Bridging Scales and Stories: A Joint Factor-Topic Model for Mixed-Format Response Data

• In Event: The Nuance of Patterns: Methods for Uncovering Intricate Quantitative Relationships

Abstract

This study introduces a joint factor–topic model for integrating rating-scale and open-ended text data within a unified Bayesian framework. By linking latent factors from confirmatory factor analysis to topics derived from LDA topic modeling via multinomial logistic regression, the model enables simultaneous analysis of mixed-format responses. Simulation studies demonstrate improved recovery of factor-to-topic effects, factor scores, and topic–word distributions compared to standalone factor or topic models. Application to real survey data from 593 secondary students reveals interpretable associations between self-perceived giftedness and career interests expressed in text. The proposed model advances multimodal data integration in educational research, providing a rigorous approach for uncovering hidden relationships, enhancing measurement accuracy, and improving topic discovery with mixed-format data.

Authors

• Yuxiao Zhang, Purdue University

• David Arthur, University of Washington - Tacoma

• Yukiko Maeda, Purdue University

• Hua-Hua Chang, Purdue University