where b~cdenotes the estimated coefficients from the restricted set of alternatives and b~c denotes the
estimated value for the same subvector of coefficients from a model with a full choice set.
The model was evaluated based on the sign of the coefficient, the relative value of the coefficient, the goodness of fit index (i.e., r2) and the likelihood ratio test. The Goodness of Fit Index, r2, measures the fraction of an initial log likelihood value, explained by the model. It is defined as 1 (L(b)/L(0)). Usually r2 must lie between 0 and 1. The purpose of the likelihood ratio test is to test the significance of all the parameters in the model. The null hypothesis is defined so that all the coefficients are zero. The
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statistic test for the null hypothesis ensures that the restrictions, 2½L~cðb~cÞ L~cðb~cÞ&, are asymptotically distributed as x2 with K (number of coefficients) degrees of freedom.
Discrete choice models explain the choice behavior of individuals as a function of choice makers’ characteristics and attributes of the alternatives in the choice set. However, in making investment or planning decisions, individual behavior is irrelevant. It is therefore necessary to aggregate these individual decisions in order to represent the behavior of the population under consideration. Most of the real world decisions are only based on an aggregate demand.
In this study, a sample enumeration technique of aggregate forecasting is used. A random sample is used as the representative for the entire population under consideration. The predicted share of the sample, choosing an alternative ‘‘i’’, is used as an estimate for W(i):