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<br /> <br />In the expressions given above, the parameters p1 and p2 represent proportions of pedestrian volumes at <br />marked sites adjusted for slight differences in exposure times over which crash data were obtained. These <br />results suggest that, in general, marked crosswalks are less safe than unmarked crosswalks on streets <br />having more than two lanes, but that the two types do not differ significantly on streets with two lanes. <br />Note that the analysis described above did not require adjustment for motor vehicle volume, since <br />matched pairs of marked and unmarked sites typically were selected at or near the same intersection <br />where vehicle volumes were similar. <br /> <br />To investigate the relationship between other factors and combinations of factors on crosswalk pedestrian <br />crashes, generalized linear regression models were fit to the data to predict crashes as functions of these <br />variables. Consider a model based on pedestrian volumes (ADP); traffic volumes (ADT); and two <br />indicator variables, one which indicates one or two travel lanes (L2), and the other which indicates three <br />or four travel lanes (L4). The resulting model has the form <br /> <br /> (4) <br /> <br /> <br />where E (Accsi) is expected pedestrian crashes at site i, yrsi is the number of years over which crash data <br />was available for site i, and β0, β1, ... , β4 are parameters to be estimated. Models of this form were fit to <br />data from marked and unmarked crosswalks separately. The models were fit by maximum likelihood <br />methods using Procedure for General Models (PROC GENMOD) software, as developed by the SAS <br />Institute. Crashes were assumed to follow a negative binomial distribution. <br /> <br />Parameter estimates for these basic models are shown in table 2. <br /> <br />Table 2. Parameter estimates for basic marked and unmarked crosswalk models. <br />Marked Crosswalks Unmarked Crosswalks Parameter <br />Estimate S.E.* p-Value Estimate S.E.* p-Value <br />Constant ($0) -14.55 1.95 < .0001 -10.25 2.72 .0002 <br />ADP ($1) .381 .065 < .0001 .602 .134 < .0001 <br />ADT ($2) 1.006 .184 < .0001 .304 .258 .2388 <br />L2 ($3) -.599 .328 .0678 -.066 .592 .9115 <br />L4 ($4) .075 .247 .7608 -.208 .553 .7076 <br />*S.E. = Standard Error <br /> <br />For marked crosswalks, the results in table 2 show that expected crashes increased to a significant degree <br />with both increasing pedestrian volume and increasing traffic volumes, with a much steeper increase for <br />traffic volume. The lane variables compare two-lane roads with roads having five or more lanes, and <br />three- or four-lane roads with roads having five or more lanes. The two-lane variable is marginally <br />significant, while the three- or four-lane variable is not. The overall lanes effect (not shown) is significant <br />(p-value of .0262). In subsequent models, a two-level lanes effect comparing two lanes with three or <br />more is used. This variable is usually significant at a level of about .02. <br /> <br />The results for unmarked crosswalks show the only statistically significant effect to be for pedestrian <br />volume. Thus, expected crashes on unmarked crosswalks increased consistently with increasing <br />pedestrian volumes (at a somewhat higher rate than that at marked crosswalks), but did not change <br />consistently with increasing traffic volumes or with number of lanes. These results suggest that multilane <br />streets with low traffic volumes might represent another subset of the data where marked and unmarked <br />crosswalks might not differ significantly with respect to safety. This issue is addressed in more detail <br />later in the report. <br /> 19