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Inferring Transition Probabilities from Repeated Cross Sections

  • Ben Pelzer (a1), Rob Eisinga (a2) and Philip Hans Franses (a3)
Abstract

This paper discusses a nonstationary, heterogeneous Markov model designed to estimate entry and exit transition probabilities at the micro level from a time series of independent cross-sectional samples with a binary outcome variable. The model has its origins in the work of Moffitt and shares features with standard statistical methods for ecological inference. We outline the methodological framework proposed by Moffitt and present several extensions of the model to increase its potential application in a wider array of research contexts. We also discuss the relationship with previous lines of related research in political science. The example illustration uses survey data on American presidential vote intentions from a five-wave panel study conducted by Patterson in 1976. We treat the panel data as independent cross sections and compare the estimates of the Markov model with both dynamic panel parameter estimates and the actual observations in the panel. The results suggest that the proposed model provides a useful framework for the analysis of transitions in repeated cross sections. Open problems requiring further study are discussed.

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Takeshi Amemiya . 1985. Advanced Econometrics. Oxford: Basil Blackwell.

R. L. Chambers , and D. G. Steel 2001. “Simple Methods for Ecological Inference in 2 × 2 Tables.” Journal of the Royal Statistical Society. Series A 164:175192.

Otis Dudley Duncan , and Beverly Davis . 1953. “An Alternative to Ecological Correlation.” American Sociological Review 18:665666.

Charles H. Franklin 1989. “Estimation across Data Sets: Two-Stage Auxiliary Instrumental Variables Estimation (2SAIV).” Political Analysis 1:123.

D. L. Hawkins , and C. P. Han 2000. “Estimating Transition Probabilities from Aggregate Samples Plus Partial Transition Data.” Biometrics 56:848854.

J. D. Kalbfleish , and J. F. Lawless 1984. “Least Squares Estimation of Transition Probabilities from Aggregate Data.” Canadian Journal of Statistics 12:169182.

Ori Rosen , Wenxin Jiang, Gary King , and Martin Tanner . 2001. “Bayesian and Frequentist Inference for Ecological Inference: The R × C Case.” Statistica Neerlandica 55:133155.

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