The Estimation of Multinomial Probit Models: A New Calibration Algorithm

This study proposes the estimation of Multinomial Probit models using Mendell-Elston's approximation to the cumulative multivariate normal for the computation of choice probabilities. The accuracy of this numerical approximation in computing probabilities is compared with other procedures used in existing calibration programs. Finally, the proposed estimation procedure is tested on simulated choice data.

[1]  Wagner A. Kamakura,et al.  Predicting Choice Shares under Conditions of Brand Interdependence , 1984 .

[2]  Michael G. Langdon,et al.  Improved Algorithms for Estimating Choice Probabilities in the Multinomial Probit Model , 1984, Transp. Sci..

[3]  M. G. Langdon,et al.  Methods of determining choice probability in utility maximising multiple alternative models , 1984 .

[4]  Naresh K. Malhotra,et al.  The Use of Linear Logit Models in Marketing Research , 1984 .

[5]  C. Read,et al.  Handbook of the normal distribution , 1982 .

[6]  C. Daganzo,et al.  ON THE ESTIMATION OF THE MULTINOMIAL PROBIT MODEL , 1982 .

[7]  J. Horowitz,et al.  An Investigation of the Accuracy of the Clark Approximation for the Multinomial Probit Model , 1982 .

[8]  Imran S. Currim.  Predictive Testing of Consumer Choice Models Not Subject to Independence of Irrelevant Alternatives , 1982 .

[9]  Robert A. Moffitt,et al.  A COMPUTATIONALLY EFFICIENT QUADRATURE PROCEDURE FOR THE ONE-FACTOR MULTINOMIAL PROBIT MODEL , 1982 .

[10]  Imran S. Currim,et al.  Using Segmentation Approaches for Better Prediction and Understanding from Consumer Mode Choice Models , 1981 .

[11]  Charles F. Manski,et al.  Alternative Estimators and Sample Designs for Discrete Choice Analysis , 1981 .

[12]  D. Guilkey,et al.  A random coefficient probit model with an application to a study of migration. , 1979, Journal of econometrics.

[13]  John P. Rice,et al.  An Approximation to the Multivariate Normal Integral: Its Application to Multifactorial Qualitative Traits , 1979 .

[14]  D. Wise,et al.  A CONDITIONAL PROBIT MODEL FOR QUALITATIVE CHOICE: DISCRETE DECISIONS RECOGNIZING INTERDEPENDENCE AND HETEROGENEOUS PREFERENCES' , 1978 .

[15]  D. McFadden,et al.  URBAN TRAVEL DEMAND - A BEHAVIORAL ANALYSIS , 1977 .

[16]  C. Daganzo,et al.  Multinomial Probit and Qualitative Choice: A Computationally Efficient Algorithm , 1977 .

[17]  Takeshi Amemiya,et al.  Qualitative Response Models , 1975 .

[18]  Michael J. Boskin,et al.  A Conditional Logit Model of Occupational Choice , 1974, Journal of Political Economy.

[19]  R C Elston,et al.  Multifactorial qualitative traits: genetic analysis and prediction of recurrence risks. , 1974, Biometrics.

[20]  J. E. Dutt,et al.  A representation of multivariate normal probability integrals by integral transforms , 1973 .

[21]  W. R. Buckland,et al.  Distributions in Statistics: Continuous Multivariate Distributions , 1973 .

[22]  Roy C. Milton,et al.  Computer Evaluation of the Multivariate Normal Integral , 1972 .

[23]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[24]  L. V. Jones,et al.  The measurement and prediction of judgment and choice. , 1970 .

[25]  E. Abbe.  EXPERIMENTAL COMPARISON OF MONTE-CARLO SAMPLING TECHNIQUES TO EVALUATE THE MULTIVARIATE NORMAL INTEGRAL , 1969 .

[26]  S. Gupta.  Probability Integrals of Multivariate Normal and Multivariate $t^1$ , 1963 .

[27]  D. G. Beech,et al.  Handbook of Statistical Tables. , 1962 .

[28]  C. W. Dunnett,et al.  The Numerical Evaluation of Certain Multivariate Normal Integrals , 1962 .

[29]  C. E. Clark.  The Greatest of a Finite Set of Random Variables , 1961 .

[30]  C. Dunnett,et al.  Approximations to the probability integral and certain percentage points of a multivariate analogue of Student's t-distribution* , 1955 .

[31]  R. Plackett.  A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS , 1954 .

[32]  P. Moran,et al.  Rank correlation and product-moment correlation. , 1948, Biometrika.

[33]  M. G. Kendall,et al.  iv) Proof of Relations connected with the Tetrachoric Series and its Generalization , 1941 .

[34]  A. C. Aitken,et al.  Note on Selection from a Multivariate Normal Population , 1935 .

[35]  Karl Pearson,et al.  Mathematical Contributions to the Theory of Evolution. XI. On the Influence of Natural Selection on the Variability and Correlation of Organs , 1903 .