Using Regularization to Evaluate Differential Item Functioning Among Multiple Covariates: A Penalized Expectation-Maximization Algorithm via Coordinate Descent and Soft-Thresholding

Testing for differential item functioning (DIF) has undergone rapid statistical developments in recent years. Namely, the moderated nonlinear factor analysis (MNLFA) model allows for simultaneous testing of DIF in multiple categorical and continuous covariates (e.g., age, gender, ethnicity, etc.). Recent work has also implemented a LASSO regularization approach to identify DIF and select anchor items for model identification. Although regularized MNLFA provides greater flexibility to evaluate DIF, less development has been made in efficiently estimating model parameters. Most previous implementations of MNLFA have directly maximized the observed marginal likelihood function, which limits the method to only a few items and covariates. Additionally, penalization in the MNLFA model has only been performed outside of the optimization routine, which results in a non-standard method for setting estimates to zero. To overcome these difficulties, I introduce a penalized expectation-maximization (EM) algorithm that efficiently estimates many more item parameters than previous implementations and performs regularization during optimization. I extend the regularized MNLFA model to include not just soft-thresholding for LASSO penalization, but also firm-thresholding for the MCP approach. A Monte Carlo simulation study and an empirical data analysis evaluates this new algorithm, comparing the LASSO and MCP approaches against previous work. Finally, a discussion of future research directions concludes the dissertation.Doctor of Philosoph