Daly, AJ, Hess, S and de Jong, G (2012) Calculating errors for measures derived from choice modelling estimates. Transportation Research Part B: Methodological, 26 (2). 333 - 341 . ISSN 0191-2615
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 this can be guaranteed to have the maximum likelihood properties, such as minimum variance. While the calculation of standard errors using the Delta method has been described for a number of such measures in the literature, including the ratio of two parameters, these results are often seen to be approximate calculations and do not claim maximum likelihood properties. In this paper, we show that many measures commonly used in transport studies and elsewhere are themselves maximum likelihood estimates and that the standard errors are thus exact, a point we illustrate for a substantial number of commonly used functions. We also discuss less appropriate methods, notably highlighting the issues with using simulation for obtaining the variance of a function of estimates.
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Environment (Leeds) > Institute for Transport Studies (Leeds)|
|Depositing User:||Symplectic Publications|
|Date Deposited:||19 Mar 2012 15:00|
|Last Modified:||16 Sep 2016 14:13|