title: Testing goodness of fit in regression: a general approach for specified alternatives.
abstract: When fitting generalized linear models or the Cox proportional hazards model, it is important to have tools to test for lack of fit. Because lack of fit comes in all shapes and sizes, distinguishing among different types of lack of fit is of practical importance. We argue that an adequate diagnosis of lack of fit requires a specified alternative model. Such specification identifies the type of lack of fit the test is directed against so that if we reject the null hypothesis, we know the direction of the departure from the model. The goodness-of-fit approach of this paper allows to treat different types of lack of fit within a unified general framework and to consider many existing tests as special cases. Connections with penalized likelihood and random effects are discussed, and the application of the proposed approach is illustrated with medical examples. Tailored functions for goodness-of-fit testing have been implemented in the R package global test.
authors: Department of Statistics, University of Milano-Bicocca, via Bicocca degli Arcimboldi 8, 20126, Milan, Italy. aldo.solari@unimib.it
authors: Aldo
authors: A
authors: Solari
authors: Saskia
authors: S
authors: le Cessie
authors: Jelle J
authors: JJ
authors: Goeman
mesh_terms: D015502:Absorptiometry, Photon; D000273:Adipose Tissue / Q000000981:diagnostic imaging; D000818:Animals; D000886:Anthropometry / Q000379:methods; D015197:Carcinogenicity Tests / Q000379:methods; D003627:Data Interpretation, Statistical; D004195:Disease Models, Animal; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D057230:Limit of Detection; D016014:Linear Models; D016016:Proportional Hazards Models; D051381:Rats; D012044:Regression Analysis; D018709:Statistics, Nonparametric