Confirmatory Factor Analysis and Measurement Invariance Testing with Ordinal Data: An Application in Revising the Flirting Styles Inventory

Abstract

Factor analysis (FA) is becoming a common practice in communication research for measurement validation, yet issues associated with FA for ordinal items have not been adequately addressed. As many attitudinal and behavioral measures in communication research consist of ordered-categorical items, this article provides an accessible introduction for applied researchers on categorical confirmatory factor analysis (cat-CFA) and measurement invariance (MI) testing for ordinal data. First, this paper presents conceptual discussions on the classical and the categorical FA models and conditions under which applications of the classical FA can lead to estimation biases. Second, model identification and specification issues with MI for ordinal data are discussed. Third, to demonstrate the techniques, cat-CFA and MI with ordinal data are applied to the revision of an existing self-report Likert-type measure, the Flirting Styles Inventory.

ACKNOWLEDGMENTS

An early version of this manuscript, titled “The Flirting Styles Inventory – Revised: Confirmatory Factor Analysis and Measurement Invariance Testing with Ordinal Data” was previously presented at the National Communication Association 100^th Annual Convention (November, 2014) in Chicago, IL.

The authors would like to express their gratitude for the detailed and helpful revision suggestions provided by Dr. Scott Reid and the two anonymous reviewers. We also want to thank Dr. Carol Woods (Senior Psychometrician, Center for Educational Testing and Evaluation at the University of Kansas), for her statistical advice.

Notes

¹ To gain a more in-depth understanding about FA, readers are encouraged to consult with Brown’s (2006) book on CFA for applied research and Kline’s (2011) book on Structural Equation Molding. Morrison’s (2009) content analysis on the EFA practices in communication research also provides an excellent nontechnical introduction to the history and the common issues of FA. For readers who are interested in the technical discussions on FA can review two handbook chapters by Brown (2013) and MacCallum (2009).

² Another two sets of invariance models for the polite and physical flirting styles were estimated in which participant sex was specified as a covariate (the revised items were regressed on sex). With the sex-as-covariate specification, the polite flirting style subscale established strong invariance.