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f (yi |π ) = π yi (1 − π )1−yi ; yi = 0, 1
E (Yi ) = π but π is between 0 and 1.
Deﬁne a link function as
g (π ) = log (π/(1 − π )) = x t β
Maps (0, 1) into (−∞, ∞).
UNM Solve equation for π , we get the logistic function.
π= exp(x t β )
1 + exp(x t β ) For one-predictor X ,
π= exp(β1 + β2 X )
1 + exp(β1 + β2 X ) If F (·) is another cumulative distribution function (CDF),
π = F (β1 + β2 X ).
π = Φ(β1 + β2 X )
where Φ(·) is the CDF of...
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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