Performance of Velicer's Minimum Average Partial Factor Retention Method With Categorical Variables

Despite strong evidence supporting the use of Velicer's minimum average partial (MAP) method to establish the dimensionality of continuous variables, little is known about its performance with categorical data. Seeking to fill this void, the current study takes an in-depth look at the performance of the MAP procedure in the presence of ordinal-level measurement. Using Monte Carlo methods, seven factors related to the data (sample size, factor loading, number of variables per factor, number of factors, factor correlation, number of response categories, and skewness) as well as two factors related to the MAP method (type of correlation matrix and power) were systematically manipulated. The results indicate that using polychoric correlations and the squared partial correlations leads to considerably more accurate estimations than using Pearson correlations and/or raising the partial correlations to the fourth power. Additionally, the MAP method is shown to be a biased estimator of dimensionality in two conditions: (a) for low factor loadings (.40) and (b) for medium factor loadings (.55) and a small number of variables per factor (<= 6). The applicability of this method with categorical variables is discussed in the context of these findings.