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A Maximum Likelihood Method for Latent Class Regression Involving a Censored Dependent Variable

Published online by Cambridge University Press:  01 January 2025

Kamel Jedidi ,
Venkatram Ramaswamy  and
Wayne S. Desarbo
Kamel Jedidi*
Affiliation:
Marketing Department, Graduate School of Business, Columbia University
Venkatram Ramaswamy
Affiliation:
Marketing Department, School of Business Administration, University of Michigan
Wayne S. Desarbo
Affiliation:
Marketing and Statistics Departments School of Business Administration, University of Michigan
*
Requests for reprints should be sent to Kamel Jedidi, Marketing Department, Graduate School of Business, Columbia University, New York, NY 10027.
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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.

Keywords

censored regressionlatent class analysismaximum likelihood estimationconsumer psychology
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 3 , September 1993 , pp. 375 - 394
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

We thank the Editor and referees for their insightful comments and suggestions.

References

Adams, J. D. (1980). Personal wealth transfers. Quarterly Journal of Economics, 95, 159–179.CrossRefGoogle Scholar
Aitkin, M., & Wilson, J. (1980). Mixture models, outliers, and the EM algorithm. Technometrics, 22, 325–331.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Akaike, H. (1974). A new look at statistical model identification. IEEE Transactions on Automatic Control, 6, 716–723.CrossRefGoogle Scholar
Amemiya, T. (1984). Tobit models: A survey. Journal of Econometrics, 24, 3–61.CrossRefGoogle Scholar
Amemiya, T. (1985). Advanced econometrics, Cambridge, MA: Harvard University Press.Google Scholar
Ashenfelter, O., & Ham, J. (1979). Education, unemployment, and earnings. Journal of Political Economy, 87, S99–S116.CrossRefGoogle Scholar
Baba, V. (1990). Methodological issues in modeling absence: A comparison of least squares and tobit analyses. Journal of Applied Psychology, 75, 428–432.CrossRefGoogle Scholar
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.Google Scholar
Blattberg, R. C., & Neslin, S. A. (1990). Sales promotion: Concepts, methods, and strategies, Englewood Cliffs, NJ: Prentice Hall.Google Scholar
Bozdogan, H. (1983). Determining the number of component clusters in standard multivariate normal mixture models using model-selection criterion, Washington, DC: Army Research Office.Google Scholar
Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extension. Psychometrika, 52, 345–370.CrossRefGoogle Scholar
Bozdogan, H. (1991). Choosing the number of component clusters in the mixture model using a new information theoretic complexity criterion of the inverse Fisher information matrix, New Brunswick, New Jersey: Rutgers University.Google Scholar
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.CrossRefGoogle Scholar
Bucklin, R. E., & Lattin, J. M. (1991). A two-state model of purchase incidence and branch choice. Marketing Science, 10, 24–39.CrossRefGoogle Scholar
Cobb, C. J., & Hoyer, W. D. (1986). Planned versus impulse purchase behavior. Journal of Retailing, 62, 384–409.Google Scholar
Dayton, C. M., & MacReady, G. B. (1988). Concomitant-variable latent class models. Journal of the American Statistical Association, 83, 173–178.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
DeSarbo, W. S., & Cron, W. L. (1988). A maximum likelihood methodology for clusterwise linear regression. Journal of Classification, 5, 249–282.CrossRefGoogle Scholar
De Soete, G., & DeSarbo, W. S. (1990). A latent class probit model for analyzing pick any/N data. Journal of Classification, 8, 45–64.CrossRefGoogle Scholar
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.Google Scholar
Elrod, T., & Winer, R. S. (1982). An empirical evaluation of aggregation approaches for developing market segments. Journal of Marketing, 46, 65–74.CrossRefGoogle Scholar
