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

van der Eijk, Cees; Rose, Jonathan

Authors

Jonathan Rose jonathan.rose@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date Mar 19, 2015
Journal PLoS ONE
Electronic ISSN 1932-6203
Publisher Public Library of Science
Peer Reviewed Peer Reviewed
Volume 10
Issue 3
Article Number 0118900
APA6 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), doi:10.1371/journal.pone.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
Publisher URL http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118900
Copyright Statement Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0
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

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://creativecommons.org/licenses/by/4.0





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