In Example 13.2 compare a 5-point discrete mixture on the log-logistic shape parameter with the variable scale model to downweight aberrant cases, namely ui ∼ L(ηi, 1/(κθi)) where θi are gamma with mean 1, and ui = log(ti).
Commuter delay in work-to-home trips Washington et al. (2003) consider the durations of delay in work-to-home trips for 96 Seattle area commuters. For such workers, the home trip is postponed to varying degrees to avoid evening rush-hour congestion. The hazard rate is effectively modelling early as against late departures for home. There is no censoring. The predictors are gender, X1(M = 1, F = 0), X2 = ratio of actual travel time (at expected departure time) to free-flow travel time, X3 = distance from work to home (km) and X4 = resident population density in workplace zone (divided by 10 000). One might expect early departure to be negatively associated with X2 and X4. Actual delay times vary from 4 to 240 min. A non-monotonic hazard is suggested when the Kaplan–Meier survival curve is used to provide estimates of H(t) and hence h(t). The hazard is low at first (durations under 20 min), has a plateau at values of 0.017 to 0.031 per minute for durations between 20 and 100 min and has a late peak between 120 and 140 min. Here we compare a Weibull with single-component and two-component log-logistic models.