To estimate the effect of other factors on the change in implied volume, we used a fixed-effects panel data regression model (37). The fixed-effects standardize the link-dependent unexplained constancy or variance that might affect the regressed variable. Some examples of link-specific characteristics are location of links near high foot traffic, recreational areas, and special roadway geometry. Because these characteristics do not change between 2010 and 2016, their influence is absorbed into the fixed effect, preventing them from biasing the other parameter estimates. The temporal unit used by the panel is 2, warranted by the before-after nature of the study. Each data point in the dataset is a unique combination of a TMC, TOD, and observation year. Because there are only two points in time, this is equivalent to estimating an OLS model on the change on each TMC for each TOD. The estimated model can be expressed asVI:i,t=β1VSFCHAMP:i,t+β2VTNC:i,t+β3FTMajArt:i*VAvgDur:i,t+β4FTMinArt:i*VAvgDur:i,t+β5PRESIDIOi,t*VI:i,2010+FEi+εi,t(4)where the entities i are TMC links by TOD and the time periods t are either 2010 or 2016, and each is used to index the remaining variables. VI:i,t is the time-implied volume. VSF − CHAMP:i,t is the volume predicted by SF-CHAMP in PCE, giving some additional weight to trucks and buses. VAvgDur:i,t is the average duration variable, as defined above. FTMajArt:i is a binary facility type flag indicating whether or not the link is a major arterial, and FTMinArt:i is a binary facility type flag indicating whether or not the link is a minor arterial. These facility type flags do not change between the two years. PRESIDIOi,t is a binary flag identifying links on the Presidio Parkway and Veterans Boulevard, where there was major construction in 2010 but not in 2016. PRESIDIOi,t is defined to be zero in 2010 and one in 2016 such that the effect of a change can be estimated. VI:i,2010 is the time-implied volume in period 1 (2010), which allows the effect of the construction change to be proportional to the starting volume on the link, as opposed to additive and the same on every link. FEi is the fixed-effect, which is effectively a constant on each entity, and εi, t is a random error term. In this specification, the Presidio flag (PRESIDIOi, t) and the TNC terms (VTNC:i,t, VAvgDur:i,t) are zero in 2010, so the 2010 time-implied volume is simply a function of the SF-CHAMP volume plus the fixed effect and an error term.

A number of variations on this specification were attempted before arriving at the preferred model. For example, specifications were tested that split the TNC volume into separate in-service and out-of-service volumes or segmented the PUDO coefficients in different dimensions. One notable variation relates to our hypothesis that TNCs have no effect on traffic congestion. If this were true, we would expect the change in background volume alone to reasonably predict the change in time-implied volume (VI). Estimating such a model reveals that the background volume is highly correlated with VI, with a coefficient of 1.78. This suggests that time-implied volumes are increasing by 78% more than SF-CHAMP would predict. It appears that the employment, population, and network changes do not fully describe the congestion changes observed during this period, and more terms are needed to do so.