Score Predictor Factor Analysis: Reproducing Observed Covariances by Means of Factor Score Predictors (original) (raw)
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Score Predictor Factor Analysis (SPFA) was introduced as a method that allows to compute factor score predictors that are -- under some conditions -- more highly correlated with the common factors resulting from factor analysis than the factor score predictors computed from the common factor model. In the present study, we investigate SPFA as a model in its own rights. In order to provide a basis for this, the properties and the utility of SPFA factor score predictors and the possibility to identify single-item indicators in SPFA loading matrices were investigated. Regarding the factor score predictors, the main result is that the best linear predictor of the score predictor factor analysis has not only perfect determinacy but is also correlation preserving. Regarding the SPFA loadings it was found in a simulation study that five or more population factors that are represented by only one variable with a rather substantial loading can more accurately be identified by means of SPFA t...
Psychometrika, 2007
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British Journal of Mathematical and Statistical Psychology, 2009
The present paper introduces model-related (MR) factor score predictors, which reflect specific aspects of confirmatory factor models. The development is mainly based on Schö nemann and Steiger's regression score components, but it can also be applied to the factor score coefficients. It is shown that the rotation of factor score predictors has no impact on the covariance matrix reproduced from the corresponding regression component patterns. Thus, regression score components or factor score coefficients can be rotated in order to obtain the required properties. This idea is the basis for MR factor score predictors, which are computed by means of a partial Procrustes rotation towards a target pattern representing the interesting properties of a confirmatory factor model. Two examples demonstrate the construction of MR factor score predictors reflecting specific constraints of a factor model.
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It is shown that the population-covariance matrix of a heterogeneous factor model may be indistinguishable from that of a standard factor model and that the standard likelihood-ratio goodness-of-fit statistic has but little power in detecting loading heterogeneity. The relation between loading heterogeneity and factor score reliability is studied and it is recommended that non-normality of the test-score distributions be tested to use factor scores with more confidence. Substantive justifications for the model assumptions and model-based methods to test specific hypotheses about the loading distribution, are discussed. In applied psychology, factor analysis is often used to develop diagnostic instruments. To obtain a good measure of a construct of interest (Cronbach & Meehl, 1955), a calibration study is performed wherein a battery of tests is administered to a large sample of subjects. Under the standard assumptions of multivariate normality of factors and residuals, test statistics and parameter estimates are computed from the covariance matrix (Jöreskog, 1971; Lawley & Maxwell, 1971). If the model fits the data, the parameter estimates are used to compute new subjects' factor scores and their confidence intervals to determine their position on the construct (Mellenbergh, 1994, 1996). In this paper, it is shown that a well-fitting factor model thus obtained does not necessarily mean that the essential assumptions hold and that factor scores The authors would like to thank an anonymous reviewer, and the editor, Roger Millsap, for their helpful comments on previous drafts and Conor V. Dolan for help with some of the statistics and graphics.
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Common factor analysis (CFA) and principal component analysis (PCA) are widely used multivariate techniques. Using simulations, we compared CFA with PCA loadings for distortions of a perfect cluster configuration. Results showed that nonzero PCA loadings were higher and more stable than nonzero CFA loadings. Compared to CFA loadings, PCA loadings correlated weakly with the true factor loadings for underextraction, overextraction, and heterogeneous loadings within factors. The pattern of differences between CFA and PCA was consistent across sample sizes, levels of loadings, principal axis factoring versus maximum likelihood factor analysis, and blind versus target rotation.
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Factor score regression has recently received growing interest as an alternative for structural equation modeling. However, many applications are left without guidance because of the focus on normally distributed outcomes in the literature. We perform a simulation study to examine how a selection of factor scoring methods compare when estimating regression coefficients in generalized linear factor score regression. The current study evaluates the regression method and the correlation-preserving method as well as two sum score methods in ordinary, logistic, and Poisson factor score regression. Our results show that scoring method performance can differ notably across the considered regression models. In addition, the results indicate that the choice of scoring method can substantially influence research conclusions. The regression method generally performs the best in terms of coefficient and standard error bias, accuracy, and empirical Type I error rates. Moreover, the regression me...
Improving Factor Score Estimation Through the Use of Observed Background Characteristics
Structural Equation Modeling: A Multidisciplinary Journal, 2016
A challenge facing nearly all studies in the psychological sciences is how to best combine multiple items into a valid and reliable score to be used in subsequent modeling. The most ubiquitous method is to compute a mean of items, but more contemporary approaches use various forms of latent score estimation. Regardless of approach, outside of large-scale testing applications, scoring models rarely include background characteristics to improve score quality. This article used a Monte Carlo simulation design to study score quality for different psychometric models that did and did not include covariates across levels of sample size, number of items, and degree of measurement invariance. The inclusion of covariates improved score quality for nearly all design factors, and in no case did the covariates degrade score quality relative to not considering the influences at all. Results suggest that the inclusion of observed covariates can improve factor score estimation.
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arXiv (Cornell University), 2016
Individual scores on common factors are required in some applied settings (e.g., business and marketing settings). Common factors are based on reflective indicators, but their scores cannot unambiguously be determined. Therefore, factor score estimates and unit-weighted scales are used in order to provide individual scores. It is shown that these scores are based on treating the reflective indicators as if they were causal-formative indicators. This modification of the causal status of the indicators should be justified. Therefore, the fit of the models implied by factor score estimates and unit-weighted scales should be investigated in order to ascertain the validity of the scores.
Communications in Statistics - Simulation and Computation, 2016
The factor score determinacy coefficient represents the common variance of the factor score predictor with the corresponding factor. The aim of the present simulation study was to compare the bias of determinacy coefficients based on different estimation methods of the exploratory factor model. Overall, determinacy coefficients computed from parameters based on maximum likelihood estimation, unweighted least squares estimation, and principal axis factoring were more precise than determinacy coefficients based on generalized least squares estimation and alpha factoring.
Recovering Predictor–Criterion Relations Using Covariate-Informed Factor Score Estimates
Structural Equation Modeling, 2018
Although it is currently best-practice to directly model latent factors whenever feasible, there remain many situations in which this approach is not tractable. Recent advances in covariateinformed factor score estimation can be used to provide manifest scores that are used in secondstage analysis, but these are currently understudied. Here we extend our prior work on factor score recovery to examine the use of factor score estimates as predictors both in the presence and absence of the same covariates that were used in score estimation. Results show that whereas the relation between the factor score estimates and the criterion are typically well recovered, substantial bias and increased variability is evident in the covariate effects themselves. Importantly, using covariate-informed factor score estimates substantially, and often wholly, mitigates these biases. We conclude with implications for future research and recommendations for the use of factor score estimates in practice.