Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation
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...
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| Format: | Article |
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Public Library of Science
2015
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| Online Access: | https://eprints.nottingham.ac.uk/28820/ |
| _version_ | 1848793650536906752 |
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| author | van der Eijk, Cees Rose, Jonathan |
| author_facet | van der Eijk, Cees Rose, Jonathan |
| author_sort | van der Eijk, Cees |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:03:40Z |
| format | Article |
| id | nottingham-28820 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:03:40Z |
| publishDate | 2015 |
| publisher | Public Library of Science |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-288202020-05-04T17:04:24Z https://eprints.nottingham.ac.uk/28820/ Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation van der Eijk, Cees Rose, Jonathan 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. Public Library of Science 2015-03-19 Article PeerReviewed van der Eijk, Cees and Rose, Jonathan (2015) Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation. PLoS ONE, 10 (3). 0118900/1-0118900/31. ISSN 1932-6203 factor analysis surveys Likert systems eigenvalues principal component analysis survey data ordered categorical data applied statistics latent variables factor retention criteria http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0118900 doi:10.1371/journal.pone.0118900 doi:10.1371/journal.pone.0118900 |
| spellingShingle | factor analysis surveys Likert systems eigenvalues principal component analysis survey data ordered categorical data applied statistics latent variables factor retention criteria van der Eijk, Cees Rose, Jonathan Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| title | Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| title_full | Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| title_fullStr | Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| title_full_unstemmed | Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| title_short | Risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| title_sort | risky business: factor analysis of survey data – assessing the probability of incorrect dimensionalisation |
| topic | factor analysis surveys Likert systems eigenvalues principal component analysis survey data ordered categorical data applied statistics latent variables factor retention criteria |
| url | https://eprints.nottingham.ac.uk/28820/ https://eprints.nottingham.ac.uk/28820/ https://eprints.nottingham.ac.uk/28820/ |