Target rotation with both factor loadings and factor correlations.

2019 ◽  
Vol 24 (3) ◽  
pp. 390-402
Author(s):  
Guangjian Zhang ◽  
Minami Hattori ◽  
Lauren A. Trichtinger ◽  
Xianni Wang
Keyword(s):  
Factor Loadings ◽  
Target Rotation

Comparison of Principal Component Solutions in Two Populations

Methodology ◽  
2016 ◽  
Vol 12 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Gregor Sočan
Keyword(s):  
Simulation Study ◽  
Principal Components ◽  
Common Factor ◽  
Principal Component ◽  
Component Model ◽  
Bootstrap Procedure ◽  
Factor Loadings ◽  
Component Loadings ◽  
Principal Component Model ◽  
Two Populations

Abstract. When principal component solutions are compared across two groups, a question arises whether the extracted components have the same interpretation in both populations. The problem can be approached by testing null hypotheses stating that the congruence coefficients between pairs of vectors of component loadings are equal to 1. Chan, Leung, Chan, Ho, and Yung (1999) proposed a bootstrap procedure for testing the hypothesis of perfect congruence between vectors of common factor loadings. We demonstrate that the procedure by Chan et al. is both theoretically and empirically inadequate for the application on principal components. We propose a modification of their procedure, which constructs the resampling space according to the characteristics of the principal component model. The results of a simulation study show satisfactory empirical properties of the modified procedure.

Analyzing Observed Composite Differences Across Groups

Methodology ◽  
2013 ◽  
Vol 9 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Holger Steinmetz
Keyword(s):  
Monte Carlo ◽  
Structural Equation Modeling ◽  
Measurement Invariance ◽  
Structural Equation ◽  
Monte Carlo Study ◽  
Equation Modeling ◽  
Factor Loadings ◽  
Latent Mean Differences ◽  
Partial Invariance ◽  
Mean Differences

Although the use of structural equation modeling has increased during the last decades, the typical procedure to investigate mean differences across groups is still to create an observed composite score from several indicators and to compare the composite’s mean across the groups. Whereas the structural equation modeling literature has emphasized that a comparison of latent means presupposes equal factor loadings and indicator intercepts for most of the indicators (i.e., partial invariance), it is still unknown if partial invariance is sufficient when relying on observed composites. This Monte-Carlo study investigated whether one or two unequal factor loadings and indicator intercepts in a composite can lead to wrong conclusions regarding latent mean differences. Results show that unequal indicator intercepts substantially affect the composite mean difference and the probability of a significant composite difference. In contrast, unequal factor loadings demonstrate only small effects. It is concluded that analyses of composite differences are only warranted in conditions of full measurement invariance, and the author recommends the analyses of latent mean differences with structural equation modeling instead.

A Comparison of Reliability Estimation Based on Confirmatory Factor Analysis and Exploratory Structural Equation Models

2021 ◽  
pp. 001316442110089
Author(s):  
Yuanshu Fu ◽  
Zhonglin Wen ◽  
Yang Wang
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Structural Equation ◽  
Reliability Estimation ◽  
Model Fit ◽  
Equation Modeling ◽  
Factor Loadings ◽  
Reliability Estimates ◽  
Confirmatory Factor ◽  
Composite Reliability

Composite reliability, or coefficient omega, can be estimated using structural equation modeling. Composite reliability is usually estimated under the basic independent clusters model of confirmatory factor analysis (ICM-CFA). However, due to the existence of cross-loadings, the model fit of the exploratory structural equation model (ESEM) is often found to be substantially better than that of ICM-CFA. The present study first illustrated the method used to estimate composite reliability under ESEM and then compared the difference between ESEM and ICM-CFA in terms of composite reliability estimation under various indicators per factor, target factor loadings, cross-loadings, and sample sizes. The results showed no apparent difference in using ESEM or ICM-CFA for estimating composite reliability, and the rotation type did not affect the composite reliability estimates generated by ESEM. An empirical example was given as further proof of the results of the simulation studies. Based on the present study, we suggest that if the model fit of ESEM (regardless of the utilized rotation criteria) is acceptable but that of ICM-CFA is not, the composite reliability estimates based on the above two models should be similar. If the target factor loadings are relatively small, researchers should increase the number of indicators per factor or increase the sample size.

Factor Structure of Shortened Children's Embedded Figures Test for Different Age Groups

1986 ◽  
Vol 63 (2) ◽  
pp. 479-486 ◽  
Author(s):  
Robert C. Hardy ◽  
John Eliot ◽  
Kenneth Burlingame
Keyword(s):  
Factor Analysis ◽  
Factor Structure ◽  
Total Population ◽  
Age Groups ◽  
Total Sample ◽  
Factor Loadings ◽  
Embedded Figures Test ◽  
Embedded Figures

240 children, 24 of each sex in Grades K to 4, were administered the entire Children's Embedded Figures Test, regardless of the failure rule. Factor loadings for items from a shortened version of the test were examined for a randomly divided sample, a sample divided by sex, a sample divided in two grade groupings, and an undivided total population. Stable factors were found for the total sample and when the sample was divided by sex. Analysis indicated that the factor analysis of the shortened form was consistent with previous analyses using the total scale.

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