title: The covariate-adjusted frequency plot.
abstract: Count data arise in numerous fields of interest. Analysis of these data frequently require distributional assumptions. Although the graphical display of a fitted model is straightforward in the univariate scenario, this becomes more complex if covariate information needs to be included into the model. Stratification is one way to proceed, but has its limitations if the covariate has many levels or the number of covariates is large. The article suggests a marginal method which works even in the case that all possible covariate combinations are different (i.e. no covariate combination occurs more than once). For each covariate combination the fitted model value is computed and then summed over the entire data set. The technique is quite general and works with all count distributional models as well as with all forms of covariate modelling. The article provides illustrations of the method for various situations and also shows that the proposed estimator as well as the empirical count frequency are consistent with respect to the same parameter.
authors: Statistics and Quantitative Methods, Faculty of Psychology and Sports Science, University of Münster, Münster, Germany.
authors: Heinz
authors: H
authors: Holling
authors: Statistics and Quantitative Methods, Faculty of Psychology and Sports Science, University of Münster, Münster, Germany.
authors: Walailuck
authors: W
authors: Böhning
authors: Southampton Statistical Sciences Research Institute, Mathematics & Medicine, Southampton, UK d.a.bohning@soton.ac.uk.
authors: Dankmar
authors: D
authors: Böhning
authors: Faculty of Psychology, University of Vienna, Vienna, Austria.
authors: Anton K
authors: AK
authors: Formann
mesh_terms: D001604:Berlin / Q000453:epidemiology; D002561:Cerebrovascular Disorders / Q000401:mortality; D005260:Female; D006801:Humans; D007231:Infant, Newborn; D008131:London / Q000453:epidemiology; D008297:Male; D015233:Models, Statistical; D054238:Perinatal Mortality; D016012:Poisson Distribution
keywords: adjusting for covariates; frequency plot; residual analysis