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Bayesian Factor Analysis for Mixed Ordinal and Continuous Responses

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  • Quinn, Kevin M.

Abstract

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.

Suggested Citation

  • Quinn, Kevin M., 2004. "Bayesian Factor Analysis for Mixed Ordinal and Continuous Responses," Political Analysis, Cambridge University Press, vol. 12(4), pages 338-353.
    • Handle: RePEc:cup:polals:v:12:y:2004:i:04:p:338-353_00
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    Cited by:

    1. Rosenthal, Howard & Voeten, Erik, 2007. "Measuring legal systems," Journal of Comparative Economics, Elsevier, vol. 35(4), pages 711-728, December.
    2. Jason Y Wu, 2019. "A spatial valence model of political participation in China," Journal of Theoretical Politics, , vol. 31(2), pages 244-259, April.
    3. Michael Peress, 2013. "Candidate positioning and responsiveness to constituent opinion in the U.S. House of Representatives," Public Choice, Springer, vol. 156(1), pages 77-94, July.
    4. Simon Hug & Tobias Schulz, 2007. "Referendums in the EU’s constitution building process," The Review of International Organizations, Springer, vol. 2(2), pages 177-218, June.
    5. Kobayashi, Yoshiharu & Heinrich, Tobias & Bryant, Kristin A., 2021. "Public support for development aid during the COVID-19 pandemic," World Development, Elsevier, vol. 138(C).
    6. Brett V. Benson & Joshua D. Clinton, 2016. "Assessing the Variation of Formal Military Alliances," Journal of Conflict Resolution, Peace Science Society (International), vol. 60(5), pages 866-898, August.
    7. Samson B. Adebayo & Ludwig Fahrmeir & Christian Seiler & Christian Heumann, 2011. "Geoadditive Latent Variable Modeling of Count Data on Multiple Sexual Partnering in Nigeria," Biometrics, The International Biometric Society, vol. 67(2), pages 620-628, June.
    8. Matthew Dimick & Daniel Stegmueller, 2015. "The Political Economy of Risk and Ideology," SOEPpapers on Multidisciplinary Panel Data Research 809, DIW Berlin, The German Socio-Economic Panel (SOEP).
    9. Mónica D. Oliveira & Inês Mataloto & Panos Kanavos, 2019. "Multi-criteria decision analysis for health technology assessment: addressing methodological challenges to improve the state of the art," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 20(6), pages 891-918, August.
    10. Christopher Hare & Keith T. Poole, 2015. "Measuring ideology in Congress," Chapters, in: Jac C. Heckelman & Nicholas R. Miller (ed.), Handbook of Social Choice and Voting, chapter 18, pages 327-346, Edward Elgar Publishing.
    11. Elena A. Erosheva & S. McKay Curtis, 2017. "Dealing with Reflection Invariance in Bayesian Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 295-307, June.
    12. Julia Gray & Jonathan Slapin, 2012. "How effective are preferential trade agreements? Ask the experts," The Review of International Organizations, Springer, vol. 7(3), pages 309-333, September.
    13. R Joseph Huddleston, 2020. "Continuous recognition: A latent variable approach to measuring international sovereignty of self-determination movements," Journal of Peace Research, Peace Research Institute Oslo, vol. 57(6), pages 789-800, November.
    14. Damien McParland & Isobel Claire Gormley, 2016. "Model based clustering for mixed data: clustMD," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 155-169, June.
    15. Jule Krüger & Ragnhild Nordås, 2020. "A latent variable approach to measuring wartime sexual violence," Journal of Peace Research, Peace Research Institute Oslo, vol. 57(6), pages 728-739, November.
    16. Scott J. LaCombe, 2021. "Measuring Institutional Design in U.S. States," Social Science Quarterly, Southwestern Social Science Association, vol. 102(4), pages 1511-1533, July.
    17. Christopher Wratil & Sara B Hobolt, 2019. "Public deliberations in the Council of the European Union: Introducing and validating DICEU," European Union Politics, , vol. 20(3), pages 511-531, September.
    18. Christopher J Fariss & James Lo, 2020. "Innovations in concepts and measurement for the study of peace and conflict," Journal of Peace Research, Peace Research Institute Oslo, vol. 57(6), pages 669-678, November.
    19. Parrish Bergquist & Christopher Warshaw, 2023. "How climate policy commitments influence energy systems and the economies of US states," Nature Communications, Nature, vol. 14(1), pages 1-9, December.

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