# Score‐based tests for parameter instability in ordinal factor models

## TL;DR

This paper introduces a new method for testing parameter instability in ordinal factor models, which is faster and more efficient than existing approaches.

## Contribution

A novel score-based testing method for parameter instability in ordinal factor models fitted with limited information estimation.

## Key findings

- The new score-based tests have a good Type I error rate and high statistical power.
- The method is computationally faster than full information estimation methods.
- The approach performs well in real data applications with complex models.

## Abstract

We present a novel approach for computing model scores for ordinal factor models, that is, graded response models (GRMs) fitted with a limited information (LI) estimator. The method makes it possible to compute score‐based tests for parameter instability for ordinal factor models. This way, rapid execution of numerous parameter instability tests for multidimensional item response theory (MIRT) models is facilitated. We present a comparative analysis of the performance of the proposed score‐based tests for ordinal factor models in comparison to tests for GRMs fitted with a full information (FI) estimator. The new method has a good Type I error rate, high power and is computationally faster than FI estimation. We further illustrate that the proposed method works well with complex models in real data applications. The method is implemented in the lavaan package in R.