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Reliable Inference in Highly Stratified Contingency Tables: Using Latent Class Models as Density Estimators

  • Drew A. Linzer (a1)
Abstract

Contingency tables are among the most basic and useful techniques available for analyzing categorical data, but they produce highly imprecise estimates in small samples or for population subgroups that arise following repeated stratification. I demonstrate that preprocessing an observed set of categorical variables using a latent class model can greatly improve the quality of table-based inferences. As a density estimator, the latent class model closely approximates the underlying joint distribution of the variables of interest, which enables reliable estimation of conditional probabilities and marginal effects, even among subgroups containing fewer than 40 observations. Though here focused on applications to public opinion, the procedure has a wide range of potential uses. I illustrate the benefits of the latent class model—based approach for greatly improved accuracy in estimating and forecasting vote preferences within small demographic subgroups using survey data from the 2004 and 2008 U.S. presidential election campaigns.

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Marisa A. Abrajano , R. Michael Alvarez , and Jonathan Nagler . 2008. The Hispanic Vote in the 2004 presidential election: insecurity and moral concerns. The Journal of Politics 70: 368–82.

Marisa A. Abrajano , R. Michael Alvarez , and Jonathan Nagler . 2008. The Hispanic Vote in the 2004 presidential election: insecurity and moral concerns. The Journal of Politics 70: 368–82.

Christopher H. Achen 2002. Toward a new political methodology: microfoundations and ART. Annual Review of Political Science 5: 423–50.

Christopher H. Achen 2002. Toward a new political methodology: microfoundations and ART. Annual Review of Political Science 5: 423–50.

Christopher H. Achen 2005. Let's put garbage-can regressions and garbage-can probits where they belong. Conflict Management and Peace Science 22: 327–39.

Christopher H. Achen 2005. Let's put garbage-can regressions and garbage-can probits where they belong. Conflict Management and Peace Science 22: 327–39.

Alan Agresti . 2002. Categorical data analysis. 2nd ed. Hoboken, NJ: John Wiley & Sons.

Alan Agresti . 2002. Categorical data analysis. 2nd ed. Hoboken, NJ: John Wiley & Sons.

Alan Agresti , James G. Booth , James P. Hobert , and Brian Caffo . 2000. Random-effects modeling of categorical response data. Sociological Methodology 30: 2780.

Alan Agresti , James G. Booth , James P. Hobert , and Brian Caffo . 2000. Random-effects modeling of categorical response data. Sociological Methodology 30: 2780.

Alan Agresti , and David B. Hitchcock 2005. Bayesian inference for categorical data analysis. Statistical Methods & Applications 14: 297330.

Alan Agresti , and David B. Hitchcock 2005. Bayesian inference for categorical data analysis. Statistical Methods & Applications 14: 297330.

J. Aitchison , and C. G. C. Aitken 1976. Multivariate binary discrimination by the kernel method. Biometrika 63: 413–20.

J. Aitchison , and C. G. C. Aitken 1976. Multivariate binary discrimination by the kernel method. Biometrika 63: 413–20.

Karen Bandeen-Roche , Diana L. Miglioretti , Scott L. Zeger , and Paul J. Rathouz 1997. Latent variable regression for multiple discrete outcomes. Journal of the American Statistical Association 92: 1375–86.

Karen Bandeen-Roche , Diana L. Miglioretti , Scott L. Zeger , and Paul J. Rathouz 1997. Latent variable regression for multiple discrete outcomes. Journal of the American Statistical Association 92: 1375–86.

William Berry , Jacqueline H. DeMeritt , and Justin Esarey . 2010. Testing for interaction in binary logit and probit models: is a product term essential? American Journal of Political Science 54: 248–66.

William Berry , Jacqueline H. DeMeritt , and Justin Esarey . 2010. Testing for interaction in binary logit and probit models: is a product term essential? American Journal of Political Science 54: 248–66.

Peter Congdon . 2005. Bayesian models for categorical data. Chichester, UK: John Wiley & Sons.

Peter Congdon . 2005. Bayesian models for categorical data. Chichester, UK: John Wiley & Sons.

Rodolfo O. de la Garza , and Jeronimo Cortina . 2007. Are Latinos Republicans but just don't know it? The Latino Vote in the 2000 and 2004 presidential elections. American Politics Research 35: 202–23.

Rodolfo O. de la Garza , and Jeronimo Cortina . 2007. Are Latinos Republicans but just don't know it? The Latino Vote in the 2000 and 2004 presidential elections. American Politics Research 35: 202–23.

Chris Fraley , and Adrian E. Raftery 2002. Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97: 611–31.

Chris Fraley , and Adrian E. Raftery 2002. Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97: 611–31.

Elizabeth S. Garrett , and Scott L. Zeger 2000. Latent class model diagnosis. Biometrics 56: 1055–67.

Elizabeth S. Garrett , and Scott L. Zeger 2000. Latent class model diagnosis. Biometrics 56: 1055–67.

