TAILIEUCHUNG - SAS/ETS 9.22 User's Guide 72

SAS/Ets User's Guide 72. 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 | 702 F Chapter 12 The ENTROPY Procedure Experimental The standard maximum likelihood approach for multinomial logit is equivalent to the maximum entropy solution for discrete choice models. The generalized maximum entropy approach avoids an assumption of the form of the link function GQ. The generalized maximum entropy for discrete choice models GME-D is written in primal form as maximize H p w p ln p w ln w subjectto Ij 0 X y Ij 0 X p Ij 0 X V w Pk pij 1 for i 1 to N Pm wijm 1 for i 1 to N and j 1 to k Golan Judge and Miller 1996 have shown that the dual unconstrained formulation of the GMED can be viewed as a general class of logit models. Additionally as the sample size increases the solution of the dual problem approaches the maximum likelihood solution. Because of these characteristics only the dual approach is available for the GME-D estimation method. The parameters fij are the Lagrange multipliers of the constraints. The covariance matrix of the parameter estimates is computed as the inverse of the Hessian of the dual form of the objective function. Censored or Truncated Dependent Variables In practice you might find that variables are not always measured throughout their natural ranges. A given variable might be recorded continuously in a range but outside of that range only the endpoint is denoted. In other words say that the data generating process is yi x-i. e. However you observe the following y ub Xi. 6 lb yi ub lb yi ub yi lb The primal problem is simply a slight modification of the primal formulation for GME-GCE. You specify different supports for the errors in the truncated or censored region perhaps reflecting some nonsample information. Then the data constraints are modified. The constraints that arise in the censored areas are changed to inequality constraints Golan Judge and Perloff 1997 . Let the variable Xu denote the observations of the explanatory variable where censoring occurs from the top Xl from the bottom and Xa in the middle region no

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