Example of Nominal Logistic Regression

A school administrator wants to assess different teaching methods. She collects data on 30 children by asking them their favorite subject and the teaching method used in their classroom.

Because the response is categorical and the values have no natural order, the administrator uses nominal logistic regression to understand how age (10–13) and teaching method (demonstration or explain) are related to the student preferences in subject (math, science, and language arts).

  1. Open the sample data, TeachingMethods.MTW.
  2. Choose Stat > Regression > Nominal Logistic Regression.
  3. In Response, enter Subject.
  4. In Model, enter 'Teaching Method' Age.
  5. In Categorical predictors (optional), enter 'Teaching Method'.
  6. Click Results. Select In addition, list of categorical predictor level values, and tests for terms with more than 1 degree of freedom.
  7. Click OK in each dialog box.

Interpret the results

The reference event is science, which indicates that Minitab compares math and language arts to science in the logistic regression table. For information on how to change the reference event, go to Select the options for Nominal Logistic Regression.

When the response has three levels, Minitab calculates two equations: Logit(1) and Logit(2). The logits are the estimated differences in log odds or logits of math and language arts compared to science. Each set contains a constant and coefficients for teaching method, which is a categorical predictor, and age, which is a continuous predictor. The coefficient for teaching method is the estimated change in the logit when the teaching method is explanation compared to demonstration, while holding age constant. The coefficient for age is the estimated change in the logit with a one-year increase in age, while holding teaching method constant.

For Logit 2, the p-values for both teaching method and age are less than the significance level of 0.10. These results indicate that the likelihood that students prefer language arts instead of science is significantly higher when the teaching method is explanation and as age increases. The estimated odds ratio for teaching method indicates that the odds of choosing language arts instead of science is about 16 times higher for these students when the teaching method changes from demonstration to explanation.

For Logit 1, the p-values for teaching method and age are not less than the significance level of 0.10. These results indicate that there is not enough evidence to conclude that a change in teaching method from demonstration to explanation or differences in age affects the preference of math versus science.

The goodness-of-fit tests are all greater than the significance level of 0.05, which indicates that there is not enough evidence to conclude that the model does not fit the data.

Nominal Logistic Regression: Subject versus Teaching Method, Age

Response Information Variable Value Count Subject Science 10 (Reference Event) Math 11 Arts 9 Total 30
Factor Information Factor Levels Values Teaching Method 2 Demonstrate, Explain
Logistic Regression Table 95% Odds CI Predictor Coef SE Coef Z P Ratio Lower Logit 1: (Math/Science) Constant -1.12266 4.56425 -0.25 0.806 Teaching Method Explain -0.563115 0.937591 -0.60 0.548 0.57 0.09 Age 0.124674 0.401079 0.31 0.756 1.13 0.52 Logit 2: (Arts/Science) Constant -13.8485 7.24256 -1.91 0.056 Teaching Method Explain 2.76992 1.37209 2.02 0.044 15.96 1.08 Age 1.01354 0.584494 1.73 0.083 2.76 0.88
Predictor Upper Logit 1: (Math/Science) Constant Teaching Method Explain 3.58 Age 2.49 Logit 2: (Arts/Science) Constant Teaching Method Explain 234.90 Age 8.66

Log-Likelihood = -26.446

Test of All Slopes Equal to Zero DF G P-Value 4 12.825 0.012
Goodness-of-Fit Tests Method Chi-Square DF P Pearson 6.95295 10 0.730 Deviance 7.88622 10 0.640
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