Determining the Number of Principal Components: A Comparison of Two Methods

The accuracy and variability of ten methods which determine the number of components to retain in a principal components analysis were examined. The methods consisted of three variations of the minimum average partial correlation method, six variations of parallel analysis, and the eigenvalue greater-than-one rule. The methods were investigated under different levels of five factors: sample size, component saturation, number of variables, number of variables per component, and the presence of unique items. The eigenvalue-greater-than-one rule was the least accurate and most variable of all the methods. In every combination of the five factors, this method overestimated the number of components to retain. Both the parallel analysis method and the minimum average partial correlation method were found to be extremely accurate across a variety of combinations of the five factors. Alternate ways of implementing these two methods were found to be more accurate and less variable than the original version proposed for each method. Component saturation and the number of variables per component were found to have the greatest effect upon the accuracy of all the methods. Higher saturation and more variables per component resulted in greater accuracy and less variability. Fewer variables also resulted in greater accuracy across all methods. The effect for sample size and unique items was not as notable or consistent across all methods