Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation

van der Eijk, Cees; Rose, Jonathan

Abstract

This paper undertakes a systematic assessment of the extent to which factor analysis the correct number of latent dimensions (factors) when applied to ordered categorical survey items (so-called Likert items). We simulate 2400 data sets of uni-dimensional Likert items that vary systematically over a range of conditions such as the underlying population distribution, the number of items, the level of random error, and characteristics of items and item-sets. Each of these datasets is factor analysed in a variety of ways that are frequently used in the extant literature, or that are recommended in current methodological texts. These include exploratory factor retention heuristics such as Kaiser’s criterion, Parallel Analysis and a non-graphical scree test, and (for exploratory and confirmatory analyses) evaluations of model fit. These analyses are conducted on the basis of Pearson and polychoric correlations.We find that, irrespective of the particular mode of analysis, factor analysis applied to ordered-categorical survey data very often leads to over-dimensionalisation. The magnitude of this risk depends on the specific way in which factor analysis is conducted, the number of items, the properties of the set of items, and the underlying population distribution. The paper concludes with a discussion of the consequences of overdimensionalisation, and a brief mention of alternative modes of analysis that are much less prone to such problems.

Citation

van der Eijk, C., & Rose, J. (2015). Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation. PLoS ONE, 10(3), Article 0118900. https://doi.org/10.1371/journal.pone.0118900

• Journal Article Type: Article
• Publication Date: Mar 19, 2015
• Deposit Date: May 27, 2015
• Publicly Available Date: May 27, 2015
• Journal: PLoS ONE
• Electronic ISSN: 1932-6203
• Publisher: Public Library of Science
• Peer Reviewed: Peer Reviewed
• Volume: 10
• Issue: 3
• Article Number: 0118900
• DOI: https://doi.org/10.1371/journal.pone.0118900
• Keywords: factor analysis, surveys, Likert systems; ; eigenvalues; principal component analysis; survey data; ordered categorical data; applied statistics; latent variables; factor retention criteria
• Public URL: https://nottingham-repository.worktribe.com/output/747179
• Publisher URL: http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118900
• Additional Information: Article is based on simulated data; all scripts (in R) to generate and analyse the data are available through the website of PLOS One