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Multinomial Logistic Regression in SPSS

Multinomial Logistic Regression in SPSS

Multinomial logistic regression is a simple extension of binary logistic regression that allows for more than two categories of the dependent variable or the outcome variable.


  1. Dependent variable should be measured at the nominal level with more than or equal to three values.

  2. Independence of observations is required and the dependent variable should have mutually exclusive and exhaustive categories.

  3. There should be no multicollinearity.

  4. A linear relationship is required between any continuous independent variable and the logical transformation of the dependent variable.

  5. There should be no outliers.

Depression is considered as the dependent variable and Fenugreek Intake is considered as the independent variable.

None is labelled as 1, mild is labelled as 2, and moderate in depression is labelled as 3; and 1 time a day is labelled as 1 and 2 times a day is labelled as 2.

In SPSS, Multinomial Logistic Regression is found in Analyze > Regression > Multinomial Logistic Regression

Then, we will get Multinomial Logistic Regression dialog box.

Add the dependent variable (Depression) in the ‘Dependent’ box and the independent variable (Fenugreek Intake) in the ‘Factor(s)’ box.

In the ‘Reference Category’ option, click on ‘First Category’. Here, the people with depression are compared to normal people, who are acting as a reference category. Therefore, ‘First Category’ is chosen.

In the ‘Specify Model’ option, select ‘Custom/Stepwise’, add ‘Fenugreek Intake’ under ‘Forced Entry Terms’, and then click on ‘Continue’. Click on ‘Include intercept in model’.

In the ‘Multinomial Logistic Regression: Statistics’ dialog box, tick the options as shown in the following image.

Click on ‘Continue’ and then on ‘Ok’.

Output of Multinomial Logistic Regression

First, we will get the ‘Model Fitting Information’ table. Here, Sig. column (p=0.000) means that the full model predicts the dependent variable statistically and significantly better than the ‘Intercept Only’ model.

Then, we will get ‘Pseudo R-Square’ table with ‘Cox and Snell’, ‘Nagelkerke’ and ‘McFadden’ pseudo R2 measures. The R-square values of ‘Cox and Snell’ and ‘Nagelkerke’ indicate the amount of variation in the dependent variable that is explained by the model.

Then, we will get ‘Likelihood Ratio Tests’ table, which is useful for nominal independent variables. It can be observed that ‘Fenugreek intake’ is significant (p=0.000).

Then, we will get ‘Parameter Estimates’ table.

Fenugreek intake was significant for both categories of depression (mild (p=0.003) and moderate (p=0.030)). Considering the value of the coefficients B, it could be inferred that if fenugreek consumption is increased, then the multinomial log-odds of getting mild depression to normal is expected to increase by 3.332 units, while all other variables of the model being held constant. 

Data: Multinomial_Logistic_regression_data.sav

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