We used principal component extraction and a direct oblimin rotation, with the number of factors　based on eigenvalues greater than 1.00. Four factors met this criterion (eigenvalues = 4.12, 1.53, 1.36, and 1.07), accounting　for a total of 62.0% variance (32%, 12%, 10%, and 8%,　respectively). However, based on a parallel analysis procedure　(variables = 13, participants = 131, replications = 100;

Glorfeld, 1995;Watkins, 2000), generated eigenvalues justified　examination of only the initial three factors (random　eigenvalue Number 1 = 1.57, Number 2 = 1.41, Number 3 =　1.31, and Number 4 = 1.20).



我的问题：

1。parallel analysis procedure分析后特征值大于1的也是4个，文献里却取3个，为什么？

2。我使用MonteCarloPA.exe程序计算(variables = 13, participants = 131, replications = 100）的结果与文献里(random　eigenvalue Number 1 = 1.57, Number 2 = 1.41, Number 3 =1.31, and Number 4 = 1.20)是一致的。这里为什么要取replications的值为100？初始样本数为131。
6 天 后
http://epm.sagepub.com/cgi/content/abstract/55/3/377

Educational and Psychological Measurement, Vol. 55, No. 3, 377-393 (1995)

DOI: 10.1177/0013164495055003002

© 1995 SAGE Publications



An Improvement on Horn's Parallel Analysis Methodology for Selecting the Correct Number of Factors to Retain

Louis W. Glorfeld

University of Arkansas



One of the most important decisions that can be made in the use of factor analysis is the number of factors to retain. Numerous studies have consistently shown that Horn's parallel analysis is the most nearly accurate methodology for determining the number of factors to retain in an exploratory factor analysis. Although Horn's procedure is relatively accurate, it still tends to error in the direction of indicating the retention of one or two more factors than is actually warranted or of retaining poorly defined factors. A modification of Horn's parallel analysis based on Monte Carlo simulation of the null distributions of the eigenvalues generated from a population correlation identity matrix is introduced. This modification allows identification of any desired upper 1 - a percentile, such as the 95th percentile of this set of distributions. The 1 - ax percentile then can be used to determine whether an eigenvalue is larger than what could be expected by chance. Horn based his original procedure on the average eigenvalues derived from this set of distributions. The modified procedure reduces the tendency of the parallel analysis methodology to overextract. An example is provided that demonstrates this capability. A demonstration is also given that indicates that the parallel analysis procedure and its modification are insensitive to the distributional characteristics of the data used to generate the eigenvalue distributions.
Monte Carlo PCA for Parallel Analysis description

http://www.softpedia.com/get/Others/Home-Education/Monte-Carlo-PCA-for-Parallel-Analysis.shtml

Monte Carlo PCA for Parallel Analysis computes Parallel Analysis criteria (eigenvalues) by performing a Monte Carlo simulation

Monte Carlo PCA for Parallel Analysis is a standalone Windows program that computes Parallel Analysis criteria (eigenvalues) by performing a Monte Carlo simulation. The user can specify 50-2500 subjects, 3-300 variables and 1-1000 replications.



Select the number of variables (3-300), subjects (100-2500), and replications (1-1000). The program then: (1) generates random normal numbers for the quantity of variables and subjects selected, (2) computes the correlation matrix, (3) performs Principal Components Analyses and calculates the eigenvalues for those variables, (4) repeats the process as many times as specified in the replications field, and (5) calculates the average and standard deviation of the eigenvalues across all replications.



For stable results, replicate at least 50-100 times. Use these eigenvalues as the criteria for Horn's Parallel Analysis for the number of factors or components to retain for rotation.