On the number of factors to retain in exploratory factor analysis for ordered categorical data.

Conducting exploratory factor analysis (EFA) using statistical extraction methods has been recommended, but little is known about the accuracy of the decisions regarding the number of factors to retain for ordered categorical item data by considering a chi-square test, fit indices, and conventional criteria, such as eigenvalue >1 and parallel analysis. With computer-generated data, the authors examined the accuracy of decisions regarding the number of factors to retain for categorical item data, by combining these pieces of information using weighted least-square with mean and variance adjustment estimation methods based on polychoric correlations. A chi-square difference test was also conducted to compare nested EFA models. The results showed that the eigenvalue >1 criterion resulted in too many factors, in general. The chi-square test, chi-square difference test, fit indices, and parallel analysis performed reasonably well when the number of scale points was four, the number of items was 24, the sample size was at least 200, and the categorical distributions were similar across items. However, parallel analysis had a tendency toward factor underextraction when the correlation among factors was .50, particularly for two-point and 12-item scales.