Poisson Regression Notes

i i for a model with p n parameters induces i yi

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Unformatted text preview: here all λi s are different. ˆ The MLE is λi = Yi . The maximum value of the log-likelihood is yi log (yi ) − l (bmax ; Y ) = yi − i log (yi !) i i ˆ ˆ ˆ For a model with p < n parameters, β induces λi = Yi . The maximum log-likelihood value is ˆ yi log (yi ) − l (b; Y ) = i ˆ yi − i log (yi !) i UNM The deviance is, D = −2[l (b; Y ) − l (bmax ; Y )] or ˆ yi log (yi /yi ) − D=2 i ˆ (yi − yi ) i [oi log (oi /ei ) − (oi − ei )] =2 i =2 oi log (oi /ei ). i Since for most cases i oi = i ei (model with β0 ). The deviance residuals are defined as di = sign(oi − ei ) [oi log (oi /ei ) − (oi − ei )] and so di2 . D= i UNM With a first order Taylor ser...
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