Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution. Issue 1 (2nd January 2021)

• Record Type: Journal Article
• Authors: Lorenzo-Seva, Urbano; Ferrando, Pere J.
• Is Part Of: Structural equation modeling. Volume 28:Issue 1(2021)
• Page Start: 138
• Page End: 147
• Publication Date: 2021-01-02
• Subjects: Not positive definite -- polychoric correlation -- smoothing method -- Heywood cases; Multivariate analysis -- Periodicals; Social sciences -- Statistical methods -- Periodicals; 519.535
• DOI: 10.1080/10705511.2020.1735393
• Languages: English
• ISSNs: 1070-5511

Abstract

ABSTRACT: Least-squares exploratory factor analysis based on tetrachoric/polychoric correlations is a robust, defensible and widely used approach for performing item analysis, especially in the first stages of scale development. A relatively common problem in this scenario, however, is that the inter-item correlation matrix fails to be positive definite. This paper, which is largely intended for practitioners, aims to provide a didactic discussion about the causes, consequences and remedies of this problem. The discussion is more applied than statistical and based on the factor analysis model, and the problem is linked to that of improper solutions. Solutions for preventing the problem from occurring, and the smoothing corrections available at present are described and discussed. A new smoothing algorithm is also proposed.