Programming Homework Help

1.(5) Train and Wilson use choice modeling to estimate the demand for transportation by water and rail. The estimated model is has a coefficient on the price of transportation equal to -5, and the coefficient on reliability is 2. Write down the estimated utility functions for rail and water, and then from the estimated functions derive the value of reliability?

2.(5) Assume consumers make decisions of whether to use mode 1, 2 or 3. The choices are driven by the indirect Utility function given as . Write down a fully expanded expression for the probability that 1 is chosen (by fully expanded I mean in terms of the indirect utility function given in the last sentence) (2). Now, show that if prices are the same for mode 1, 2, and 3, that the probability of each is equal to 1/3.

For parts 3 and 4, I took data from the National Household Travel Survey which is available for download on https://nhts.ornl.gov/. This is an incredibly detailed summary of trips made by individuals. As there are nearly 1 million records, multiple datasets, etc., I processed it as follows for the HW assignment. First, kept only travel decisions related to trips to work. I grouped modal decisions into private motorized (car, suv, etc.), non-motorized (walk bike), and public (bus, subway). I also considered trips o of 20 miles or less. The resulting data was quite voluminous so I drew a sample of 5000 observations for this homework.

3.(10)

a.(4) Estimate a logit model where the dependent variable takes a value of 1 if motorized and a value of zero otherwise (motor=1). Explain the decision in terms of trip distance (trpmiles). Present your estimates in a table. Predict the probability of traveling by motorized or not, and graph the predicted value against trip distance.

b.(6) To the model in a, add in number of cars available in the household (hhvehcnt). Present your estimates in a table. Predict the probability of traveling by motorized or not, and graph the predicted value against the number of cars in the household for trip distances of 1, 5, and 20.

4.(10) Now consider a three alternative model (1=motorized, 2=public, and 3=walk/bike). Estimate the model and explain the mode choice (m1) in terms of trip distance and number of vehicles in the household and present the estimates in a table(2). Why is the first column blank(2)? Develop graph that has probability of motorized, public, and non-motorized plotted against the number of vehicles per household for a trip distance of 1 mile(3). Finally, develop a graph of the probability of walking against the number of cars for trip distances of 1, 5, and 20 miles (3).