I appreciate that similar questions have been asked and answered to this, but I think that my case is substantively different as the specific interpretation of the coefficient is not relevant.
I have a set of choice experiment results that I am using to calculate the 'Valuation of Travel Time' for the participants. The standard process for doing this is to fit a logistic regression model to the result of whether someone accepts a specific level of compensation for a specific travel time. You can then divide the time coefficient by the compensation one to generate the valuation of travel time (don't worry if doesn't make sense). Hence for the below model:
| term | estimate | std.error | z value | p.value |
|---|---|---|---|---|
| (Intercept) | 1.256319853 | 0.1096819372 | 11.45420919 | 2.24E-30 |
| time | 0.1015354957 | 0.003527728861 | -28.78211442 | 3.59E-182 |
| comp | 0.1532430136 | 0.005337402709 | 28.7111582 | 2.77E-181 |
The 'VTT' is (approximately) 0.101..102/0.153... - which, is £0.67 per minute, or £40 per hour.
I want to provide a 95% confidence interval for this valuation and I've been searching for the correct method. My instinct is that it's just:
upper limit: time_coef + 1.96time_SE / comp_coef - 1.96comp_SE
lower limit: time_coef - 1.96time_SE / comp_coef + 1.96comp_SE
Without a detailed understanding of VTT methodology, does this look correct?
Edit - following useful feedback, I can include the covariance table if anyone else is able to use this data to help me validate that I am using the correct method.
| (Intercept) | time | comp | |
|---|---|---|---|
| (Intercept | 1.203013e-02 | -1.265604e-04 | 9.785909e-06 |
| time | -1.265804e | 1.244487e-05 | -1.437472e-05 |
| comp | 9.785909e-06 | -1.437472e-05 | 2.848787e-05 |
