Random Parameter Model

A discrete choice model that lets preference parameters vary randomly across individuals according to a specified distribution, rather than assuming identical preferences.

Source: Train 2009

Instead of estimating one weight per attribute for the whole sample, it assumes each individual has their own weight drawn from a distribution, and estimates the parameters of that distribution rather than a single value. Estimation proceeds by simulation, drawing repeatedly from the assumed distributions and averaging the resulting choice probabilities. The output is a mean and a spread for each attribute, showing both the average preference and how much it varies across the population. Because each respondent completes several tasks, the model can also recover individual-level weights conditional on the choices that respondent actually made.

Source: Train 2009

Because assuming everyone shares identical preferences almost always describes choice data poorly, and the resulting average can describe nobody. The model also relaxes an assumption of simpler specifications that the ratio of choice probabilities between two alternatives is unaffected by other alternatives, which is frequently violated in practice. It additionally accommodates the fact that the same respondent answers several choice tasks, whose responses are correlated. It also produces more plausible predictions of how demand would respond to a new option, since substitution patterns are no longer constrained by the simpler model's assumptions.

Source: Train 2009

The normal distribution is the common default, which permits the coefficient to take either sign and is therefore problematic for attributes such as cost where the sign should be fixed. Lognormal and triangular distributions constrain the sign at the cost of a more difficult estimation. The choice matters, since it determines what proportion of the population the model implies holds counterintuitive preferences, and it should be reported rather than left implicit. Reporting the proportion of the distribution falling on the counterintuitive side of zero is a useful diagnostic that published studies frequently omit.

Source: Train 2009

The mean of each distribution gives the average preference weight, and the standard deviation gives the extent of heterogeneity. A large spread relative to the mean indicates that the average conceals substantial variation and that policies designed around it will suit only part of the population. Individual-level weights can also be estimated conditional on each respondent's observed choices, which supports segmentation without requiring discrete classes. These individual estimates support targeting without requiring the population to be divided into discrete groups, which a latent class approach would impose. Reporting how much of the heterogeneity observed characteristics explain is a useful accompaniment.

Source: Greene & Hensher 2003

The heterogeneity it recovers is a property of the assumed distribution as much as of the data, so different distributional assumptions produce different pictures of how preferences vary. It describes variation without explaining it, unless observed characteristics are entered to account for the spread. Estimation is computationally demanding and results can be sensitive to the number of simulation draws, which should be reported alongside the estimates. Comparison against a latent class specification on the same data is a useful check, since agreement between two different representations of heterogeneity strengthens either conclusion.

Source: Train 2009