Effect of the Number of Scale Points on Chi-Square Fit Indices in Confirmatory Factor Analysis

This article investigates the effect of the number of item response categories on chi-square statistics for confirmatory factor analysis to assess whether a greater number of categories increases the likelihood of identifying spurious factors, as previous research had concluded. Four types of continuous single-factor data were simulated for a 20-item test: (a) uniform for all items, (b) symmetric unimodal for all items, (c) negatively skewed for all items, or (d) negatively skewed for 10 items and positively skewed for 10 items. For each of the 4 types of distributions, item responses were divided to yield item scores with 2,4, or 6 categories. The results indicated that the chi-square statistic for evaluating a single-factor model was most inflated (suggesting spurious factors) for 2-category responses and became less inflated as the number of categories increased. However, the Satorra-Bentler scaled chi-square tended not to be inflated even for 2-category responses, except if the continuous item data had both negatively and positively skewed distributions.