Factor scores seemed to be cutting-edge back in the 1980s when the first author was beginning to take graduate statistics courses. The concept and practice extend back to the 1920s, although early on it was considered much less important than the determination of the actual factors themselves.[1] This practice developed as a rational response to the early practice of summing or averaging items on a scale to produce an overall score. Of course, summing or averaging items assumes that all items contribute equally to the latent score. EFA demonstrated convincingly very early on that not all items are equally good measures of a construct and, therefore, better items should carry more weight in estimating an individual’s score.

The practice of weighting items according to the results of EFA analyses held the potential of improving measurement. Researchers working prior to wide scale access to computers were then able to sum the weighted item scores to approximate what might be the true score of each individual on the construct being examined.[2] Thus, the computation of weighted factor scores makes sense and was a natural progression over a period of many decades of research. However, it is important to recognize the intricate nature of the factor score computation. There are many methods of computing factor scores and no single universal technique. In addition, factor scores can be sensitive to the extraction and rotation methods used (DiStefano, Zhu, & Mindrila, 2009).

The practice of factor score estimation introduced a new assumption into our analyses: that the factor loadings (correlations between an item and the factor) are stable and reasonable estimates of the dynamics within a population. A corollary, of course, is that the factor loadings are valid (invariant) for all subgroups being examined. A similar set of assumptions and corresponding issues is present in linear modeling /regression analyses, particularly when researchers are using multiple regression to predict outcomes for individuals. (For papers on prediction in regression, see Osborne, 2000, 2008.) Specifically, the issue is that these procedures can overfit the data. Most samples contain idiosyncratic aspects that most quantitative analyses will take advantage of in order to fit the model, despite those sample characteristics being nonreproducible (Thompson, 2004, p. 70). Because of this issue, we recommended in earlier chapters that we focus on replication and evaluate the anticipated precision or variability across samples to evaluate the goodness of EFA results. However, factor score estimation can be considered a relatively common practice and thus a book about EFA might not be complete without mentioning this practice. Therefore, here are our goals for this chapter: