Multinomial Regression

What is Multinomial regression?

Multinomial Regression is a statistical tool used to quantify the relationship between a categorical variable of interest and one or more explanatory variable(s). The resulting model can be used to evaluate evidence for hypotheses about the relationship and to make predictions under the following conditions.

1. The observations are representative of the population of interest and independent.

2. The relationship between explanatory variables and log odds of the response variable are linear.

How to use this app?

Step 1: To use this app, go to the 'Dataset and Model' tab and upload your .csv type dataset, or select a sample dataset.

Step 2: Fit your model by inputting your desired regression equation in the form:

response_name ~ explanatory_1_name + explanatory_2_name + ... + explanatory_k_name

Designate interaction terms using the * or : symbol between the two variable names. Using the asterisk will include both variables and their interaction (recommended), whereas the colon will only include the interaction. For example, an interaction between explanatory variable 1 and 2 can be specified as follows.

response_name ~ explanatory_1_name * explanatory_2_name + ... + explanatory_k_name

response_name ~ explanatory_1_name : explanatory_2_name + ... + explanatory_k_name

Step 3: You can check the assumptions provided in the 'Assumptions' tab. We recommend assessing assumptions visually using the provided graphical summary and confirming using the numerical summaries. The app will provide results for a Breusch-Pagan test assessing common variance of the residuals and Shapiro-Wilkes (n ≤ 5000) or Kolmogorov-Smirnov (n > 5000) tests for normality. While these tests might be helpful, they can be rather sensitive for small sample sizes leading us to detect minuscule transgressions.

Step 4: You can check the effect of outlying, influential, or leverage points in the 'Outliers' tab. Many models exhibit some influential points and researchers should ensure that the results of their model hold when using a robust regression model.

Step 5: The resulting model and interpretation of key values can be found in the 'Interpreation' tab

Step 6 (Optional): If your model has an interaction, the appropriate analyses will be reported in the 'Interaction' tab.

Please contact us if you have any questions at datascience@colgate.edu.