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SAS/ETS 9.22 User's Guide 97

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SAS/Ets 9.22 User's Guide 97. Provides detailed reference material for using SAS/ETS software and guides you through the analysis and forecasting of features such as univariate and multivariate time series, cross-sectional time series, seasonal adjustments, multiequational nonlinear models, discrete choice models, limited dependent variable models, portfolio analysis, and generation of financial reports, with introductory and advanced examples for each procedure. You can also find complete information about two easy-to-use point-and-click applications: the Time Series Forecasting System, for automatic and interactive time series modeling and forecasting, and the Investment Analysis System, for time-value of money analysis of a variety of investments | 952 F Chapter 17 The MDC Procedure The IIA property of the conditional logit model follows from the assumption that the random components of utility are identically and independently distributed. The other models in PROC MDC namely nested logit HEV mixed logit and multinomial probit relax the IIA property in different ways. For an example of Hausman s specification test of IIA assumption see Example 17.6 Hausman s Specification Test on page 985. Heteroscedastic Extreme-Value Model The heteroscedastic extreme-value HEV model Bhat 1995 allows the random components of the utility function to be nonidentical. Specifically the HEV model assumes independent but nonidentical error terms distributed with the Type I extreme-value distribution. The HEV model allows the variances of the random components of utility to differ across alternatives. Bhat 1995 argues that the HEV model does not have the IIA property. The HEV model contains the conditional logit model as a special case. The probability that an individual i will choose alternative j from the set Ci of available alternatives is Pi j 1 n r 1 k2Ci k j xn 0 - xik 0 0j w 0k y w dw where the choice set Ci has ni elements and x exp exp x y x exp x T x are the cumulative distribution function and probability density function of the Type I extreme-value distribution. The variance of the error term for the j th alternative is 6n202. If the scale parameters 0j of the random components of utility of all alternatives are equal then this choice probability is the same as that of the conditional logit model. The log-likelihood function of the HEV model can be written as N L XX dj ln Pi 7 i 1 j 2Ci where dij 1 if individual i chooses alternative j 0 otherwise Since the log-likelihood function contains an improper integral function it is computationally difficult to get a stable estimate. With the transformation u exp w the probability can be written Pi j k2Ci k j Xij0 - xik0 - 0jln u 0k exp u du 0 Gij u exp u du 1 0 1 Mixed Logit .