I have been developing various regression models for road crash frequency. I use generalized linear models (SPSS GENLIN or SAS GENMOD procedures), negative binomial (NB) distribution, log link function. For example: annual crash frequency on road segment = a x (traffic volume)^b x (curvature change rate)^c etc. Now I am trying to assess individual impact of variables, let's say traffic volume or curvature change rate. From literature I am not aware of any standard procedure for that. I have seen various charts (predicted crash frequency on Y-axis, traffic volume on X-axis) or tables with "impact coefficients" (example: standard traffic volume equals impact 1.0, increased traffic volume = impact 1.5, etc.). I also saw calculations of elasticity or marginal effects, but usually only for Poisson regression and I am not sure whether the same applies for NB. I would like to find some specific paper dealing with this issue AND dataset used so that I would do calculations myself to obtain the same results to make sure I know how to do it. Could somebody help me with this, please? Thank you.
Hi Jiri,
It seems like you are looking for a way to compare the contribution of input/predictor variables to prediction of crashes - which can be approached from the perspective of discerning predictor relative importance. If that seems about right given your goals, such a question could be examined by a procedure like dominance analysis, which is used to discern the relative importance of predictor variables.
Whereas I am not familiar with published extensions of dominance analysis to NB models, given that logit models are a generalized linear model, the Azen & Traxel (2009) paper below should be relevant with a different variance and link function using a pseudo-R2 like the Estrella or McFadden.
If you use Stata (or could be interested in doing so), such models could be fit using domin (from Stata's SSC).
- joe
Article The Dominance Analysis Approach for Comparing Predictors in ...
Article Using Dominance Analysis to Determine Predictor Importance i...
Data DOMIN: Stata module to conduct dominance analysis
Please use step wise multiple regression models and multivariate analysis to know the impact of every variables.
Joseph gave the correct answer! This is exactly how I would proceed. And in fact, he wrote the marvelous domin command in Stata!
The best approach, I think, is to compare the incident rate ratios (IRRs) for each variable. These are the exponentiated coefficients of the count regression model, which are of course adjusted for the effects of one another, as in any regression model. The IRR represents compares the incident rate across the levels of the predictor variables. Variables with large IRRs relative to their standard errors are more important than those with lower values. This is perhaps the simplest approach.
Thank you, William. Yes, I saw IRR applied in some papers also, especially from econometrics. Is it the same as 'elasticity'? The terms sometimes differ between various fields :-)
Jiri
No, IRR is different from elstaciity. The IRR is simply the result one gets from exponentiating (exp(B)) the count regression coefficients, whether Poisson or Neg. Bin. In that way they are similar to the odds ratios obtained with exponentiating logistic regression coefficients, although the interpretation deals with incidents rather than than whether an outcome is 1 or 0.
Hope that helps.
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