Logistic Regression - Assumptions

Residuals follow a binomial rather than a normal distribution. Normality of variables is not a stringent requirement.

A “nonlinear” (specifically an S-shaped, or sigmoidal, curve) relationship between IVs and the DV; however, this represents a linear relationship between the logit (natural log of the odds of the dependent occurring or not) and the set of IVs. See Addendum 2 for an illustration that compares probabilities, odds, and the logit.

Uses a maximum-likelihood rather than least-squares statistical model. In least squares, we select
regression coefficients that result in the smallest sum of squared differences between the observed
and the predicted values of the DV. In maximum-likelihood, the coefficients that make our observed results “most likely” are selected.

Does not assume homoscedasticity.

Assumes that there is little or no multicollinearity

Predicts the odds of an event occurring (see Addendum 1), which is based on the probability of

that event occurring. Precisely, the odds of an event occurring is: Odds=P/(1-P)
={prob. of event occurring}/[1-prob. of event occurring]
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Terminology for use with Logistic Regression -

Probability = P = probability of an event occurring (range of 0 - 1)


 Odds = P/(1-P) = ratio of the probability of an event occurring to the probability of the event not occurring (range of 0 – positive infinity)

Odds ratio = Odds1/ Odds2= ratio of two odds

Logit = ln(Odds) = predicted logged odds (range of neg. infinity - pos. infinity)


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References:


Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). New York: John Wiley &

Sons, Inc.

Menard, S. (1995). Applied logistic regression analysis. Thousand Oaks, CA: Sage Publications.

Pampel, F. C. (2000). Logistic regression: A primer. Thousand Oaks, CA: Sage Publications.