Analysis of Interactions and Nonlinear Effects with Missing Data: A Factored Regression Modeling Approach Using Maximum Likelihood Estimation

Abstract

When estimating multiple regression models with incomplete predictor variables, it is necessary to specify a joint distribution for the predictor variables. A convenient assumption is that this distribution is a multivariate normal distribution, which is also the default in many statistical software packages. This distribution will in general be misspecified if predictors with missing data have nonlinear effects (e.g., x²) or are included in interaction terms (e.g., x·z). In the present article, we introduce a factored regression modeling approach for estimating regression models with missing data that is based on maximum likelihood estimation. In this approach, the model likelihood is factorized into a part that is due to the model of interest and a part that is due to the model for the incomplete predictors. In three simulation studies, we showed that the factored regression modeling approach produced valid estimates of interaction and nonlinear effects in regression models with missing values on categorical or continuous predictor variables under a broad range of conditions. We developed the R package mdmb, which facilitates a user-friendly application of the factored regression modeling approach, and present a real-data example that illustrates the flexibility of the software.     

The criterion-related validity of conscientiousness in personnel selection: A meta-analytic reality check

A key finding in personnel selection is the positive correlation between conscientiousness and job performance. Evidence predominantly stems from concurrent validation studies with incumbent samples but is readily generalized to predictive settings with job applicants. This is problematic because the extent to which faking and changes in personality affect the measurement likely vary across samples and study designs. Therefore, we meta-analytically investigated the relation between conscientiousness and job performance, examining the moderating effects of sample type (incumbent vs. applicant) and validation design (concurrent vs. predictive). The overall correlation of conscientiousness and job performance was in line with previous meta-analyses ($\overline{r}=.17,k=102,n=23,305$). In our analyses, the correlation did not differ across validation designs (concurrent: $\overline{r}=.18,k=78,n=19,132$; predictive: $\overline{r}=.15,k=24,n=4173$), sample types (incumbents: $\overline{r}=.18,k=92,n=20,808$; applicants: $\overline{r}=.14,k=10,n=2497$), or their interaction. Critically, however, our review revealed that only a small minority of studies (~12%) were conducted with real applicants in predictive designs. Thus, barely a fraction of research is conducted under realistic conditions. Therefore, it remains an open question if self-report measures of conscientiousness retain their predictive validity in applied settings that entail faked responses. We conclude with a call for more multivariate research on the validity of selection procedures in predictive settings with actual applicants.