Validity of factor score predictors in Bayesian and Maximum likelihood confirmatory factor analyses

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The overarching goal of the intended project is to provide benchmarks for the magnitude for coefficients of determination and to minimize bias for coefficients of determination as indicators of the factorial validity of factor score predictors and unit-weighted sum scales computed from Bayesian and maximum likelihood confirmatory factor analysis. The focus on factor score predictors and unit-weighted sum scales is due to the necessity to estimate individual scores whenever individuals are assigned to jobs or interventions. Three subgoals are to be investigated in separated simulation studies: The first subgoal is the comparison of magnitude and bias of coefficients of determination computed from confirmatory factor analyses based on maximum likelihood estimation and Bayesian estimation. The consequences of model misspecification due to non-specified cross-loadings in maximum likelihood estimation and the consequences of specification of expected variations of non-salient loadings (priors) in Bayesian estimation are compared. Besides the effect of population models and sample size, the effect of categorical data versus continuous, multivariate normal distributed data will also be investigated. The second subgoal refers to the effect of magnitude and bias of coefficients of determination on criterion validities, as they can be computed from factor score predictors. A direct comparison of modelling predictor-criterion relationships within structural equation models with the predictor-criterion relationships based on factor score predictors will be performed. The magnitude of the coefficient of determination necessary to achieve an acceptable similarity of predictor-criterion relationships based on latent modeling and factor score predictors will be ascertained. The third subgoal is the investigation of the effect of the magnitude of determination coefficients on the estimation of between-group mean differences based on factor score predictors and unit-weighted sum scales. For this purpose, latent between-group mean differences will be generated in multifactorial population models. It will then be investigated in the samples to what degree between-group differences based on factor score predictors and unit-weighted sum scales can be identified on those factors on which they occur in the population. Not only the correct identification of between-group differences on the respective factors is in the focus but also the correct non-occurrence of between-group differences on factors, where no between-group differences occur in the population. In the context of the second and third subgoal the maximum likelihood estimation and the Bayesian estimation will also be compared for different population models, sample sizes, as well as for continuous and categorical variables.