An Explanatory Multidimensional Random Item Effects Rating Scale Model

Abstract

Random item effects item response theory (IRT) models, which treat both person and item effects as random, have received much attention for more than a decade. The random item effects approach has several advantages in many practical settings. The present study introduced an explanatory multidimensional random item effects rating scale model. The proposed model was formulated under a novel parameterization of the nominal response model (NRM), and allows for flexible inclusion of person-related and item-related covariates (e.g., person characteristics and item features) to study their impacts on the person and item latent variables. A new variant of the Metropolis-Hastings Robbins-Monro (MH-RM) algorithm designed for latent variable models with crossed random effects was applied to obtain parameter estimates for the proposed model. A preliminary simulation study was conducted to evaluate the performance of the MH-RM algorithm for estimating the proposed model. Results indicated that the model parameters were well recovered. An empirical data set was analyzed to further illustrate the usage of the proposed model.

Cross-Classified Item Response Theory Modeling With an Application to Student Evaluation of Teaching

“…It connects Fisher’s (1925) identity and Robbins and Monro’s (1951) root-finding algorithm for noise-corrupted regression functions and produces MLEs of model parameters. The MH-RM algorithm has been applied in many latent variable modeling contexts (e.g., Cai, 2010a, 2010b; Chung & Cai, 2021; Falk & Cai, 2016; Huang et al, 2022; Ju & Falk, 2019; Monroe & Cai, 2014; Yang & Cai, 2014).…”