factor extraction models were subjected to various research contexts. A Monte Carlo method was used to simulate data under 540 different conditions; specifically, this study is a four (sample size) by three (number of variables) by three (initial communality levels) by three (number of common factors) by five (ratios of categorical to continuous variables) design. Factor loading matrices derived through the tested factor extraction methods were evaluated through four measures of factor pattern agreement and three measures of congruence.\nTo varying degrees, all of the design factors, as main effects, yielded significant differences in measures of factor loading sensitivity, agreement between sample and population, and congruence. However, in all cases, the main effects were components of interactions that yielded differences in values of these measures that were at least medium in effect size. The number of factors imbedded in the population was a component in six interactions that resulted in medium effect size differences in measures of agreement between population and sample factor loading matrices. of factor loading sensitivity, general pattern agreement, per element agreement, congruence, factor score correlations, and factor loading bias; in terms of the number of interactions that yielded at least medium effect size differences in measures of sensitivity, agreement, and congruence. The number of factors design factor exerted a larger influence than any of the other design factors. The level of communality interacted with the number of factors, number of observed variables, and sample size main effects to yield at least medium effect size differences in factor loading sensitivity, general pattern agreement, per element agreement, congruence, factor score correlations, factor loading bias, and RMSE; in terms of the number of factors that included communality as a component, this design factor exerted the second largest amount of influence on the measures of sensitivity, agreement, and congruence. The level of dichotomization, sample size, and number of observed variables were included in smaller numbers of interactions; however, these interactions yielded differences in all of the outcome variables that were at least medium in effect size.\nAcross the majority of interactions among the manipulated research contexts, the ordinary least squares factor extraction method yielded factor loading matrices that were in better agreement with the population than either the maximum likelihood or the principal axis methods. In three of the four measures of congruence, the ordinary least squares method yielded factor loading matrices that exhibited less bias and error than the other two tested factor extraction methods. In general, the ordinary least squares method yielded factor loading matrices that correlated more strongly with the population than either of the other two tested methods.\nThe suggested use of ordinary least squares factor analytic techniques represents the major, empirically derived recommendation derived from the results of this study. In all tested conditions, the ordinary least squares factor extraction method identified common factors with a high degree of efficacy. Suggested studies for future would incorporate the limiting constraints associated with this dissertation into methodological studies to extend the generalizability of conclusions and recommendations into areas that are beyond the scope of this dissertation.

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