The odds, or the ratio of the probability of success to that of failure, can only take on positive values. Taking the logarithm of the odds ratio transforms the support to the entire real number line and thus converts the problem into something analogous to linear regression, where the support extends from -∞ to ∞.
Why are the log odds used in the link function instead of just the regular odds ratio?
The odds, or the ratio of the probability of success to that of failure, can only take on positive values. Taking the logarithm of the odds ratio transforms the support to the entire real number line and thus converts the problem into something analogous to linear regression, where the support extends from -∞ to ∞.
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