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StatsToDo : Multinomial Logistic Regression Explained

Introduction Example R Code Example Explained
This page provides explanations and example R codes for Multinomial 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 Multinomial Logistic Regression is an extension of the Binomial Logistic Regression, as explained in the Binomial Logistic Regression Explained Page . The dependent variable in this case are group names, with more than two groups

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 algorithm produces m-1 formulae, m being the number of groups. The probabilities of belonging to the groups are estimated, and the estimated diagnosis assigned to that with the highest probability. Details on how this is carried out are described in the panel Example Explained

### References

https://stats.idre.ucla.edu/r/dae/multinomial-logistic-regression/