What are the steps to interpret logistic regression analysis results?

2 Check the assumptions

The second step is to check the assumptions of the logistic regression model and assess its validity. These assumptions include that the outcome variable follows a Bernoulli distribution, the explanatory variables are independent of each other and do not exhibit multicollinearity, the relationship between the log odds of the outcome and the explanatory variables is linear, and the error terms are independent and identically distributed. To verify these assumptions, you can use various tests and plots such as the Hosmer-Lemeshow test, variance inflation factor, residual plot, and leverage plot. If any of these assumptions are violated, you may need to modify your model or use a different method.

3 Interpret the coefficients

The third step is to interpret the coefficients of the logistic regression model and their significance. The coefficients indicate how much the log odds of the outcome change when the corresponding explanatory variable increases by one unit, holding all other variables constant. To make the interpretation easier, you can exponentiate the coefficients and obtain the odds ratios, which indicate how much the odds of the outcome change when the corresponding explanatory variable increases by one unit, holding all other variables constant. You can also calculate the confidence intervals and the p-values of the coefficients, which indicate the uncertainty and the statistical significance of the estimates. A coefficient is statistically significant if its p-value is less than a predefined threshold, such as 0.05.

4 Predict the probabilities

The fourth step is to predict the probabilities of the outcome for different values of the explanatory variables using the logistic regression model. You can use the equation of the model to calculate the log odds of the outcome for any combination of the explanatory variables, and then apply the inverse logit function to obtain the probabilities. Alternatively, you can use the software tool to generate the predictions for you. You can use the predicted probabilities to classify the observations into two groups based on a cutoff value, such as 0.5, and compare them with the actual outcomes to evaluate the accuracy of the model.

5 Assess the performance

The fifth step is assessing the performance of the logistic regression model and its ability to predict the outcome. Various metrics and methods can be used to measure this performance, such as the confusion matrix, which summarizes true positives, false positives, true negatives, and false negatives. Additionally, accuracy, sensitivity, and specificity can be calculated to determine how well the model is performing. Furthermore, the ROC curve plots sensitivity against false positive rate for different cutoff values, while AUC represents the overall discrimination power of the model. These metrics and methods can then be used to compare different models or optimize the cutoff value for your model.

6 Communicate the results

The sixth and final step is to communicate the results of the logistic regression analysis clearly and concisely. Summarize the main findings and implications of the model, such as which explanatory variables are significant and how they affect the odds of the outcome, what are the predicted probabilities of the outcome for different scenarios or groups of interest, and how well the model fits the data and predicts the outcome. Additionally, make sure to discuss any limitations and assumptions of the model that may affect the interpretation or generalization of results. To support your claims and enable others to reproduce your analysis, provide relevant tables, graphs, and code.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?