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Unformatted text preview: ; Y ) − l (b; Y )]
N =2 yi log
i =1 yi
yi + (ni − yi )log ni − yi
ni − yi D s approximate sampling distribution is chi-square.
UNM R computes the null deviance. For all i
g (πi ) = β0 → π = g −1 (β0 )
Fitted values yi = ni π
N −2 yi log (ˆ ) + (ni − yi )log (1 − π ) +
i =1 ni
yi with degrees of freedom N − 1.
g (πi ) = β0 + β1 Xi 1 + . . . + βp Xpi
πi are estimated with covariates and yi = ni πi
UNM Residual deviance:
N D = −2 yi log (ˆi ) + (ni − yi )log (1 − πi ) +
i =1 ni
yi with degrees of freedom N − (p + 1).
Hypothesis testing: H0 : β1 = β2 = . . . = βp = 0 vs.
H1 : at least one βi = 0.
D ∗ = Null deviance − Residual deviance
dof = (N − 1) − (N − (p + 1)) = p.
D ∗ approximately follows a χ2p) .
( UNM Alternatively if we just focus on the Residual deviance
(grouped Binomial case),
dof = (n1 + n2 + . . . + nN ) − (p + 1)
or dof = no....
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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.
- Fall '13