Multinomial logistic regression is a powerful statistical technique used to model and analyze relationships between multiple categorical outcome variables and one or more predictor variables. Interpreting the results of multinomial logistic regression in SPSS requires a comprehensive understanding of the output to derive meaningful insights. We provide a step-by-step guide to interpreting multinomial logistic regression results in SPSS, empowering researchers to glean valuable information from their data.

### Understanding the Output

Upon running a multinomial logistic regression analysis in SPSS, the output typically comprises several sections, each containing valuable information about the model’s performance, predictor variables, and significance levels. Let’s break down the key components of the output and explore how to interpret them effectively.

#### 1. Model Summary:

The model summary section provides an overview of the fit statistics for the multinomial logistic regression model. Key metrics include the -2 Log-Likelihood, which assesses the goodness of fit of the model, and the Hosmer and Lemeshow test, which evaluates the model’s calibration. A lower -2 Log-Likelihood value and a non-significant Hosmer and Lemeshow test indicate better model fit.

#### 2. Omnibus Tests of Model Coefficients:

This section presents the overall significance of the model, indicating whether the predictor variables collectively have a significant effect on the outcome variables. The chi-square test statistic and its associated p-value provide insights into the overall model fit. A significant p-value suggests that the model as a whole is useful for predicting the outcome variables.

#### 3. Coefficients Table:

The coefficients table displays the estimated coefficients (log odds) for each predictor variable included in the model. These coefficients represent the change in the log odds of the outcome variables associated with a one-unit change in the predictor variable, holding all other variables constant. Positive coefficients indicate an increase in the log odds of the outcome, while negative coefficients signify a decrease.

#### 4. Odds Ratios:

The odds ratios table presents the exponentiated coefficients, also known as odds ratios. These ratios quantify the change in the odds of the outcome variables for a one-unit increase in the predictor variable. An odds ratio greater than 1 indicates a higher likelihood of the outcome, while a ratio less than 1 suggests a lower likelihood.

### Interpreting the Results

Now that we’ve dissected the output, let’s delve into the process of interpreting multinomial logistic regression results in SPSS:

#### 1. Assessing Model Fit:

Begin by examining the model summary statistics, focusing on the -2 Log-Likelihood and the Hosmer and Lemeshow test. A lower -2 Log-Likelihood value and a non-significant Hosmer and Lemeshow test indicate better model fit.

#### 2. Evaluating Predictor Variables:

Next, scrutinize the coefficients table to identify the predictor variables and their corresponding coefficients. Pay attention to the significance levels (p-values) associated with each coefficient. A significant p-value (< 0.05) suggests that the predictor variable has a statistically significant effect on the outcome variables.

#### 3. Interpreting Coefficients and Odds Ratios:

Once you’ve identified significant predictor variables, interpret their coefficients and odds ratios. Focus on the direction (positive or negative) and magnitude of the coefficients. A positive coefficient indicates an increase in the log odds of the outcome variables, while a negative coefficient signifies a decrease. Additionally, examine the corresponding odds ratios to quantify the change in the odds of the outcome variables associated with each predictor variable.

#### 4. Drawing Conclusions:

Based on your analysis of the coefficients and odds ratios, draw conclusions about the relationships between the predictor variables and the outcome variables. Identify which predictor variables have the most substantial impact on the likelihood of each outcome category.

Interpreting multinomial logistic regression results in SPSS is a systematic process that involves evaluating model fit, scrutinizing predictor variables, and interpreting coefficients and odds ratios. By following the steps outlined in this guide, researchers can derive meaningful insights from their data and make informed decisions based on the findings of their multinomial logistic regression analysis.