# Binary Logistic Regressions

Binary logistic regressions, by design, overcome many of the restrictive assumptions of linear regressions.  For example, linearity, normality and equal variances are not assumed, nor is it assumed that the error term variance is normally distributed.

The major assumptions are:

1. That the outcome must be discrete, otherwise explained as, the dependent variable should be dichotomous in nature (e.g., presence vs. absent);
2. There should be no outliers in the data, which can be assessed by converting the continuous predictors to standardized, or

z

scores, and remove values below -3.29 or greater than 3.29.
3. There should be no high intercorrelations (multicollinearity) among the predictors.  This can be assessed by a correlation matrix among the predictors. Tabachnick and Fidell (2012) suggest that as long correlation coefficients among independent variables are less than 0.90 the assumption is met.

Also, there should be a linear relationship between the odds ratio, orEXP(B),and each independent variable.  Linearity with an ordinal or interval independent variable and the odds ratio can be checked by creating a new variable that divides the existing independent variable into categories of equal intervals and running the same regression on these newly categorized versions as categorical variables.  Linearity is demonstrated if the beta coefficients increase or decrease in linear steps (Garson, 2009).

A larger sample is recommended in fitting with the maximum likelihood method; using discrete variables requires that there are enough responses in each category.

References:

Garson, G. D. (2009). Logistic Regression. Retrieved on August 12, 2009 from http://faculty.chass.ncsu.edu/garson/PA765/logistic.htm

Tabachnick, B. G. & Fidell, L. S. (2012). Using multivariate statistics (6th ed.).  Boston, MA: Pearson.

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