# Multidimensional Generalized Partial Preference Model for Forced-Choice Items

## TL;DR

This paper introduces a new IRT model for forced-choice items that offers more flexibility and statistical elegance compared to existing methods.

## Contribution

The paper proposes the multidimensional generalized partial preference model (MGPPM) for forced-choice items.

## Key findings

- MGPPM shows satisfactory parameter recovery in simulations with triplet and tetrad data.
- MGPPM is more statistically elegant than the Thurstonian IRT and Triplet-2PLM models.
- The new model provides more flexible IRT modeling under different assumptions.

## Abstract

A ranking pattern approach is proposed to build item response theory (IRT) models for forced-choice (FC) items. This new approach is an addition to the two existing approaches, sequential selection and Thurstone’s law of pairwise comparison. A new dominance IRT model, the multidimensional generalized partial preference model (MGPPM), is proposed for FC items with any number (greater than 1) of statements. The maximum marginal likelihood estimation using an expectation-maximization algorithm (MML-EM) and Markov chain Monte Carlo (MCMC) estimation are developed. A simulation study is conducted to show satisfactory parameter recovery on triplet and tetrad data. The relationships between the newly proposed approach/model and the existing approaches/models are described, and the MGPPM, Thurstonian IRT (TIRT) model, and Triplet-2PLM are compared when applied to simulated and real triplet data. The new approach offers more flexible IRT modeling than the other two approaches under different assumptions, and the MGPPM is more statistically elegant than the TIRT and Triple-2PLM.