A challenge in estimating these models is that they assume a linear relationship between the dependent variable and the regressors, but the relationship between volume and travel time is nonlinear. To deal with this, the VDFs from SF-CHAMP were used to convert the observed travel times into implied passenger car equivalent (PCE) volumes. They take the formT=T0(1+α(VC)β)(1)where T is the congested travel time, T0 is the free-flow travel time, V is the traffic volume in PCEs, C is the link capacity, and α and β are calibrated parameters. Solving for V, we getVI=C(TT01α)1/β(2)where the subscript on VI is used to designate a time-implied volume, as derived from the travel times. The panel models use VI as their dependent variable. It is in units of PCEs, so it is linearly related to the volume measures in the descriptive variables.

The analysis was conducted for five multi-hour time periods, so it is important that all volumes and capacities are either hourly or for the period as a whole. Here, we defined them for the period as a whole and scaled the hourly capacities to the period total using the same peak hour factors that were used by SF-CHAMP.