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StatsToDo : Binomial Logistic Regression Explained

Introduction Example R Code Example Explained
This page provides explanations and example R codes for Binomial Logistic Regression, which is one of the algorithms based on the Generalized Linear Models.

The two terms General Linear Model and Generalized Linear Models have different meanings. General Linear model is an extension of the least square analysis where the dependent variable is Guassian (parametric, normally distributed measurements) is discussed in the General Linear Model Explained Page . Generalized Linear Models is an extension and adaptation of the General Linear Model to include dependent variables that are non-parametric, and includes Binomial Logistic Regression, Multinomial Regression, Ordinal Regression, and Poisson Regression. R uses the function glm for Generalized Linear Models.

The Binomial Logistic Regression is commonly referred to as logistic regression, and in this page the abbeviation BinLogReg is used. In this model, the dependent variable is binomial, one of two outcomes, no/yes, True/false, 0/1.

In R, the independent variables can be measurements or factors

• Measurements are numerical, and can be binary(0/1), ordinal, or parametric
• Factors are text, and consists of group names. Unless otherwise assigned, R arrange group names alphabetically, and use the first name as the reference group
The formula obtained is y = intercept + b1x1 + b2x2 + ....., where b is the coefficient and also the log(odds Ratio) against the reference value. The reference values are 0 for measurement and the reference group for factors. y is then the log odds ratio of outcomes against the reference outcome (outcome name that is alphabetically first)

The probability of outcome is then calculated by logistic transform p = 1 / (1 + exp(-y))

### References

[https://en.wikipedia.org/wiki/Logistic_regression] Logistic Regression by Wikipedia

Cox, DR (1958). "The regression analysis of binary sequences (with discussion)". J Roy Stat Soc B. 20 (2): 215 - 242. JSTOR 2983890.

Portney LR, Watkins MP (2000) Foundations of Clinical Research Applications to Practice Second Edition.ISBN 0-8385-2695 0 p. 597 - 603