Fair, R. (1978). A theory of extramarital affairs. Journal of Political Economy, 86, 45–61.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Greene, W. H. (1990). Econometric analysis, New York: Macmillan.Google Scholar
Greene, W. H., & Quester, A. (1982). Divorce risk and wives' labor supply behavior. Social Science Quarterly, 63, 16–27.Google Scholar
Gross, A. L. (1980). A maximum likelihood approach to test validation with missing and censored dependent variables. Psychometrika, 55, 533–549.CrossRefGoogle Scholar
Hoyer, W. D. (1984). An examination of consumer decision-making for a common repeat purchase product. Journal of Consumer Research, 11, 822–829.CrossRefGoogle Scholar
Inman, J. J., McAlister, L., & Hoyer, W. D. (1990). Promotion signal: Proxy for a price cut?. Journal of Consumer Research, 17, 74–81.CrossRefGoogle Scholar
Kinsey, J. (1981). Determinants of credit card accounts: An application of tobit analysis. Journal of Consumer Research, 8, 172–182.CrossRefGoogle Scholar
Maddala, G. S. (1983). Limited dependent and qualitative variables in econometrics, New York: Cambridge University Press.CrossRefGoogle Scholar
McLachlan, G. J., & Basford, K. E. (1988). Mixture models: Inference and applications to clustering, New York: Marcel Dekker.Google Scholar
Moore, W. L. (1980). Levels of aggregation in conjoint analysis: An empirical comparison. Journal of Marketing Research, 17, 516–523.CrossRefGoogle Scholar
Narasimhan, C. (1984). A price discrimination theory of coupons. Marketing Science, 3, 128–146.CrossRefGoogle Scholar
Olsen, R. J. (1978). Note on the uniqueness of the maximum likelihood estimator for the tobit model. Econometrica, 46, 1211–1215.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Quandt, R., & Ramsey, J. (1978). Estimating mixtures of normal distributions and switching regressions. Journal of the American Statistical Association, 73, 730–752.CrossRefGoogle Scholar
Rissanen, J. (1989). Stochastic complexity in statistical inquiry, Teaneck, NJ: World Scientific Publications.Google Scholar
Schmee, J., & Hahn, G. J. (1979). A simple method for regression analysis with censored data. Technometrics, 21, 417–432.CrossRefGoogle Scholar
Sclove, S. L. (1977). Population mixture models and clustering algorithms. Communications in Statistics, Series A, 6, 417–434.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Sclove, S. L. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333–343.CrossRefGoogle Scholar
Teachman, J. D. (1980). Analysis of population diversity. Sociological Methods and Research, 8, 341–362.CrossRefGoogle Scholar
Teicher, H. (1961). Identifiability of mixtures. Annals of Mathematical Statistics, 32, 244–248.CrossRefGoogle Scholar
Teicher, H. (1963). Identifiability of finite mixtures. Annals of Mathematical Statistics, 34, 1265–1269.CrossRefGoogle Scholar
Tellis, G. J. (1988). Advertising exposure, loyalty, and brand purchase: A two-stage model of choice. Journal of Marketing Research, 25, 134–144.CrossRefGoogle Scholar
Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions, New York: Wiley & Sons.Google Scholar
Tobin, J. (1958). Estimation of relationship for limited dependent variables. Econometrica, 26, 24–36.CrossRefGoogle Scholar
Windham, M. P., & Cutler, A. (1991). Information ratios for validating cluster analyses, New Brunswick, New Jersey: Rutgers University.Google Scholar
Witte, A. D. (1980). Estimating the economic model for crime with individual data. Quarterly Journal of Econometrics, 94, 57–84.Google Scholar
Yakowitz, S. J. (1970). Unsupervised learning and the identification of finite mixtures. IEEE Transactions Information Theory and Control, IT-16, 330–338.CrossRefGoogle Scholar
Yakowitz, S. J., & Spragins, J. D. (1968). On the identifiability of finite mixtures. Annals of Mathematical Statistics, 39, 209–214.CrossRefGoogle Scholar