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develop the final model form, generalized estimating equations (GEEs) were used, since they provide a practical method to analyze correlated data with reasonable statistical efficiency. PROC GENMOD uses GEE and permits the analysis of correlated data. Another feature of the final model is that the distribution of pedestrian crashes at a crosswalk is assumed to follow a negative binomial distribution. The negative binomial is a distribution with an additional parameter (k) in the variance function. PROC GENMOD estimates k by maximum likelihood. (Refer to McCullagh and Nelder (chapter 11),(26) Hilbe,(27) or Lawless(28) for discussions of the negative binomial distribution.) The final model is a negative binomial regression model that was fitted with the observed number of pedestrian crashes as the dependent measure. A negative binomial model is an extension of traditional linear models that allows the mean of a population to depend on a linear predictor through a nonlinear link function and allows the response probability distribution to be a negative binomial distribution. PROC GENMOD is capable of performing negative binomial regression GENMOD using GEE methodology.(29) The final model uses the observed number of pedestrian crashes at a crosswalk as the dependent measure. The independent measures are estimated average daily pedestrian volume (pedestrian ADT), average daily traffic volume (traffic ADT), an indicator variable for marked crosswalks (CM); two indicator variables for number of lanes (one that indicates two travel lanes, L2; the other indicates three or four travel lanes, L4); and two indicators for median type (no raised median, Mnone, and raised median, Mraised). There are two interactions in the model. The first interaction in an interaction between pedestrian ADT and the indicator for marked crosswalk, ADP*CM. The second interaction in the model is between traffic ADT and the indicator for marked crosswalk, ADT*CM. The linear predictor has the form: (7) where ηi is the linear predictor for site i = 1 ,2, ..., 2,000. The number of years of accident data available for a site is used as an offset. β0, β1, ... , β9 are parameters to be estimated. The estimates of the parameters were obtained using PROC GENMOD. Parameter estimates for the final model are shown in table 9. Table 9. Parameter estimates for final model combining marked and unmarked crosswalks. Marked Parameter Estimate S.E.* p-Value Constant ($0) −8.2455 0.4633 < 0.0001 ADP ($1) 0.0011 0.0004 0.0149 ADT ($2) 0.0000 0.0000 0.7842 CM ($3) 0.3257 0.3988 0.4141 L2 ($4) −0.4786 0.3180 0.1323 L4 ($5) 0.0053 0.2638 0.9840 Mnone ($6) 0.1541 0.2090 0.4610 Mraised ($7) −0.5439 0.3064 0.0759 ADP*CM ($8) −0.0008 0.0004 0.0780 ADT*CM ($9) 0.0001 0.0000 0.0016 Dispersion 2.1970 0.5898 – *S.E. = Standard Error 26