Estimation of Two-Level Hurdle Model with Two-Side Truncated Generalized Poisson Distribution using RTMB

• In Event: Innovations for Complexity in Models and Design: Inference, Estimation, Classification, and Longitudinal Issues

Abstract

Generalized linear mixed models (GLMMs) are extensively used in educational research to analyze categorical, ordinal, and other non-normally distributed outcomes conditional on explanatory covariates. For instance, multilevel hurdle models are commonly employed to address zero inflation in the conditional distribution of outcome variables. However, modeling student GPA often requires modifications to these models, such as truncation to reflect the upper bound of GPA scores and the use of generalized Poisson distribution to handle under-dispersion. This paper demonstrates how such modified multilevel hurdle models can be estimated using the R package RTMB, which enables user-defined objective functions and performs estimation via Laplace approximation for integration, Newton’s method for inner optimization, and the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm for outer optimization.

Authors

• Jiachen Liu, Michigan State University

• William H. Schmidt, Michigan State University

• Barbara Schneider, Michigan State University

• Richard T. Houang, Michigan State University

• Yuehua Cui, Michigan State University

• Haolei Weng, Michigan State University

• David Yeager, University of Texas at Austin