Sample size and grouping in the estimation of disaggregate models—A simple case

Abstract

Using a very simple form of disaggregate model for household car ownership, it appears that two widely held beliefs about disaggregate modelling — that analysis should always be carried out on individual households, and that sample sizes of 500 to 1000 are generally sufficient - are not necessarily valid. Though the results may not be generalizable to the full class of problems to which disaggregate analysis addresses itself, it does seem that more attention needs to be given to the questions of sample size and grouping.

In addition, the standard test of goodness of fit (the so-called “rho-squared” test) is shown to be extremely weak. A far stronger and to some extent complementary, test is to compare the log-likelihood value given by the model with that on the basis of the “full” or “saturated” model — a test which has recently been clearly presented by a number of writers in the statistical literature. When using dummy variables, it is important that pair-wise tests on coefficients relating to various levels of the same attribute should be carried out, as well as the standard test assessing difference from zero.

These points are illustrated by a number of simple examples.