7. Consider the two-class logistic model with the linear predictor: p(x) log( ·1 - p(x)) = Bo + B₁x₁ + ß₂x2 + … + ßpïp. (a). Write down an expression for the odds (b). Show that the odds ratio O(x) = = p(1|x) p(2|x)* comparing the odds for two new cases with explanatory variables x and x' does not depend on Bo. (c). What does this imply if we simply want to rank new cases in terms of p(1|x).
7. Consider the two-class logistic model with the linear predictor: p(x) log( ·1 - p(x)) = Bo + B₁x₁ + ß₂x2 + … + ßpïp. (a). Write down an expression for the odds (b). Show that the odds ratio O(x) = = p(1|x) p(2|x)* comparing the odds for two new cases with explanatory variables x and x' does not depend on Bo. (c). What does this imply if we simply want to rank new cases in terms of p(1|x).
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:7. Consider the two-class logistic model with the linear predictor:
p(x)
log (₁ - p(x)) = ³0 + B₁X1 + B₂X2 + ... + BpXp·
1
(a). Write down an expression for the odds
O(x):
=
p(1|x)
p(2x)
(b). Show that the odds ratio comparing the odds for two new cases with explanatory
O(x')
variables x and x' does not depend on Bo.
(c). What does this imply if we simply want to rank new cases in terms of p(1|x).
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