When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions.

Rhemtulla, Mijke; Brosseau-Liard, Patricia É.; Savalei, Victoria

doi:10.1037/a0029315

Cited by 2,816Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceStatistical Distribution Estimation and Applications

When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions.

Rhemtulla, Mijke, Brosseau-Liard, Patricia É., Savalei, Victoria·2012·Psychological Methods

DOI 10.1037/a0029315

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Abstract

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category thresholds. Results revealed that factor loadings and robust standard errors were generally most accurately estimated using cat-LS, especially with fewer than 5 categories; however, factor correlations and model fit were assessed equally well with ML. Cat-LS was found to be more sensitive to sample size and to violations of the assumption of normality of the underlying continuous variables. Normal theory ML was found to be more sensitive to asymmetric category thresholds and was especially biased when estimating large factor loadings. Accordingly, we recommend cat-LS for data sets containing variables with fewer than 5 categories and ML when there are 5 or more categories, sample size is small, and category thresholds are approximately symmetric. With 6-7 categories, results were similar across methods for many conditions; in these cases, either method is acceptable.

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Variables with five or more categories can be treated as continuous with negligible drawbacks.
“Due to previous work showing that variables containing five or more categories can be treated as continuous with negligible drawbacks, we treated both measures as continuous52.”
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Authors: Rhemtulla, M., Brosseau-Liard, P. É., & Savalei, V.
Affiliations: University of Kansas (US)
University of British Columbia (CA)
ORCID: Rhemtulla, Mijke
Brosseau-Liard, Patricia É.
Savalei, Victoria
Venue: Psychological Methods
Publisher: American Psychological Association (APA)
Published: 2012-09
Volume: 17
Issue: 3
Pages: 354-373
ISSN: 1082-989X (ISSN-L)
1939-1463
DOI: 10.1037/a0029315
OpenAlex: W1970325005
Cited by: 2,816
References: 64
Citations by year: 2026: 599 · 2025: 297 · 2024: 231 · 2023: 267 · 2022: 243 · 2021: 220 · 2020: 196 · 2019: 182 · 2018: 157 · 2017: 162 · 2016: 104 · 2015: 69 · 2014: 64 · 2013: 21 · 2012: 3
FWCI: 66.46
Type: journal article
Language: en
Open access: closed
Locations: Psychological Methods (publishedVersion)
PubMed (publishedVersion)
Funders: Social Sciences and Humanities Research Council of Canada
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
Keywords: robust estimation, confirmatory factor analysis, ordinal variables, small sample size, non-normality, factor loadings, factor correlation, model fit, robust standard errors
MeSH terms: Factor Analysis, Statistical, Humans, Models, Statistical, Bias, Likelihood Functions, Least-Squares Analysis, Sample Size

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