Bayesian Factor Analysis for Mixed Ordinal and Continuous Responses
Open accessAbstract
Many situations exist in which a latent construct has both ordinal and continuous indicators. This presents a problem for the applied researcher because standard measurement models are not designed to accommodate mixed ordinal and continuous data. I address this problem by formulating a measurement model that is appropriate for such mixed multivariate responses. This model unifies standard normal theory factor analysis and item response theory models for ordinal data. I detail a Markov chain Monte Carlo algorithm for model fitting. I apply the model to cross-national data on political-economic risk and find that the model works well. Software for fitting this model is publicly available in the MCMCpack(Martin and Quinn 2004, “MCMCpack 0.4–8”)R package.
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The State Democracy Index uses Bayesian factor analysis for mixed data because the democracy indicators may be binary, ordinal, or continuous.
“In particular, I use Bayesian factor analysis for mixed data (Quinn 2004) because the democracy indicators may be binary (e.g., same-day voter registration), ordinal (e.g., disenfranchisement of all, some, or no felons), or continuous (e.g., legislative district efficiency gap).”
From Laboratories of Democratic Backsliding (2023) · cites this paper as Quinn 2004
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Cites
Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013) · doi:10.1201/b16018 · Cited by 27,276 · see citing works
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Research works printed but not linked: 12
- Albert, James H., and Siddhartha Chib. 1993. ''Bayesian Analysis of Binary and Polychotomous Response Data.'' Journal of the American Statistical Association 88:669-679.
- Beck, Thorsten, George Clarke, Alberto Groff, Philip Keefer, and Patrick Walsh. 2001. ''New Tools and New Tests in Comparative Political Economy: The Database of Political Institutions.'' World Bank Economic Review 15:165-176.
- Clinton, Joshua, Simon Jackman, and Douglas Rivers. 2004. ''The Statistical Analysis of Roll Call Voting: A Unified Approach.'' American Political Science Review 98:355-370.
- Green, Donald P., and Jack Citrin. 1994. ''Measurement Error and the Structure of Attitudes: Are Positive and Negative Judgements Opposites?'' American Journal of Political Science 38:256-281.
- Ihaka, Ross, and Robert Gentleman. 1996. ''R: A Language for Data Analysis and Graphics.'' Journal of Computational and Graphical Statistics 5:299-314.
- Jackman, Simon. 2000. ''Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo.'' American Journal of Political Science 44:375-404.
- Johnson, Valen, and James Albert. 1999. Ordinal Data Modeling. New York: Springer.
- Lawley, D. N. 1967. ''Some New Results in Maximum Likelihood Factor Analysis.'' Proceedings of the Royal Society of Edinburgh A 67:256-264.
- North, Douglass C., and Barry R. Weingast. 1989. ''Constituents and Commitment: The Evolution of Institutions Governing Public Choice in Seventeenth Century England.'' Journal of Economic History 49:803-832.
- Robert, Christian P., and George Casella. 1999. Monte Carlo Statistical Methods. New York: Springer.
- Sobel, Andrew C. 1999. State Institutions, Private Incentives, Global Capital. Ann Arbor: University of Michigan Press.
- Tanner, M. A., and W. Wong. 1987. ''The Calculation of Posterior Distributions by Data Augmentation.'' Journal of the American Statistical Association 82:528-550.
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Laboratories of Democratic Backsliding
GRUMBACH, J. M. (2023) · American Political Science Review · doi:10.1017/s0003055422000934 · Cited by 135 · see citing works
“In particular, I use Bayesian factor analysis for mixed data (Quinn 2004) because the democracy indicators may be binary (e.g., same-day voter registration), ordinal (e.g., disenfranchisement of all, some, or no felons), or continuous (e.g., legislative district efficiency gap).”
Method
- Authors
- Quinn, K. M.
- Affiliations
- Harvard University (US)
- Corresponding author
- Quinn, Kevin M.
- ORCID
- Quinn, Kevin M.
- Venue
- Political Analysis
- Publisher
- Cambridge University Press (CUP)
- Published
- 2004
- Volume
- 12
- Issue
- 4
- Pages
- 338-353
- ISSN
- 1047-1987 (ISSN-L)
- 1476-4989
- OpenAlex
- W2113779710
- Cited by
- 282
- References
- 1
- Citations by year
- 2026: 6 · 2025: 35 · 2024: 21 · 2023: 5 · 2022: 6 · 2021: 29 · 2020: 10 · 2019: 38 · 2018: 5 · 2017: 15 · 2016: 13 · 2015: 10 · 2014: 12 · 2013: 13 · 2012: 11
- FWCI
- 13.20
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Political Analysis (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Berkley Law Scholarship Repository (University of California, Berkeley) (submittedVersion)
- Funders
- National Science Foundation (0350613)
- 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 › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Keywords
- Bayesian factor analysis, measurement model, item response theory, latent constructs, Markov chain Monte Carlo, cross-country data
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