Indeterminacy of Factor Score Estimates In Slightly Misspecified Confirmatory Factor Models

Two methods to calculate a measure for the quality of factor score estimates have been proposed. These methods were compared by means of a simulation study. The method based on a covariance matrix reproduced from a model leads to smaller effects of sampling error

Varimax rotation based on gradient projection needs between 10 and more than 500 random start loading matrices for optimal performance

Gradient projection rotation (GPR) is a promising method to rotate factor or component loadings by different criteria. Since the conditions for optimal performance of GPR-Varimax are widely unknown, this simulation study investigates GPR towards the Varimax criterion in principal component analysis. The conditions of the simulation study comprise two sample sizes (n = 100, n = 300), with orthogonal simple structure population models based on four numbers of components (3, 6, 9, 12), with- and without Kaiser-normalization, and six numbers of random start loading matrices for GPR-Varimax rotation (1, 10, 50, 100, 500, 1,000). GPR-Varimax rotation always performed better when at least 10 random matrices were used for start loadings instead of the identity matrix. GPR-Varimax worked better for a small number of components, larger (n = 300) as compared to smaller (n = 100) samples, and when loadings were Kaiser-normalized before rotation. To ensure optimal (stationary) performance of GPR-Varimax in recovering orthogonal simple structure, we recommend using at least 10 iterations of start loading matrices for the rotation of up to three components and 50 iterations for up to six components. For up to nine components, rotation should be based on a sample size of at least 300 cases, Kaiser-normalization, and more than 50 different start loading matrices. For more than nine components, GPR-Varimax rotation should be based on at least 300 cases, Kaiser-normalization, and at least 500 different start loading matrices.Comment: 19 pages, 8 figures, 2 tables, 4 figures in the Supplemen

A Schmid-Leiman-Based Transformation Resulting in Perfect Inter-correlations of Three Types of Factor Score Predictors

Factor score predictors are computed when individual factor scores are of interest. Conditions for a perfect inter-correlation of the best linear factor score predictor, the best linear conditionally unbiased predictor, and the determinant best linear correlation-preserving predictor are presented. A transformation resulting in perfect correlations of the three predictors is proposed

Hierarchies of factor solutions in the intelligence domain : applying methodology from personality psychology to gain insights into the nature of intelligence

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Unit-weighted scales imply models that should be tested!

In several studies unit-weighted sum scales based on the unweighted sum of items are derived from the pattern of salient loadings in confirmatory factor analysis. The problem of this procedure is that the unit-weighted sum scales imply a model other than the initially tested confirmatory factor model. In consequence, it remains generally unknown how well the model implied by the unit-weighted sum scales fits the data. Nevertheless, the derived unit-weighted sum scales are often used in applied settings. The paper demonstrates how model parameters for the unit-weighted sum scales can be computed and tested by means of structural equation modeling. An empirical example based on a personality questionnaire and subsequent unit-weighted scale analyses are presented in order to demonstrate the procedure. Accessed 6,132 times on https://pareonline.net from February 18, 2013 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Oblique Mean-Target-rotation

Oblique target rotation in the context of exploratory factor analysis is a relevant method for the investigation of the oblique independent clusters model. It was argued that minimizing single cross-loadings by means of target rotation may lead to effects of sampling error of the inter-correlations of the target rotated factors. It was therefore proposed to compute the mean cross-loadings for each block of salient loadings in the independent clusters model and to perform target rotation in order to minimize the block-wise mean cross-loadings. A simulation study based on correlated independent factor models revealed that mean oblique target rotation resulted in a smaller negative bias of the factor inter-correlations than conventional target rotation. Therefore, this method can be recommended when target rotation is performed in the context of oblique independent factor models. An R-script and an SPSS-script for this form of target rotation are provided in the Appendix