# Logistic Regression

Regular regression has a basic assumption that the outcome variable is measured on the interval or ratio level.  You can “fudge” on this assumption a little when there are lots of categories in a discrete space, such as with GPAs.  When the dependent variable is binary (dichotomous) or categorical, then regular regression really doesn’t work very well.  To solve this problem, some brilliant researchers came up with the idea of logistic regression.  Logistic regression (aka the logit model) is designed to work with categorical data.  The math behind the model is based on probability and can be overwhelming for the non-mathematician.

A rather morbid (pun intended) example of research that used this technique was the development of a scale that predicts the likelihood of trauma victims dying in emergency rooms.  Note that death is a binary variable; either the patient died or did not die.  There is no such thing as being a little dead.  This method works by computing an odds ratio and places particular cases into a category based on the odds.

An annoying characteristic of logistic regression is that since the math is quite different, no R2 statistic is computed.  Several researchers have developed “pseudo R2” statistics, but none have risen to the top of the heap as an accepted best estimate of shared variance.  Probably the most common of these is the “Likelihood Ratio R2” statistic.  There are also no beta coefficients, so researchers tend to talk about “odds ratios” when interpreting individual predictor variables.

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