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

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- R C (Copas, 1986, Hosmer et al., 1997)RC=M( yi− m ˆiπi)i=1Summation of the raw Pearson residualsAsymptotical moments:VarRˆCM−i=1ˆ πEtwith Q X ( X ) t WX XiR CM− ˆ πii=12( 1−ˆ π ) = 0it( 1−ˆ π ) = ( 1−2 ˆ π ) ( Wˆ−WQWˆ ˆ ˆ ) ( 1−2 ˆ π )i−1= ˆ , Wˆdiag( m iˆ π (1 ˆi−πi))= .Test:ZCRC−=VarRC−Mi=1Mi=1ˆ πiˆ π( 1−ˆ π )ii( 1−ˆ π )is standard normal under the hypothesisi1/ 2O.Kuss, Global Goodness-of-Fit Tests in Logistic Regression with Sparse Data, 2.11.02
Example:Occupational hand eczema in haidresser apprentices,M=574 (340 „successes“),Several covariates (p=6): genetical disposition, workhazards, confounders,N=334,Distribution of the m i :m i Frequency1 205 (61%)2 68 (20%)3 35 (11%)>3 26 (8%)Assessing goodness-of-fit:p-valueX 2 0,053D 0,012X 2 O 0,044X 2 M 0,031HL-Test 0,451X 2 F 0,408IM-Test 0,365R C 0,062Who is right???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 and 8: 3. The Problem of Sparse DataThe χ
Page 9 and 10: ... but what is the solution???- In
Page 11: - IM-Test (White, 1982; Orme, 1988)
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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