The directed acyclic graphs (DAGs) depend upon the multivariate distribution of variables from the observational data. As clarified in the previous chapter, some assumptions are required to apply this method including causal Markov condition, faithfulness and causal sufficiency. In order to make an analysis of DAGs for each trip purpose, a lower triangular correlation matrix should be computed. This input of the unconditional correlation matrix between pairs of variables is the starting point for estimating causal graphs in the TETRAD III algorithm. Then, it explores both conditional and unconditional independence relations among input variables. This study employs 17 variables as considered in the previous SEMs: one binary choice variable (auto choice), one mode attribute (travel time differential), five socioeconomic characteristics (household size, vehicle ownership, income, bike use and single-family residence), and ten land use measures at trip origin and destination (population density, employment density, dissimilarity index, connectivity and road length at both trip ends).
To obtain reasonable results, three constraints are imposed in the estimation process. One is that four socioeconomic variables except bike use precede travel time, bike use and land use measures. It implies that these socioeconomics cannot be effects of others. Another constraint is that land use variables at origin do not cause those at destination, and vice versa. Last one is that land use measures can only be causes of travel time differential, bike use and auto choice variables. It suggests that opposite causation from the latter variables to land use patterns is a long-term process; moreover,
it is beyond the scope of this study. A 1% significance level is applied to produce the directed graphs as suggested by Spirtes et al. (2000).
The result of estimated DAG for HBW trips is illustrated in Figure 5.4. The direct graph indicates that automobile choice for HBW trips is causally affected by five factors: travel time differential (TRAVEL TIME: +), bike use (BIKE USE: –), number of vehicles (NOVEHICLE: +), single-family residence (SF RESID: +), and employment density at origin (O_EMPDEN: –). Increased difference between driving time and walk time from an origin to a destination promotes individual trip-makers to drive. More vehicles available and single-family residence causally affect the increase in the chances of making automobile choices. On the contrary, an increase in bike use experiences discourages travelers to use an automobile. In particular, only one land use measure shows significant causal connection to automobile choice probability. Employment density at trip origin has a negative causal impact on the likelihood of automobile mode choice for HBW trips. These results are quite consistent with those of the SEMs for HBW trips except that household size and employment density at destination are not causally connected with automobile choice in the DAGs.
Additional attention needs to be paid to travel time differential. According to the estimated direct graphs, it is causally influenced by two socioeconomic attributes and many land use variables: household size (HHSIZE: +), household income (INCOME: +), population density at origin (O_POPDEN: –), employment density at both origin (O_EMPDEN: –) and destination (D_EMPDEN: +), road length at both origin (O_ROADMI: –) and destination (D_ROADMI: +), connectivity at origin
(O_CONNECT: –), and dissimilarity at destination (D_DISSINDEX: –). These causal connections are similar to the results of SEM estimation except that dissimilarity index at destination is no more direct cause in the directed graphs. The result suggests these variables indirectly affect automobile choice probability through travel time differential.
For instance, increases in land use variables at origin reduce travel time differential;
decreased time differential then lowers the chances of automobile mode choice.
There are two colliders, population density at destination and dissimilarity index at origin at which causal information flowing from other variables comes into collision.
Bi-directed or double-headed edges are also observed between land use variables at both trip ends. They suggest that there should be an unmeasured common cause or a latent variable between two variables. For example, roadway development and improvement can be a common cause between connectivity and road length at trip origin. There are undirected edges between socioeconomic factors. Personal judgment and the arguments of relevant studies are introduced to provide causal orientation for each pair of variables.
Figure 5.5 displays the result of estimated directed graphs for HBO trips. It is found that five variables causally influence the likelihood to drive for HBO trips: travel time differential (TRAVEL TIME: +), bike use (BIKE USE: –), number of vehicles (NOVEHICLE: +), single-family residence (SF RESID: +), and dissimilarity index at destination (D_DISINDEX: +). Travel time, vehicle ownership and single-family residential type have positive causal relationship with the chances of automobile choice for HBO trips. In addition, more experiences of using a bike reduce the likelihood that an individual drives for shopping and recreational trips. When compared with the result
for HBW trips, they are quite similar except that dissimilarity at destination instead of employment density at origin becomes direct cause. The estimated outcomes seem to be little consistent with those of the SEM estimation for HBO trips because the latter claims that five land use measures are causally connected with driving probability. Furthermore, the positive sign of dissimilarity index implies that higher level of land use mix at destination encourages people to drive more. Details in the issues will be discussed later.
From the perspective of the causes of travel time differential for HBO trips, it is causally explained by household income (INCOME: +), number of vehicles (NOVEHICLE: +), population density (O_POPDEN: –) and roadway length (O_ROADMI: –) at trip origin, and employment density (D_EMPDEN: +) and dissimilarity (D_DISSINDEX: –) at destination. Although it is argued that three dimensions of land use patterns all causally influence travel time differential, only four land use measures as direct causes are relatively fewer than eight land use variables in the SEM results. Overall, it is confirmed that land use variables have indirect impacts on automobile choice probability through travel time differential.
Four colliders are observed in the directed graphs: employment density, dissimilarity index and connectivity at trip origin, and population density at destination.
A number of bi-directed edges between land use measures suggest the existence of unmeasured common causes between them. Improved facilities for alternative transportation, for instance, can be a common cause between travel time differential and bike use. Same approach as used for HBW trips is applied to construct causal connections between socioeconomic variables.
125 Figure 5.4 Directed Acyclic Graphs (DAGs) on Binary Mode Choice for Home-based Work Trips (1% significance level).
Note: Double-headed or bi-directed edges, x1↔x2 in a pattern suggest that there is a latent common cause between two variables.
Names in parentheses indicate variable names that are used in the analytical process.
AUTO CHOICE
126 Figure 5.5 Directed Acyclic Graphs (DAGs) on Binary Mode Choice for Home-based Other Trips (1% significance level).
Note: Double-headed or bi-directed edges, x1↔x2 in a pattern suggest that there is a latent common cause between two variables.
Names in parentheses indicate variable names that are used in the analytical process.
D_EMPDEN
5.3 Household Automobile Trip Generation Models