Latent Theme Dictionary Model for Finding Co-occurrent Patterns in Process Data

TL;DR

This paper introduces a novel latent theme dictionary model (LTDM) for analyzing process data, effectively identifying co-occurring event patterns and behavioral similarities, with theoretical validation and practical application to educational assessment data.

Contribution

The paper develops a new LTDM framework for process data, including theoretical properties and a Bayesian inference algorithm, advancing analysis of complex temporal categorical data.

Findings

LTDM accurately identifies co-occurring event patterns.

Theoretical properties of the model are established.

Application to PISA data yields interpretable insights.

Abstract

Process data, temporally ordered categorical observations, are of recent interest due to its increasing abundance and the desire to extract useful information. A process is a collection of time-stamped events of different types, recording how an individual behaves in a given time period. The process data are too complex in terms of size and irregularity for the classical psychometric models to be applicable, at least directly, and, consequently, it is desirable to develop new ways for modeling and analysis. We introduce herein a latent theme dictionary model (LTDM) for processes that identifies co-occurrent event patterns and individuals with similar behavioral patterns. Theoretical properties are established under certain regularity conditions for the likelihood based estimation and inference. A non-parametric Bayes LTDM algorithm using the Markov Chain Monte Carlo method is proposed for computation. Simulation studies show that the proposed approach performs well in a range of situations. The proposed method is applied to an item in the 2012 Programme for International Student Assessment with interpretable findings.