# Multinomial Logistic Regression

Statistics Solutions provides a data analysis plan template for the multinomial logistic regression analysis. You can use this template to develop the data analysis section of your dissertation or research proposal.

The template includes research questions stated in statistical language, analysis justification and assumptions of the analysis. Simply edit the blue text to reflect your research information and you will have the data analysis plan for your dissertation or research proposal.

**Data Analysis Plan: Multinomial Logistic Regression**

Copy and paste the following into a word document to use as your data analysis plan template.

*Research Question:*

RQ: Does independent variable(s) predict dependent variable?

H_{o}: Independent variable(s) does not predict dependent variable.

H_{a}: Independent variable predicts dependent variable.

*Data Analysis*

To examine the research question, a multinomial logistic regression will be conducted to investigate whether independent variable(s) predicts the dependent variable, which has more than two categorical levels. For this research question, the independent variables are independent variable 1, independent variable 2, etc.; the dependent variable is dependent variable. The overall model significance for the multinomial logistic regression will be examined by the collective effect of the independent variable(s), presented with a χ^{2 }coefficient. The Nagelkerke *R ^{2}* will assess the variability accounted for on the dependent variable by the independent predictor variable. Individual predictors will be assessed by the Wald coefficient. Predicted probabilities of an event occurring will be determined by Exp (

*B*). For significant predictors, an Exp (

*B*) greater than one indicates that a one unit increase in the independent variable, the dependent variable will be X times more likely to be coded 1. Significant predictors with a Exp (

*B*) less than 1 will be evaluated by 1/Exp (

*B*), meaning that a one unit increase in the independent variable will be X times more likely to be coded 0.

Multinomial 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. There should be no multicollinearity among the independent variables, there should be no outliers, and there should be a linear relationship between the odd ratio and the independent variable. Linearity with an ordinal or interval independent variable and the odd 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 *B* coefficients increase or decrease in linear steps. Finally, a larger sample is recommended with the maximum likelihood method; using discrete variables requires that there are enough responses in each category.

*Reference*

Statistics Solutions. (2016). Data analysis plan: Multinomial Logistic Regression [WWW Document]. Retrieved from http://www.statisticssolutions.com/academic-solutions/member-resources/member-profile/data-analysis-plan-templates/data-analysis-plan-multinomial-logistic-regression/