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. 2015 Jun;75(3):406-427.
doi: 10.1177/0013164414547959. Epub 2014 Aug 29.

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations

Seda Can  1 , Rens van de Schoot  2 , Joop Hox  2
Affiliations

Collinear Latent Variables in Multilevel Confirmatory Factor Analysis: A Comparison of Maximum Likelihood and Bayesian Estimations

Seda Can et al. Educ Psychol Meas. 2015 Jun.

Abstract

Because variables may be correlated in the social and behavioral sciences, multicollinearity might be problematic. This study investigates the effect of collinearity manipulated in within and between levels of a two-level confirmatory factor analysis by Monte Carlo simulation. Furthermore, the influence of the size of the intraclass correlation coefficient (ICC) and estimation method; maximum likelihood estimation with robust chi-squares and standard errors and Bayesian estimation, on the convergence rate are investigated. The other variables of interest were rate of inadmissible solutions and the relative parameter and standard error bias on the between level. The results showed that inadmissible solutions were obtained when there was between level collinearity and the estimation method was maximum likelihood. In the within level multicollinearity condition, all of the solutions were admissible but the bias values were higher compared with the between level collinearity condition. Bayesian estimation appeared to be robust in obtaining admissible parameters but the relative bias was higher than for maximum likelihood estimation. Finally, as expected, high ICC produced less biased results compared to medium ICC conditions.

Keywords: Bayesian estimation; collinearity; inadmissible parameter estimates; maximum likelihood estimation; multilevel confirmatory factor analysis.

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Conflict of interest statement

Declaration of Conflicting Interests: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Figures

Figure 1.
Figure 1.
The path diagram of multilevel confirmatory factor analysis model tested in the study.
Figure 2.
Figure 2.
Percentages of inadmissible solutions in between level multicollinearity conditions across intraclass correlations (ICCs).
See this image and copyright information in PMC

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