In traffic safety analysis, weight factors are often applied, to correct for road length, traffic volume, numbers of kilometers driven, etc. Also, many data are subdivided into classes (road type: freeway, 80 km/hr, two lanes, rural area, etc); combining factors often leads to a cross-classification. Analysis of accidents (numbers of deaths, e.g.) is mostly done by using the Poisson model, which has become a standard in traffic safety research. The best known paradigm for the analysis of unweighted Poisson data is Goodman (1970), on which Goodman's ECTA is based too. Goodman's procedure leads to orthogonal row-, column- and interaction effects, in exactly the same way as in analysis of variance. For the weighted Poisson model, at SWOV, a computer program was developed ('WPM': Weighted Poisson Method', by De Leeuw and Oppe, 1976) and the question was, whether there existed a comparable procedure in SAS. In using SAS-GENMOD, one can perform weighted Poisson regression, but not an orthogonal decomposition of effects; this has been achieved by defining contrast vectors for a 'hypervariable', for which all variables are subclasses, such that interaction contrasts can be defined too. One problem in implementing Goodman's procedure was the fact that in WPM (following Goodman) 0.5 was added to each cell count; SAS-GENMOD however, only accepts counts. It will be discussed how SAS-GENMOD can be made dealing with real numbers. Furthermore, the distinction between four types of sums of squares (Ti - T4) is very important and parallels 'sequential' and 'partialized' sums of squares. Apart from this, there is a choice between test statistics ('likelihood ratio test statistic', LR, or 'Wald statistic' - which yields Pearson's chi-squared test statistic). Also, parametrisation in SAS is different from other well known packages. Most common are the 'S'-restrictions: sum of parameter values is zero; this defines the ANOVA-model. Other restrictions are the J.t-Model restrictions: the last level is set zero. For the weighted Goodman design, more examples and setups will be given. Test statistics and sums of squares for different parameterizations will be given with the examples. (Author/publisher)
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