Factor analysis is a deceptively difficult technique to conduct appropriately. Many researchers undertake factor analysis without eliminating unsuitable items in advance. This omission can complicate the outcome and hence obscure the discovery of interesting factors. This document addresses the procedures that should be completed before executing a factor analysis.
Prior to conducting a factor analysis, the researcher must ensure that all unsuitable items are removed. Three classes of unsuitable items can be distinguished.
The remainder of this document describes how to identify these items.
To some extent, each class of items can be discerned from the correlation matrix. To generate the correlation matrix in the factor analysis program, press "Descriptives" and tick "Coefficients". This process will present a correlation matrix in the output of factor analysis.
Using this matrix, you can identify some of the items that do not relate to other items. Ideally, for each item, 20% or more of the correlations should exceed 0.3 or so. When fewer of the correlations exceed 0.3, the researcher should consider removing that item.
You can also identify some of the items that correlate with other items above and beyond the factors. Specifically, when a correlation exceeds 0.9, one of the corresponding items should be removed for several reasons. First, these items tend to undermine confirmatory factor analysis. Second, one of these items seems to be redundant and thus inefficient. Third, very high correlations can produce a positive determinant or some other underlying problem that thwarts the program.
Finally, you can identify some of the items that correlate with more than one factor. In particular, suppose that Item 1 correlates with eight other items (ie eight of the coefficients exceed 0.3 or so). Suppose the remaining items correlate with only four other items. This pattern of findings suggests that Item 1 correlates with two or more factors and should thus be removed.
Another table that can help identify unsuitable items is the anti-image correlation matrix.
To generate this matrix in the factor analysis program, press "Descriptives" and tick "Anti-image". This process will present a matrix in the output of factor analysis.
Using this matrix, you can identify items that do not correlate with any of the factors. To achieve this goal, you should examine the diagonals, which are called the "sampling adequacy of individual items". When these values are less than 0.5, the corresponding item should be removed.
Finally, this matrix can uncover items that correlate with other items above and beyond the factors. In particular, each of the values that are not locate on the diagonal represent the correlation between the corresponding items after controlling the other items and then multiplied by -1. Values that exceed 0.3 or so represent items that are correlated with each other above and beyond the factors. Hence, one of these items should be eliminated.
Last Update: 6/2/2016