M. Ghosh , and J. N. K. Rao 1994. Small area estimation: an appraisal. Statistical Science 9: 5576.

M. Ghosh , and J. N. K. Rao 1994. Small area estimation: an appraisal. Statistical Science 9: 5576.

Leo A. Goodman 1974a. The analysis of systems of qualitative variables when some of the variables are unobservable. Part I—a modified latent structure approach. The American Journal of Sociology 79: 1179–259.

Leo A. Goodman 1974a. The analysis of systems of qualitative variables when some of the variables are unobservable. Part I—a modified latent structure approach. The American Journal of Sociology 79: 1179–259.

Leo A. Goodman 1974b. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61: 215–31.

Leo A. Goodman 1974b. Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika 61: 215–31.

B. Grund 1993. Kernel estimators for cell probabilities. Journal of Multivariate Analysis 46: 283308.

B. Grund 1993. Kernel estimators for cell probabilities. Journal of Multivariate Analysis 46: 283308.

Jacques A. Hagenaars , and Allan L. McCutcheon 2002. Applied latent class analysis. New York: Cambridge University Press.

Jacques A. Hagenaars , and Allan L. McCutcheon 2002. Applied latent class analysis. New York: Cambridge University Press.

Peter Hall . 1981. On nonparametric multivariate binary discrimination. Biometrika 68: 287–94.

Peter Hall . 1981. On nonparametric multivariate binary discrimination. Biometrika 68: 287–94.

Steven G. Heeringa , Brady T. West , and Patricia A. Berglund 2010. Applied survey data analysis. Boca Raton, FL: Chapman and Hall.

Steven G. Heeringa , Brady T. West , and Patricia A. Berglund 2010. Applied survey data analysis. Boca Raton, FL: Chapman and Hall.

Guan-Hua Huang . 2005. Selecting the number of classes under latent class regression: a factor analytic analogue. Psychometrika 70: 325–45.

Guan-Hua Huang . 2005. Selecting the number of classes under latent class regression: a factor analytic analogue. Psychometrika 70: 325–45.

John Jackson . 1989. An errors-in-variables approach to estimating models with small area data. Political Analysis 1: 157–80.

John Jackson . 1989. An errors-in-variables approach to estimating models with small area data. Political Analysis 1: 157–80.

Jeffrey R. Lax , and Justin H. Phillips 2009. How should we estimate public opinion in the states? American Journal of Political Science 53: 107–21.

Jeffrey R. Lax , and Justin H. Phillips 2009. How should we estimate public opinion in the states? American Journal of Political Science 53: 107–21.

G. S. Maddala 1983. Limited-Dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press.

G. S. Maddala 1983. Limited-Dependent and Qualitative Variables in Econometrics. New York: Cambridge University Press.

Geoffrey J. McLachlan , and David Peel . 2000. Finite mixture models. New York: John Wiley & Sons.

Geoffrey J. McLachlan , and David Peel . 2000. Finite mixture models. New York: John Wiley & Sons.

Karen L. Nylund , Tihomi Asparouhov , and Bengt O. Muthén 2007. Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Structural Equation Modeling 14: 535–69.

Karen L. Nylund , Tihomi Asparouhov , and Bengt O. Muthén 2007. Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Structural Equation Modeling 14: 535–69.

David K. Park , Andrew Gelman , and Joseph Bafumi . 2004. Bayesian multilevel estimation with poststratification: state-level estimates from national polls. Political Analysis 12: 375–85.

David K. Park , Andrew Gelman , and Joseph Bafumi . 2004. Bayesian multilevel estimation with poststratification: state-level estimates from national polls. Political Analysis 12: 375–85.

J. N. K. Rao 2003. Small area estimation. Hoboken, NJ: John Wiley & Sons.

J. N. K. Rao 2003. Small area estimation. Hoboken, NJ: John Wiley & Sons.

Jeffrey S. Simonoff 1995. Smoothing categorical data. Journal of Statistical Planning and Inference 47: 4169.

Jeffrey S. Simonoff 1995. Smoothing categorical data. Journal of Statistical Planning and Inference 47: 4169.

D. M. Titterington 1980. A comparative study of kernel-based density estimates for categorical data. Technometrics 22: 259–68.

D. M. Titterington 1980. A comparative study of kernel-based density estimates for categorical data. Technometrics 22: 259–68.

Jeroen K. Vermunt , Joost R. Van Ginkel , L. Andries Van der Ark , and Klaas Sijtsma . 2008. Multiple imputation of incomplete categorical data using latent class analysis. Sociological Methodology 38: 369–97.

Jeroen K. Vermunt , Joost R. Van Ginkel , L. Andries Van der Ark , and Klaas Sijtsma . 2008. Multiple imputation of incomplete categorical data using latent class analysis. Sociological Methodology 38: 369–97.

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Political Analysis
  • ISSN: 1047-1987
  • EISSN: 1476-4989
  • URL: /core/journals/political-analysis
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