Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-19T00:36:55.680Z Has data issue: false hasContentIssue false
  • English
  • Français

Bayesian Factor Analysis for Mixed Ordinal and Continuous Responses

Published online by Cambridge University Press:  04 January 2017

Kevin M. Quinn
Kevin M. Quinn*
Affiliation:
Department of Government and CBRSS, 34 Kirkland Street, Harvard University, Cambridge, MA 02138. e-mail: kevin_quinn@harvard.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Research Article
Information
Political Analysis , Volume 12 , Issue 4: Special Issue on Bayesian Methods , Autumn 2004 , pp. 338 - 353
Copyright
Copyright © Society for Political Methodology 2004 

References

Albert, James H., and Chib, Siddhartha. 1993. “Bayesian Analysis of Binary and Polychotomous Response Data.” Journal of the American Statistical Association 88: 669–679.Google Scholar
Alvarez, Mike, Cheibub, José Antonio, Limongi, Fernando, and Przeworski, Adam. 1999. “ACLP Political and Economic Database.” (Available from http://www.ssc.upenn.edu/∼cheibub/data/.)Google Scholar
Beck, Thorsten, Clarke, George, Groff, Alberto, Keefer, Philip, and Walsh, Patrick. 2001. “New Tools and New Tests in Comparative Political Economy: The Database of Political Institutions.” World Bank Economic Review 15: 165–176.Google Scholar
Borner, Silvio, Brunetti, Aymo, and Weder, Beatrice. 1995. Political Credibility and Economic Development. New York: St. Martins.CrossRefGoogle Scholar
Clinton, Joshua, Jackman, Simon, and Rivers, Douglas. 2004. “The Statistical Analysis of Roll Call Voting: A Unified Approach.” American Political Science Review 98: 355–370.Google Scholar
Coplin, William D., ed. 2003. Political Risk Yearbook, 2003. East Syracuse, NY: Political Risk Services.Google Scholar
Cowles, M. K. 1996. “Accelerating Monte Carlo Markov Chain Convergence for Cumulative Link Generalized Linear Models.” Statistics and Computing 6: 101–111.Google Scholar
Gelman, Andrew, Carlin, John B., Stern, Hal S., and Rubin, Donald B. 2003. Bayesian Data Analysis, 2nd ed. London: Chapman & Hall.Google Scholar
Gill, Jeff. 2002. Bayesian Methods: A Social and Behavioral Sciences Approach. Boca Raton, FL: Chapman & Hall/CRC.Google Scholar
Green, Donald P., and Citrin, Jack. 1994. “Measurement Error and the Structure of Attitudes: Are Positive and Negative Judgements Opposites?” American Journal of Political Science 38: 256–281.Google Scholar
Henisz, Witold J. 2002a. “The Political Constraint Index (POLCON) Dataset.” (Available from http://www-management.wharton.upenn.edu/henisz/POLCON/ContactInfo.html.)Google Scholar
Henisz, Witold J. 2002b. Politics and International Investment: Measuring Risk and Protecting Profits. London: Edward Elgar.Google Scholar
Howell, Llewelyn D., and Coplin, William D., eds. 2001. The Handbook of Country and Political Risk Analysis, 3rd ed. East Syracuse, NY: Political Risk Services.Google Scholar
Ihaka, Ross, and Gentleman, Robert. 1996. ” R: A Language for Data Analysis and Graphics.” Journal of Computational and Graphical Statistics 5: 299–314.Google Scholar
Jackman, Simon. 2000. “Estimation and Inference via Bayesian Simulation: An Introduction to Markov Chain Monte Carlo.” American Journal of Political Science 44: 375–404.Google Scholar
Jöreskog, Karl G. 1969. “A General Approach to Confirmatory Maximum Likelihood Factor Analysis.” Psychometrika 34: 183–220.Google Scholar
Johnson, Valen, and Albert, James. 1999. Ordinal Data Modeling. New York: Springer.Google Scholar
Knack, Stephen, and Keefer, Philip. 1995. “Institutions and Economic Performance: Cross-Country Tests Using Alternative Institutional Measures.” Economics and Politics 7: 207–227.Google Scholar
Lawley, D. N. 1967. “Some New Results in Maximum Likelihood Factor Analysis.” Proceedings of the Royal Society of Edinburgh A 67: 256–264.Google Scholar
Lawley, D. N., and Maxwell, A. E. 1971. Factor Analysis as a Statistical Method. London: Butterworth.Google Scholar
Lopes, Hedibert Freitas, and West, Mike. 1999. “Model Uncertainty in Factor Analysis.” Discussion Paper No. 98–38, Durham, NC: Institute of Statistics and Decision Sciences, Duke University.Google Scholar
Marshall, Monty G., Gurr, Ted Robert, and Harff, Barbara. 2002. “State Failure Task Force Problem Set.” (Available from http://www.cidcm.umd.edu/inscr/stfail/index.htm.)Google Scholar
Martin, Andrew D., and Quinn, Kevin M. 2004. “MCMCpack 0.4–8.” (Available from http://mcmcpack.wustl.edu/.)Google Scholar
North, Douglass C., and Weingast, Barry R. 1989. “Constituents and Commitment: The Evolution of Institutions Governing Public Choice in Seventeenth Century England.” Journal of Economic History 49: 803–832.CrossRefGoogle Scholar
Robert, Christian P., and Casella, George. 1999. Monte Carlo Statistical Methods. New York: Springer.Google Scholar
Sobel, Andrew C. 1999. State Institutions, Private Incentives, Global Capital. Ann Arbor: University of Michigan Press.CrossRefGoogle Scholar
Tanner, M. A., and Wong, W. 1987. “The Calculation of Posterior Distributions by Data Augmentation.” Journal of the American Statistical Association 82: 528–550.Google Scholar
Treier, Shawn, and Jackman, Simon. 2003. “Democracy as a Latent Variable.” Unpublished manuscript, Stanford University.Google Scholar