Post-hoc Rasch analysis of optimal categorization of an ordered-response scale.

The purpose of this study was to determine the optimal categorization of a self-efficacy ordered-response scale using the Rasch analysis and compare the performance of the Rasch statistics and parameter estimates with conventional statistics. A 50-item scale to measure psychomotor self-efficacy was administered to a total of 2,022 children, including 1,009 boys and 1,013 girls. The data analysis started by collapsing the original five adjacent categories into two, three, and four categories, and a total of 14 data sets were derived. Each of these data sets, including the original one, was analyzed using the Rasch rating scale model, and a set of Rasch model-data fit, category, and separation statistics and parameter estimates, as well as three conventional statistics, were computed and compared. It was found that, instead of the five-category construct designed, the best order of category meanings of the scale in respondents' perceptions was a three-category construct. The Rasch threshold estimates were sensitive indexes in determining the order of the categorization, and that item separation statistics were useful in determining the optimal categorization after its order was confirmed. The commonly used coefficient alpha was found not helpful at all in determining the optimal categorization. The Rasch analysis was demonstrated to be a useful post-hoc analytic approach in determining the optimal categorization of an ordered-response scale.