Calculating Errors for Measures Derived From Choice Modeling Estimates

The calibration of choice models produces a set of parameter estimates and an associated covariance matrix, usually based on maximum likelihood estimation. However, in many cases, the values of interest to analysts are in fact functions of these parameters rather than the parameters themselves. It is thus also crucial to have a measure of variance for these derived quantities and it is preferable that these should also have the maximum likelihood properties of minimum variance et cetera. While the calculation of standard errors has been described for a number of such measures in the literature, including the ratio of two parameters, these results are often based on rather ad hoc calculations. In this paper, the authors present a general way of obtaining standard errors for such derived functions, describe the properties for these errors, give formulae for the standard errors for a number of commonly used quantities and develop a freeware software tool for the calculation of standard errors.