5 Probit Choice Probabilities The logit model is limited in three important ways. It cannot represent random taste variation. It exhibits restrictive substitution patterns due to the IIA property. And it cannot be used with panel data when unobserved factors | P1 GEM IKJ P2 GEM IKJ QC GEM ABE T1 GEM August 20 2002 12 28 Char Count 0 CB495-05Drv CB495 Train KEY BOARDED 5 Probit Choice Probabilities The logit model is limited in three important ways. It cannot represent random taste variation. It exhibits restrictive substitution patterns due to the IIA property. And it cannot be used with panel data when unobserved factors are correlated over time for each decision maker. GEV models relax the second of these restrictions but not the other two. Probit models deal with all three. They can handle random taste variation they allow any pattern of substitution and they are applicable to panel data with temporally correlated errors. The only limitation of probit models is that they require normal distributions for all unobserved components of utility. In many perhaps most situations normal distributions provide an adequate representation of the random components. However in some situations normal distributions are inappropriate and can lead to perverse forecasts. A prominent example relates to price coefficients. For a probit model with random taste variation the coefficient of price is assumed to be normally distributed in the population. Since the normal distribution has density on both sides of zero the model necessarily implies that some people have a positive price coefficient. The use of a distribution that has density only on one side of zero such as the lognormal is more appropriate and yet cannot be accommodated within probit. Other than this restriction the probit model is quite general. The probit model is derived under the assumption of jointly normal unobserved utility components. The first derivation by Thurstone 1927 for a binary probit used the terminology of psychological stimuli which Marschak 1960 translated into economic terms as utility. Hausman and Wise 1978 and Daganzo 1979 elucidated the generality of the specification for representing various aspects of choice behavior. Utility is decomposed into .
