Title a Parallel Analysis with Polychoric Correlation Matrices

Description The Function performs a parallel analysis using simulated polychoric correlation matrices. The nth-percentile of the eigenvalues distribution obtained from both the randomly generated and the real data polychoric correlation matrices is returned. A plot comparing the two types of eigenvalues (real and simulated) will help determine the number of real eigenvalues that outperform random data. The function is based on the idea that if real data are non-normal and the polychoric correlation matrix is needed to perform a Factor Analysis, then the Parallel Analysis method used to choose a non-random number of factors should also be based on randomly generated polychoric correlation matrices and not on Pearson correlation matrices. Version 1.1.1, fixed a minor bug in the regarding the estimated time needed to complete the simulation. Also in this version, the function is now able to manage supplied data.matrix in which variables representing factors (i.e.,variables with ordered categories) are present and may cause an error when the Pearson correlation matrix is calculated. Version 1.1.2 simply has updated the function that calculates the polycoric correlation matrix due to changes in the psych() package. Version 1.1.3 tackles two problems signalled by users: 1) the possibility to make available the results of simulation for plotting them in other softwares. Now the random.polychor.pa will show, upon request, all the data used in the scree-plot. 2) The function polichoric() of the psych() package does not handle data matrices that include 0 as possible category and will cause the function to stop with