16.2x ln Section 16.1.5w e presenta n exampleo f transportationc hoice.U se the sample data on automobile and public transportation tim es in t ransp o rt. dat for the following exercises.

(a) Estimate the logit model explaining the choice of automobile transportation as a function of difference in travel time (DTIME. Compare the parameter estimates and their standard errors to the estimates from the probit model in equation

(l6.r5).

(b) Based on the logit model results, estimate the marginal effect of an increase in DTIME given that DTIME : 20. Use (16.11) but replace the standard normal density function 0(.) UV the logistic density function I(.) given in (16.16).

Compare this result to that for the probit model in Section 16.1.5, where the estimated marginal effect is 0.0104.

(c) Using the logit estimates, calculate the probability of a person choosing automobile transportation given that the time differential DTIME: 30. Compare this value to the probit estimate of the probability of choosing automobile transportation, which is 0.798.

(d) For eacho f the 2l observations,e stimatet he probability of choosinga utomobile transportation using the logit model. Predict the choice of transportation mode using the rule AUTO : I if the predicted probability is 0.5 or larger, otherwise AUTO : 0. Define a successful prediction to be when we predict that a person will choose the automobile (AUTO: 1) when they actually did (AUTO : l), OR when we predict that a person will choose public transportation (AUTO : O)

when they did (AUTO : 0). Calculate the percentage of correct predictions in the N: 21 cases.