Abstract
The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.
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Adams, J. D. (1980). Personal wealth transfers.Quarterly Journal of Economics, 95, 159–179.
Aitkin, M., & Wilson, J. (1980). Mixture models, outliers, and the EM algorithm.Technometrics, 22, 325–331.
Aitkin, M., & Rubin, D. B. (1985). Estimation and hypothesis testing in finite mixture models.Journal of the Royal Statistical Society, Series B, 47, 67–75.
Akaike, H. (1974). A new look at statistical model identification.IEEE Transactions on Automatic Control, 6, 716–723.
Amemiya, T. (1984). Tobit models: A survey.Journal of Econometrics, 24, 3–61.
Amemiya, T. (1985).Advanced econometrics. Cambridge, MA: Harvard University Press.
Ashenfelter, O., & Ham, J. (1979). Education, unemployment, and earnings.Journal of Political Economy, 87, S99-S116.
Baba, V. (1990). Methodological issues in modeling absence: A comparison of least squares and tobit analyses.Journal of Applied Psychology, 75, 428–432.
Berndt, E. K., Hall, B. H., & Hausman, J. A. (1974). Estimation and inference in non-linear structural models.Annals of Economic and Social Measurement, 3, 653–665.
Blattberg, R. C., & Neslin, S. A. (1990).Sales promotion: Concepts, methods, and strategies. Englewood Cliffs, NJ: Prentice Hall.
Bozdogan, H. (1983).Determining the number of component clusters in standard multivariate normal mixture models using model-selection criterion (Technical Report # VIC/DQM/A83-1). Washington, DC: Army Research Office.
Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extension.Psychometrika, 52, 345–370.
Bozdogan, H. (1991, June).Choosing the number of component clusters in the mixture model using a new information theoretic complexity criterion of the inverse Fisher information matrix. Conference paper presented at the 1991 joint meeting of the Classification and Psychometric Societies, Rutgers University, New Brunswick, New Jersey.
Bozdogan, H., & Sclove, S. L. (1984). Multi-sample cluster analysis using Akaike's information criterion.Annals of the Institute of Statistical Mathematics, 36, 163–180.
Bucklin, R. E., & J. M. Lattin (1991). A two-state model of purchase incidence and branch choice.Marketing Science, 10, 24–39.
Cobb, C. J., & Hoyer, W. D. (1986). Planned versus impulse purchase behavior.Journal of Retailing, 62, 384–409.
Dayton, C. M., & MacReady, G. B. (1988). Concomitant-variable latent class models.Journal of the American Statistical Association, 83, 173–178.
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood estimation from incomplete data via the E-M algorithm.Journal of Royal Statistical Society, Series B, 39, 1–38.
DeSarbo, W. S., & Cron, W. L. (1988). A maximum likelihood methodology for clusterwise linear regression.Journal of Classification, 5, 249–282.
De Soete, G., & DeSarbo, W. S. (1990). A latent class probit model for analyzing pick any/N data.Journal of Classification, 8, 45–64.
Dynkin, E. B. (1961). Necessary and sufficient statistics for a family of probability distributions.Selected translations in mathematical statistics and probability (pp. 17–40) Providence, RI: American Mathematical Society.
Elrod, T., & Winer, R. S. (1982). An empirical evaluation of aggregation approaches for developing market segments.Journal of Marketing, 46, 65–74.
Fair, R. (1978). A theory of extramarital affairs.Journal of Political Economy, 86, 45–61.
Fisher, G. A., & Tesler, R. C. (1986). Family bonding of the mentally ill: An analysis of family visits with residences of board and care homes.Journal of Health and Social Behavior, 27, 236–249.
Greene, W. H. (1990).Econometric analysis. New York: Macmillan.
Greene, W. H., & Quester, A. (1982). Divorce risk and wives' labor supply behavior.Social Science Quarterly, 63, 16–27.
Gross, A. L. (1980). A maximum likelihood approach to test validation with missing and censored dependent variables.Psychometrika, 55, 553–549.
Hoyer, W. D. (1984). An examination of consumer decision-making for a common repeat purchase product.Journal of Consumer Research, 11, 822–829.
Inman, J. J., McAlister, L., & Hoyer, W. D. (1990). Promotion signal: Proxy for a price cut?Journal of Consumer Research, 17, 74–81.
Kinsey, J. (1981). Determinants of credit card accounts: An application of tobit analysis.Journal of Consumer Research, 8, 172–182.
Maddala, G. S. (1983).Limited dependent and qualitative variables in econometrics. New York: Cambridge University Press.
McLachlan, G. J., & Basford, K. E. (1988).Mixture models: Inference and applications to clustering. New York: Marcel Dekker.
Moore, W. L. (1980). Levels of aggregation in conjoint analysis: An empirical comparison.Journal of Marketing Research, 17, 516–523.
Narasimhan, C. (1984). A price discrimination theory of coupons.Marketing Science, 3, 128–146.
Olsen, R. J. (1978). Note on the uniqueness of the maximum likelihood estimator for the tobit model.Econometrica, 46, 1211–1215.
Park, W. C., Iyer, E. S., & Smith, D. C. (1989). The effects of situational factors on in-store grocery shopping behavior: The role of store environment and time available for shopping.Journal of Consumer Research, 15, 422–433.
Quandt, R., & Ramsey, J. (1978). Estimating mixtures of normal distributions and switching regressions.Journal of the American Statistical Association, 73, 730–752.
Rissanen, J. (1989).Stochastic complexity in statistical inquiry. Teaneck, NJ: World Scientific Publications.
Schmee, J., & Hahn, G. J. (1979). A simple method for regression analysis with censored data.Technometrics, 21, 417–432.
Sclove, S. L. (1977). Population mixture models and clustering algorithms.Communications in Statistics, Series A, 6, 417–434.
Sclove, S. L. (1983). Application of the conditional population-mixture model to image segmentation.IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-5, 428–433.
Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis.Psychometrika, 52, 333–343.
Teachman, J. D. (1980). Analysis of population diversity.Sociological Methods and Research, 8, 341–362.
Teicher, H. (1961). Identifiability of mixtures.Annals of Mathematical Statistics, 32, 244–248.
Teicher, H. (1963). Identifiability of finite mixtures.Annals of Mathematical Statistics, 34, 1265–1269.
Tellis, G. J. (1988). Advertising exposure, loyalty, and brand purchase: A two-stage model of choice.Journal of Marketing Research, 25, 134–144.
Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985).Statistical analysis of finite mixture distributions. New York: Wiley & Sons.
Tobin, J. (1958). Estimation of relationship for limited dependent variables.Econometrica, 26, 24–36.
Windham, M. P., & Cutler, A. (1991, June).Information ratios for validating cluster analyses. Conference paper presented at the 1991 joint meeting of the Classification and Psychometric Societies, Rutgers University, New Brunswick, New Jersey.
Witte, A. D. (1980). Estimating the economic model for crime with individual data.Quarterly Journal of Econometrics, 94, 57–84.
Yakowitz, S. J. (1970). Unsupervised learning and the identification of finite mixtures.IEEE Transactions Information Theory and Control, IT-16, 330–338.
Yakowitz, S. J., & Spragins, J. D. (1968). On the identifiability of finite mixtures.Annals of Mathematical Statistics, 39, 209–214.
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Jedidi, K., Ramaswamy, V. & Desarbo, W.S. A maximum likelihood method for latent class regression involving a censored dependent variable. Psychometrika 58, 375–394 (1993). https://doi.org/10.1007/BF02294647
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DOI: https://doi.org/10.1007/BF02294647