Global Goodness-of-Fit Tests in Logistic Regression with Sparse Data

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The problem is well-known, ...- The X 2 and D goodness-of-fit statistics do not haveapproximate chi-squared distributions when appliedto logistic regression models with a continuouscovariate, unless there are many observations at eachlevel of the covariate. (Agresti, 1990)- Neither X 2 nor D is appropriate in the many stratastandard asymptotic model, because under this modelthere is no χ 2 -limiting distribution. (Santner/Duffy,1989)- Thus, p-values calculated for X 2 and D when M ≈N,using the χ 2 -distribution, are incorrect.(Hosmer/Lemeshow, 1989)- The effect of sparseness is noticed mainly on D andX 2 , which fail to have the properties required forgoodness-of-fit statistics. (McCullagh/Nelder, 1989)O.Kuss, Global Goodness-of-Fit Tests in Logistic Regression with Sparse Data, 2.11.02
... but what is the solution???- In principle it would seem preferable to accept thefailure of the chi-square limit and to use a moreaccurate approximation to the null distributionwithout accumulating cells. (Lloyd, 1999)- Thus, to analyze lack of fit when explanatoryvariables are continuous, we apply goodness-of-fitstatistics and related residual measures by groupingobserved and fitted values for a partition of the spaceof explanatory variable values. (Agresti, 1989)- It is good statistical practice, however, not to rely oneither D or X 2 as an absolute measure of goodness offit in these circumstances. It is much better to look forspecific deviations from the model of a type that iseasily understood scientifically. (McCullagh/Nelder,1989)O.Kuss, Global Goodness-of-Fit Tests in Logistic Regression with Sparse Data, 2.11.02
Page 3: Data:Response1 01 Y 1 m 1 -Y 1 m 1C
Page 7: 3. The Problem of Sparse DataThe χ
Page 11 and 12: - IM-Test (White, 1982; Orme, 1988)
Page 13 and 14: Example:Occupational hand eczema in
Page 15 and 16: 6. Simulation Results6.1. Null hypo
Page 17 and 18: Back to the example:p-Wert p*-WertX
Page 19: 8. Literature- Agresti A. Categoric

Global Goodness-of-Fit Tests in Logistic Regression with Sparse Data

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