- We observe Binomial event with two outcomes : 0 and 1 , with
*p* representing probability of event 1 and *(1-p)* representing probability of event 0
- When observing binary variable, we’re often interested at estimating ratio between events
*(1-p)/p *– in order to determine the bias on the event that is more likely to occur
- In order to handle the scale of probability ratio – we’re actually interested in logarithmic ration :
*log((1-p)/p)*
- Additionally – this ratio can be interpreted as measure of
*growth* of process (in direction of events described by given probability)
- deriving
*p *as linearly dependent variable in the context above, naturally introduce *logistic distribution function* :
- it seems that derivation of logit function in literature goes in reverse direction (from logistic function to logarithm of probability ratio)
- note that cumulative distribution function can represent a “natural” linkage function in case of binary variable (which is the basic of
*probit* model)

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This entry was posted on August 1, 2010 at 1:47 pm and is filed under statistics.

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