An Investigation of Factored Regression Missing Data Methods for Multilevel Models with Cross-Level Interactions

Abstract

A growing body of literature has focused on missing data methods that factorize the joint distribution into a part representing the analysis model of interest and a part representing the distributions of the incomplete predictors. Relatively little is known about the utility of this method for multilevel models with interactive effects. This study presents a series of Monte Carlo computer simulations that investigates Bayesian and multiple imputation strategies based on factored regressions. When the model’s distributional assumptions are satisfied, these methods generally produce nearly unbiased estimates and good coverage, with few exceptions. Severe misspecifications that arise from substantially non-normal distributions can introduce biased estimates and poor coverage. Follow-up simulations suggest that a Yeo–Johnson transformation can mitigate these biases. A real data example illustrates the methodology, and the paper suggests several avenues for future research.

KEYWORDS:

• Missing data
• multiple imputation
• factored regression
• multilevel modeling
• moderation

Notes

1 Similar model-fitting procedures are available in the R package mdmb (Robitzsch & Lüdtke, 2021).

2 The separation prior parameterizes the random effect structure as a correlation and two variances. To provide comparability with the other priors, the covariance was computed by multiplying the estimated correlation at each iteration by the square root of the product of the variances.

3 We also investigated the J = 50 condition and included this figure in Section I of the online supplemental material; however, the findings were essentially the same, and the regression slopes for the normal distribution model were unbiased in all conditions.