Deviance for Binary Data Notes

An approximate 95 condence interval for i is i 196se

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Unformatted text preview: are obtained by software package. An approximate 95% confidence interval for βi is ˆ ˆ βi ± (1.96)SE (βi ). To test H0 : βi = 0 vs Ha : βi = 0, Z= ˆ βi − 0 ˆ SE (βi ) which is approximately a N (0, 1). If zobs is the observed value of Z , p-value=2P (Z > zobs ). SAS reports Z 2 ≈ χ21) ( UNM Saturated model. Model with the the maximum number of parameters that can be estimated. Y1 , Y2 , . . . , YN are independent and Yi ∼ Binomial (ni , πi ), log-likelihood is (except for constant), N [yi log (πi ) − yi log (1 − πi ) + ni log (1 − πi )] l (β ; Y ) = i =1 Saturated model: All πi s are different and β = (π1 , π2 , . . . , πN )T The maximum likelihood estimates are πi = yi /ni (bmax ). ˆ The max. log-likelihood is N [yi log (yi /ni )−yi log (1−(yi /ni ))+ni log (1−(yi /ni ))] l (bmax ; Y ) = i =1 UNM For model with p < N parameters, estimates πi . ˆ ˆ Fitted values, yi = ni πi ˆ The log-likelihood, N ˆ ˆ ˆ [yi log (yi /ni ) − yi log (1 − (yi /ni )) + ni log (1 − (yi /ni ))] l (b ; Y ) = i =1 The deviance (textbook) D = 2[l (bmax...
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This note was uploaded on 01/27/2014 for the course STAT 574 taught by Professor Gabrielhuerta during the Fall '13 term at New Mexico.

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