Factor Analysis for Nominal (First Choice) Data

Abstract

We show how a factor analysis model can be fitted to nominal data using the computer program Mplus. The model is akin to multinomial logistic regression with unobserved predictors (the common factors) and was proposed in the one factor case, in the 1970s, within an item response theory (IRT) framework. Recently, extensions to multiple factors and alternative parameterizations to facilitate parameter interpretation have been proposed. We present four examples in which several versions of the model are estimated using Mplus: a) a one-factor model applied to situational items measuring assertiveness, b) an exploratory factor analysis applied to attitudinal data, c) a confirmatory factor analysis applied to educational data with testlets, and d) the newest parameterization of the model applied to an emotional stability scale. All data files and computer codes are provided as supplementary materials.

Keywords:

• IRT
• item response theory
• multidimensional nominal categories model
• Nominal factor analysis
• situational 15 judgment tests

Acknowledgement

The authors acknowledge the support of the Center for Scientific Computing at the Autonoma University of Madrid (CCC-UAM).

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Additional information

Funding

This research was partially supported by grant PSI2015-66366-P from the Spanish Department of Economy and Competitiveness (Revuelta, PI) and by grant SES-1659936 from the National Science Foundation (Maydeu-Olivares, PI).