TITLE:
Applied Psychometrics: The Modeling Possibilities of Multilevel Confirmatory Factor Analysis (MLV CFA)
AUTHORS:
Theodoros A. Kyriazos
KEYWORDS:
Multilevel Confirmatory Factor Analysis, MLV CFA, ML CFA, Hierarchical Factor Structure, Multilevel CFA Model, Between Groups, Within Groups, Intraclass Correlation Coefficient (ICC)
JOURNAL NAME:
Psychology,
Vol.10 No.6,
May
9,
2019
ABSTRACT: Multilevel CFA models (MLV CFA) modeling permits more sophisticated construct validity research by examining relationships among factor structures, factor loadings, and errors at different hierarchical levels. In the MLV CFA models, the latent variable or variables have two kinds of elements: 1) the between-group elements (Level 2 or higher level) and 2) the within-group elements (Level 1 of lower level). The between-group elements represent the general part of the model and the within-group element the individual part. The within-level variation includes an individual-level measurement error variance, which generally expands the impact of the within-level variation to the intraclass correlations. Multilevel CFA therefore generates results corresponding to those generated by perfectly reliable measures. If the same measurement model is specified across levels, by defining each item loading to be invariant with its across-level counterpart, the researcher can equate the factor scales across levels. Thus, the factor variances at different levels are directly comparable. The fit of this constrained MLV CFA model can be evaluated by comparing it with an unconstrained model specified with freely estimated factor loadings at each level. In the present work the steps of the above procedure are fully described and additional issues relevant to the use of MLV CFA are discussed in detail.