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Multinomial Logistic Regression

A multinomial logistic regression (or multinomial regression for short) is used when the outcome variable being predicted is nominal and has more than two categories that do not have a given rank or order. This model can be used with any number of independent variables that are categorical or continuous.

Assumptions

In addition to the two mentioned above:

  1. Independence of observations
  2. Categories of the outcome variable must be mutually exclusive and exhaustive
  3. No multicollinearity between independent variables
  4. Linear relationship between continuous variables and the logit transformation of the outcome variable
  5. No outliers or highly influential points

Running Logistic Regression in SPSS

  1. Analyze > Regression > Multinomial Logistic...
  2. Move the nominal outcome variable to the "Dependent" box.
  3. Move all continuous predictor variables into the "Covariates" box and all nominal predictor variables into the "Factors" box.
    • Ordinal variables can be assigned as covariates or factors. It's up to the researcher.
  4. Click on the "Statistics" button to select additional statistics and plots you want included with your output.
    • Click "Continue" to return to the main dialogue box.
  5. Click "OK" to run the test. 

Interpreting Output

  • Pseudo R-Square
    • One way to assess variance explained, though not the easiest to interpret
    • Cox & Snell, Nagelkerke, & McFadden
  • Goodness-of-Fit
    • Provides results of the Chi-Square Goodness-of-Fit test used to assess the significance of the overall model
    • A statistically significant result on the "Pearson" measure indicates that the model is not a good fit for the data
  • Model Fitting Information
    • Another way to assess the fit of the model
    • Significance here means that the model with the variables is a better predictor than the model without the variables
  • Likelihood Ratio Tests
    • Indicates the significance of each predictor variable
  • Parameter Estimates
    • Provides a measure of the contribution of each predictor variable in the model (like the "Coefficients" output for a linear regression)
    • Wald test - used to determine the significance (sig.) for each predictor variable
    • Exp(B) is an odds ratio used to predict the probability of an event occurring based on a one-unit change in the predictor variable when all other predictors are kept constant.

Reporting Results in APA Style

A multinomial logistic regression was performed to create a model of the relationship between the predictor variables and membership in the three groups (low SES, mid SES, and high SES). The fit between the model containing only the intercept and data improved with the addition of the predictor variables, X^2(20, N = 625) = 61.20, Nagelkerke R2 = .33, p < .001. 

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