Purpose: The purpose of this project was to develop a better way to deal with measurement error in predictors and to address the impact of non-normality in latent variable distributions. Predictors that contain measurement error yield attenuated correlation or regression coefficient estimates, which results in bias in treatment effect estimates. This problem is exacerbated in multilevel models when level-1 values are simply aggregated to an upper level as group means. By introducing a multilevel and multidimensional measurement model, the measurement error in the predictor can be more properly handled.

Project Activities: The research team first developed software in R that can run the necessary models. Using simulation studies, the researchers then investigated the extent to which various model facets lead to bias in the parameter estimates. A second set of simulation studies compared the new model against current approaches in terms of parameter recovery under different conditions, including non-normal distributions of the trait being measured. The researchers also used real data to demonstrate the utility of the new model. By the end of the project, the team released a user-friendly version of the software and disseminated the results of the research at conferences and in journals.

Products and Publications

Yang, J. S., & Zheng, X. (2018). Item response data analysis using Stata item response theory package. Journal of Educational and Behavioral Statistics, 43(1), 116–129.

Zheng, X., & Yang, J. S. (2016). Using sample weights in item response data analysis under complex sample designs. In Quantitative Psychology Research: The 80th Annual Meeting of the Psychometric Society, Beijing, 2015 (pp. 123–137). Springer International Publishing.

Zheng, X., Yang, J. S., & Harring, J. R. (2022). Latent growth modeling with categorical response data: A methodological investigation of model parameterization, estimation, and missing data. Structural Equation Modeling: A Multidisciplinary Journal, 29(2), 182–206.