Stepwise Multinomial Logistic Regression

Figure 1. Step summary
Step summary

When you have a lot of predictors, one of the stepwise methods can be useful by automatically selecting the "best" variables to use in the model. The forward entry method starts with a model that only includes the intercept, if specified. At each step, the term whose addition causes the largest statistically significant change in -2 Log Likelihood is added to the model. The final model should only include important predictors.

Figure 2. Likelihood ratio tests
Likelihood ratio tests

The chi-square statistics in the likelihood ratio tests table are slightly different from those in the step summary. This is because the tests in the step summary only account for the terms in the model at each step, while the likelihood ratio tests account for all terms in the final model. Thus, for example, the chi-square statistic for testing Years with current employer (employ) is 43.518 in the step summary and 28.276 in the likelihood ratio tests. That means that some of the variation in the dependent variable explained by Years with current employer (employ) is also explained by variables added in later steps. Contrarily, the chi-square statistic for testing Number of people in household (reside) is higher in the likelihood ratio tests than in the step summary, thus its partial relationship with the dependent is stronger when accounting for all other predictors than when Years at current address (address) is not included.

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