Estimating a Three-Level Contextual Effects Model Given Error-Prone Measures of Contextual Variables and Missing Data

• Activity Number: 423
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Yongyun Shin*+
• Companies: Virginia Commonwealth University
• Keywords: Contextual effect ; Bias ; Ignorable missing data ; Maximum likelihood ; Efficient estimation ; Reliability

Abstract

In a three-level linear model where occasions are nested within children attending schools, the association between a time-varying covariate and the outcome may be different at different levels to yield a contextual effects model. The conventional analysis is to use the covariate and its aggregated sample means as regressors. The effects of the sample means controlling for the covariate are defined as the contextual effects. This approach, however, produces biased contextual effects, which introduce bias in the variance estimates and the effects of other child- and school-level covariates that are correlated with the covariate. Furthermore, the outcome and covariates may be subject to missingness at any of the levels. The author expresses the desired model given the latent population means of the contextual covariate instead of its sample means, shows the bias in the conventional approach, and introduces maximum likelihood estimation that corrects the bias, that efficiently handles ignorable missing data at any level, and that produces multiple imputation including the latent population means. The multiple imputation facilitates exploration of multiple models for model selection.