Logistic Regression | take #1

August 1, 2010
  • 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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