Computing and evaluating factor scores.

Abstract

A variety of methods for computing factor scores can be found in the psychological literature. These methods grew out of a historic debate regarding the indeterminate nature of the common factor model. Unfortunately, most researchers are unaware of the indeterminacy issue and the problems associated with a number of the factor scoring procedures. This article reviews the history and nature of factor score indeterminacy. Novel computer programs for assessing the degree of indeterminacy in a given analysis, as well as for computing and evaluating different types of factor scores, are then presented and demonstrated using data from the Wechsler Intelligence Scale for Children-Third Edition. It is argued that factor score indeterminacy should be routinely assessed and reported as part of any exploratory factor analysis and that factor scores should be thoroughly evaluated before they are reported or used in subsequent statistical analyses.

Mapping and evaluation of landscape ecological status using geographic indices extracted from remote sensing imagery of the Pearl River Delta, China, between 1998 and 2008

“…Because the number of equations (m) is less than the number of variables (p), factor scores cannot be calculated accurately, but estimates can be derived. Grice (2001) and Williams et al (2010) have described a detailed implementation of this procedure and thus there is no need to repeat the description here.…”

Analysis of Corporate Entrepreneurship in Public R&D Institutions

“…While a factor loading states the correlation between an item (question) and a factor (thus being an actual number), a factor score is a random variable, depicting the latent (indirect) scores of each respondent on the respective factor-derived from the direct answered scores of each respondent on the items that build that factor. The factor scores themselves are computed via least square regression, and they predict the location of each respondent on the factor [27,32]. According to [33], the least square method applied for computing the factor scores is a multivariate regression procedure, taking into account the correlations between factors, between factors and items, and between the items themselves.…”

Reliability Estimates for Three Factor Score Estimators

“…Accordingly, the factor score determinacy, i.e., the correlation of the regression score estimator with the corresponding common factors (Grice, 2001) is…”

“…In the following, the reliability estimate for the regression score estimator is compared with the determinacy coefficient (Grice, 2001), which represents the validity of the factor score predictor. The covariances of the regression factor score estimator with the corresponding common factor are the diagonal elements of…”

“…The coefficient of determinacy, i.e., the correlation of the factor score estimator with the factor (Grice, 2001) has been related to the validity of factor score estimators (Gorsuch, 1983). However, the reliability of factor score estimators has rarely been investigated.…”