Let's say I have contingent valuation data for a recreation trip where the dependent variable is y=0 if they would take the trip and y=1 otherwise. The independent variables are the added cost of the trip, a risk factor and whether the respondent takes a day or overnight trip. The logit generates a constant, a<0, and slopes on the cost, risk and overnight variables, b>0, c>0, d<0. Willingness to pay for a day trip with no risk is WTP =-a/b. The y=1 on this dependent variable can be decomposed into 3 categories: (1) stay at home, (2) visit another recreation site, or (3) do something else. I've estimated the binary logit where the 3 categories are collapsed into y=1 and the multinomial where y = 0, 1, 2, and 3. When I constrain the b and c coefficients to be equal across response categories the constant is 62% larger in the multinomial logit. This makes WTP significantly higher in the multinomial logit.
My question is: Why is the constant so much larger in the multinomial logit?
