The aim of the paper was investigating if the factor can be well identified by using the parallel analysis (PA) on 2-point unidimensional IRT items. In simulation study, 8 and 20 items, the slope parameter, location of item, and the form of correlation matrix were four independent variables. The phi and tetrachoric correlations were both used because all the indicators were dichotomous. The random data were generated 1000. The total replication of experiments was 500. Note that there is no non-Gramian matrix was obtained when sample size is 500 or 1000.
Overall, the factor loading had the greatest impact on PA. Sample size affected the PA on phi correlation and location of items affected the PA on tetrachoric correlation. Results also shows that the larger sample size, higher factor loading, and the closer the proportions responding to two categories would result in good performance of PA. And the 95th- or 99th-percentile criteria yielded good results than mean criterion.
1、It based on factor analysis, so it is a model-based approach. By the way, it analyzed the data generated from the true model.
2、It is restricted to dominance model, so the linear factor analysis is a good choice.
3、A appropriate method for analyzing dominance model and unfolding model have to be proposed before PA is used.