Statistics and Its Interface

Volume 15 (2022)

Number 1

A generalized semi-parametric model for jointly analyzing response times and accuracy in computerized testing

Pages: 91 – 104

DOI: https://dx.doi.org/10.4310/21-SII681

Authors

Fang Liu (School of Mathematics and Statistics, Northeast Normal University, Changchun, China)

Jiwei Zhang (School of Mathematics and Statistics, Yunnan University, Kunming, China)

Ningzhong Shi (School of Mathematics and Statistics, Northeast Normal University, Changchun, China)

Ming-Hui Chen (Department of Statistics, University of Connecticut, Storrs, Ct., U.S.A.)

Abstract

The Cox proportional hazards model has been widely used for modeling response-time data in educational and psychological research. However, based on the Kaplan-Meier (KM) plots in an empirical example, we find that the proportionality of the hazard ratios does not seem to be an appropriate assumption, and there are considerable differences in survival rates among different items. To overcome such a problem, we consider a class of flexible nonproportional hazards models known as the generalized odds-rate hazards class of regression models. This class is general enough to include several commonly used models, including the proportional hazards model and the proportional odds model, as special cases. A fully Bayesian method is developed for parameter estimation and the deviance information criterion (DIC) and the logarithm of the pseudomarginal likelihood (LPML) are employed for model comparison. Simulation studies are conducted and a detailed analysis of the Programme for International Student Assessment (PISA) science data is carried out to further illustrate the proposed methodology.

Keywords

Cox model, DIC, GORH models, item response theory (IRT), LPML, MCMC

Received 20 April 2020

Accepted 6 May 2021

Published 11 August 2021