Parallel analysis with unidimensional binary data

The present simulation investigated the performance of parallel analysis for unidimensional binary data. Single-factor models with 8 and 20 indicators were examined, and sample size (50, 100, 200, 500, and 1,000), factor loading (.45, .70, and .90), response ratio on two categories (50/50, 60/40, 70/30, 80/20, and 90/10), and types of correlation coefficients (phi and tetrachoric correlations) were manipulated. The results indicated that parallel analysis performed well in identifying the number of factors. The performance improved as factor loading and sample size increased and as the percentages of responses on two categories became close. Using the 95th and 99th percentiles of the random data eigenvalues as the criteria for comparison in parallel analysis yielded higher correct rate than using mean eigenvalues.