Recovering Transitions From Repeated Cross-Sectional Samples
Abstract
This paper proposes a dynamic Markov model for the estimation of binary state-to-state transition probabilities from a sequence of independent cross-sectional samples. It discusses parameter estimation and inference using maximum likelihood (ML) methodology. The model is illustrated by the application of a three-wave panel study on pupils’ interest in learning physics. These data encompass more information than what is used to estimate the model, but this surplus information allows us to assess the accuracy and the precision of the transition estimates. Bootstrap and Bayesian simulations are used to evaluate the accuracy and the precision of the ML estimates. To mimic genuine cross-sectional data, samples of independent observations randomly drawn from the panel are also analyzed.
References
(1985). Estimating gross labor-force flows. Journal of Business and Economic Statistics, 3, 254–283.
(1995). Cross-level inference. Chicago, Ill: University of Chicago Press.
(1992). A survey of exact inference for contingency tables. Statistical Science, 7, 131–153.
(1947). Significance tests for 2 × 2 tables. Biometrika, 34, 123–138.
(1975). Discrete multivariate analysis: Theory and practice. Cambridge, MA: MIT Press.
(2000). Inferring latent brand dependencies. Journal of Marketing Research, 37, 72–87.
(2001). Simple methods for ecological inference in 2 × 2 tables. Journal of the Royal Statistical Society, Series A, 164, 175–192.
(2002). Regressions, short and long. Econometrica, 70, 357–368.
(1997). Bootstrap methods and their application. Cambridge, MA: Cambridge University Press.
(2003). Bayesian inference in incomplete multi-way tables. Durham, NC: Institute of Statistics and Decision Sciences, Duke University.
(1993). An introduction to the bootstrap. New York: Chapman & Hall.
(2008). Information loss for 2 × 2 tables with missing cell counts: Binomial case. Statistica Neerlandica, 62, 239–254.
(1997). Confidentiality and disclosure limitation methodology. Challenges for national statistics and statistical research. Pittsburgh, PA: Department of Statistics, Carnegie Mellon University.
(1997). Specification and testing of Markov chain models: An application to convergence in the European Union. Oxford Bulletin of Economics and Statistics, 59, 385–403.
(1935). The logic of inductive inference (with discussion). Journal of the Royal Statistical Society, 98, 39–82.
(1996). Maximum entropy econometrics. Robust estimation with limited data. New York: Wiley.
(1994). Recovering information from incomplete or partial multisectoral economic data. Review of Economics and Statistics, 76, 541–549.
(1989). Do the marginal totals of a contingency table contain information regarding the table proportions? Communications in Statistics – Theory and Methods, 18, 147–156.
(1986). Maximum likelihood estimation of the parameters of the bivariate binomial distribution. Communication in Statistics – Theory and Methods, 15, 747–754.
(1996). Estimating transition probabilities from aggregate samples augmented by haphazard recaptures. Biometrics, 52, 625–638.
(2003). An information theoretic approach to ecological estimation and inference. In , Ecological inference. New methodological strategies (pp. 162–187). New York: Cambridge University Press.
(1984). Least squares estimation of transition probabilities from aggregate data. Canadian Journal of Statistics, 12, 169–182.
(1985). The analysis of panel data under a Markovian assumption. Journal of the American Statistical Association, 80, 863–871.
(2002). Information-based estimators for the non-stationary transition probability matrix: An application to the Danish pork industry. Journal of Econometrics, 107, 275–290.
(1981). Estimation of time-independent Markov processes with aggregate data: A comparison of techniques. Econometrica, 49, 517–518.
(1984). Hypothesis tests for Markov process models estimated from aggregate frequency data. Journal of the American Statistical Association, 79, 922–928.
(1997). A solution to the ecological inference problem. Reconstructing individual behavior from aggregate data. Cambridge, MA: Cambridge University Press.
(2003). Ecological inference. New methodological strategies. New York: Cambridge University Press.
(1992). Bivariate discrete distributions. New York: Marcel Dekker.
(1984). The information in aggregate data from Markov chains. Biometrika, 71, 419–430.
(1970). Estimating the parameters of the Markov probability model from aggregate time series data. Amsterdam: North-Holland.
(1990). Some results on the estimation of a higher order Markov chain. Communications in Statistics. Part B. Simulation and Computation, 19, 363–380.
(1977). Estimation of time-varying Markov processes with aggregate data. Econometrica, 45, 183–198.
(1995). Individual choice and ecological analysis. Pasadena, CA: California Institute of Technology.
(1992). Generalized linear models (2nd ed.). London: Chapman & Hall.
(1990). The effect of the U.S. welfare system on marital status. Journal of Public Economics, 41, 101–124.
(1993). Identification and estimation of dynamic models with a time series of repeated cross-sections. Journal of Econometrics, 59, 99–123.
(2002). Bayesian estimation of transition probabilities from repeated cross sections. Statistica Neerlandica, 56, 23–33.
(2001). Estimating transition probabilities from a time series of repeated cross sections. Statistica Neerlandica, 55, 248–261.
(2002). Inferring transition probabilities from repeated cross sections. Political Analysis, 10, 113–133.
(2003). Ecological panel inference from repeated cross sections. In , Ecological inference. New methodological strategies (pp. 188–205). New York: Cambridge University Press.
(1977). The marginal totals of a 2 × 2 table. Biometrika, 64, 37–42.
(2000). Ecological correlation studies. In , Spatial epidemiology. Methods and applications (pp. 205–220). Oxford: Oxford University Press.
(1998). Reconstruction of contingency tables with missing data. Durham, NC: Institute of Statistics and Decision Sciences, Duke University.
(1999). Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. Journal of Educational and Behavioral Statistics, 24, 179–207.
(2003). Prior and likelihood choices in the analysis of ecological inference , Ecological inference. New methodological strategies (pp. 13–50). New York: Cambridge University Press.
(1997). On the exact convolution of discrete random variables. Applied Mathematics and Computation, 83, 69–77.
(1995). Technical change and the structure of production. A nonstationary Markov analysis. European Review of Agricultural Economics, 22, 41–60.
