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

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5. Which Solution is the Best???Up to now there is only one large, systematicinvestigation of global goodness-of-fit tests in logisticregresssion (Hosmer et al., 1997)Results:R C and X 2 M were "winners"But some need of supplement:- Add new tests- Varying m iO.Kuss, Global Goodness-of-Fit Tests in Logistic Regression with Sparse Data, 2.11.02
6. Simulation Results6.1. Null hypothesisSingle continuous covariate x 1 with x 1 ∼N(0,1),β 0 =0, β 1 =0,693, M=500, 1000 runs, α=0,05m i ≡1 m i ≡2 m i ≡1-10 m i ≡10X 2 0,000 0,010 0,002 0,046D 1,000 0,977 0,585 0,114X 2 O 0,061 0,043 0,040 0,041X 2 M 0,063 0,052 0,045 0,052HL test 0,055 0,051 0,054 0,052X 2 F 0,000 0,051 0,055 0,062IM test 0,057 0,049 0,045 0,049R C 0,053 0,052 0,046 0,051Three continuous covariates x i with x i iid N(0,1),β 0 =0, β 1 =0.693, β 2 =0.405, β 3 =0.223,M=500, 1000 runs,α=0,05m i ≡1 m i ≡2 m i ≡1-10 m i ≡10X 2 0,000 0,001 0,009 0,043D 1,000 0,959 0,866 0,118X 2 O 0,074 0,039 0,042 0,026X 2 M 0,078 0,052 0,059 0,057HL-Test 0,049 0,049 0,052 0,042X 2 F 0,000 0,052 0,058 0,058IM-Test 0,051 0,049 0,058 0,051R C 0,058 0,046 0,048 0,049O.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 and 8: 3. The Problem of Sparse DataThe χ
Page 9 and 10: ... but what is the solution???- In
Page 11 and 12: - IM-Test (White, 1982; Orme, 1988)
Page 13: Example:Occupational hand eczema in
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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