Linear factor analysis models used to examine constructs underlying the responses are not very suitable for dichotomous or polytomous response formats. The associated problems cannot be eliminated by polychoric or tetrachoric correlations in place of the Pearson correlation. Therefore, we considered parameters obtained from the NOHARM and FACTOR programs (which use parametric methods) and from the DETECT and DIMTEST programs (which use nonparametric methods) for different sample sizes of a real large dataset (50, 80, 100, 160, 200, 300, 500, 1000, 3000, 5000). A parallel analysis (PA) based on the tetrachoric correlation with the FACTOR program produced inconsistent results among the sampling sizes. However, the analyses based on the Pearson correlation could not adequately determine the dimension numbers. Although DETECT and NOHARM determined the multidimensionality at acceptable level for the 50 sample size, they yielded the most consistent results at sample sizes of 1000 and above.