Monte Carlo EM method for estimating multinomial probit models

Computational Statistics and Data Analysis

Volumn 34, Issue 1, 2000, Pages 33-50

  Natarajan, Ranjini ^a   McCulloch, Charles E ^b   Kiefer, Nicholas M ^b  

^a University of Florida ^*  (United States)

^b Department of Obstetrics Gynecology   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; MATHEMATICAL MODELS; MAXIMUM LIKELIHOOD ESTIMATION; SAMPLING;

GIBBS SAMPLING; MULTINOMIAL PROBIT MODELS;

MONTE CARLO METHODS;

EID: 0034225899     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-9473(99)00073-0     Document Type: Article

References (30)

1. J.H Albert S Chib Bayesian analysis of polychotomous response data. J. Amer. Statist. Assoc. 88 1993 669 679
2. G.M Allenby P.J Lenk Modeling household purchase behavior with logistic normal regression. J. Amer. Statist. Assoc. 89 1994 1218 1231
3. Aptech Systems, 1994. The GAUSS System, Version 3.0. Maple Valley, WA.
4. J.R Ashford R.R Sowden Multi-variate probit analysis. Biometrics 26 1970 535 546
5. J.G Booth J.P Hobert Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. Roy. Statist. Soc. B 61 1999 265 285
6. A Börsch-Supan V Hajivassiliou Smooth unbiased multivariate probability simulators for maximum likelihood estimation of limited dependent variable models. J. Econometrics 58 1994 347 368
7. K.S Chan J Ledolter Monte carlo EM estimation for time series models involving counts. J. Amer. Statist. Assoc. 90 1995 242 252
8. Daganzo, C., 1980. Multinomial Probit. Acedemic Press, New York, 1980.
9. B Dansie Parameter estimability in the multinomial probit model. Transportation Res. 19B 1985 526 528
10. A.P Dempster N.M Laird D.B Rubin Maximum likelihood estimation from incomplete observations. J. Roy. Statist. Soc. B 39 1977 1 38
11. Devroye, L., 1986. Non-Uniform Random Variate Generation. Springer, New York.
12. Diebolt, J., Ip, E.H.S., 1998. Stochastic EM: Method and Applications. in: Markov Chain Monte Carlo in Practice, Eds: Gilks, Richardson, Spiegelhalter. Chapman & Hall, New York, NY.
13. S Geman D Geman Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 1984 721 741
14. Geweke, J.F., 1989. Efficient simulation from the multivariate normal distribution subject to linear inequality constraints and the evaluation of constraint probabilities. Mimeo. Department of Economics, Duke University, Durham, NC.
15. Geweke, J.F., Keane, M.P., Runkle, D.E., 1994. Statistical inference in the multinomial multiperiod probit model. Research Department Staff Report 177. Federal Reserve Bank of Minneapolis, MN.
16. S.W Guo E.A Thompson A Monte Carlo method for combined segregation and linkage analysis. Amer. J. Hum. Genet. 51 1992 1111 1126
17. Hajivassiliou, V., McFadden, D., Ruud, D., 1992. Simulation of multivariate normal orthant probabilities: methods and programs. Discussion Paper 1021. Cowles Foundation, Yale University, CT.
18. J Hausman D Wise A conditional probit model for qualitative choice: discrete decisions recognizing interdependence and heterogeneous preferences. Econometrica 45 1978 319 339
19. R.I Jennrich M.D Schluchter Unbalanced repeated measures models with structured covariance matrices. Biometrics 42 1986 805 820
20. M.P Keane A computationally practical simulation estimator for panel data. Econometrica 62 1994 95 116
21. N.M Kiefer T.J Kelly K Burdett Menu pricing: an experimental approach. J. Bus. Econom. Statist. 3 1994 329 337
22. Lerman, S., Manski, C., 1981. On the use of simulated frequencies to approximate choice probabilities. In: Manski, C., McFadden, D. (Eds.), Structural Analysis of Discrete Data with Econometric Applications. MIT Press, Cambridge, MA, pp. 305–319.
23. T.A Louis Finding the observed information matrix when using the EM algorithm. J. Roy. Statist. Soc. B 44 1982 226 233
24. C.E McCulloch Maximum likelihood variance components estimation for binary data. J. Amer. Statist. Assoc. 89 1994 330 335
25. R McCulloch P.E Rossi An exact likelihood analysis of the multinomial probit model. J. Econometrics 64 1994 207 240
26. D McFadden A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57 1989 995 1027
27. X.L Meng D.B Rubin Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika 80 1993 267 278
28. Searle, S., Casella, G., McCulloch, C.E., 1992. Variance Components. Wiley, New York.
29. S Stern A method for smoothing simulated moments of discrete probabilities in multinomial probit models. Econometrica 60 1992 943 952
30. Tanner, M.A., 1993. Tools for Statistical Inference. Methods for the Exploration of Posterior Distributions and Likelihood Functions. Springer, New York.