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

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.