Abstract
Ordered categorical panel data is modeled assuming an underlying continuous-time finite-space Markov chain. The tridiagonal form of the intensity matrix renders the implementation of the maximum likelihood method more stable numerically. The intensities describe rates of transitions between adjacent categories producing a very natural interpretation.
References
Agresti, A. (1989) “A Survey of models for repeated ordered categorical response data”, Statistics in Medicine, vol. 8, pp. 1209–1224.
Anderson, T. & Goodman, L. (1956) “Statistical Inference about Markov Chains”, Annals of Mathematical Statistics vol. 28, pp. 89-110.
Becker, R.; Chambers, J. & Wilks, A. (1988) The New S Language, Wadsworth & Brooks Cole Advanced Books & Software.
Bentley, D. & Cooke, K. (1973) Linear Algebra with Differential Equations. Holt, Rinehart andWinston, Inc.,
Billinsgsley, P. (1961) ”Statistical methods in Markov chains”, University of Chicago.
Chambers, J. & Hastie, T. Statistical Models in S. Wadsworth & Brooks Cole Advanced Books & Software.
Cox, D. & Miller, H. (1968) The of Stochastic Processes. John Wiley & Sons Inc., N.Y.
Fahrmeir, L. & Kaufmann, H.(1987) “Regression models for non-stationary categorical timeseries”, Journal of Time Series Analysis, vol. 8, # 2, pp. 147-160.
Goodman, L. (1962) “Statistical Methods for analyzing processes of change”, American Journalof Sociology, vol. 68, pp. 57–78.
G¨öttlein, A. & Pruscha, H. (1992) “Ordinal time series models with application to forest damagedata”, pp. 113-118.
Hagenaars, J. (1990) Categorical Longitudinal data. Sage Publications, pp. 13-87, 147-183. Horn & Johnson (1985), Matrix Algebra.
Kalbfleisch, J.& Lawless, J. (1985) “The Analysis of Panel Data under a Markov assumption”, Journal of the American Statistical Association vol. 80, #392, pp. 863-871.
Kaufmann, H. (1987) “Regression models for nonstationary categorical time series: asymptotic estimation theory”, The Annals of Statistics, vol. 15, #1, pp. 79-98.
McCullagh, P. (1980) “Regression models for ordinal data”, Journal R. Statistical Society, series B, vol. 42,# 2, pp. 109-142.
Sweeting, T. (1980) “Uniform asymptotic normality of the maximum likelihood estimator”, The Annals of Statistics, vol. 8, pp. 1375-1381.
Ware, J.; Lipsitz, S. & Speizer, F. (1988) “Issues in the analysis of repeated categorical out-comes”, Statistics in Medicine, vol. 7, pp. 95-107.