Odds ratios that are greater than 1 indicate that the event is more likely to occur as the predictor increases. Odds ratios that are less than 1 indicate that the event is less likely to occur as the predictor increases.
For categorical predictors, the odds ratio compares the odds of the event occurring at 2 different levels of the predictor. Minitab sets up the comparison by listing the levels in 2 columns, Level A and Level B. Level B is the reference level for the factor. Odds ratios that are greater than 1 indicate that the event is less likely at level B. Odds ratios that are less than 1 indicate that the event is more likely at level B. For information on how to select the reference level for the analysis, go to Specify the coding scheme for Fit Binary Logistic Model.
For more information, go to Odds Ratios for Fit Binary Logistic Model.
To determine how well the model fits your data, examine the statistics in the Model Summary table.
For binary logistic regression, the data format affects most of the model summary and goodness-of-fit statistics. The AIC and the Hosmer-Lemeshow test are unaffected by the data format and are, therefore, comparable between formats. For more information, go to How data formats affect goodness-of-fit in binary logistic regression.
The higher the deviance R^{2}, the better the model fits your data. Deviance R^{2} is always between 0% and 100%.
Deviance R^{2} always increases when you add additional predictors to a model. For example, the best 5-predictor model will always have an R^{2} that is at least as high as the best 4-predictor model. Therefore, deviance R^{2} is most useful when you compare models of the same size.
For binary logistic regression, the format of the data affects the deviance R^{2} value. The deviance R^{2} is usually higher for data in Event/Trial format. Deviance R^{2} values are comparable only between models that use the same data format.
Deviance R^{2} is just one measure of how well the model fits the data. Even when a model has a high R^{2}, you should check the residual plots and goodness-of-fit tests to assess how well a model fits the data.
Use adjusted deviance R^{2} to compare models that have different numbers of predictors. Deviance R^{2} always increases when you add a predictor to the model. The adjusted deviance R^{2} value incorporates the number of predictors in the model to help you choose the correct model.
Use AIC to compare different models. The smaller the AIC, the better the model fits the data. However, the model with the smallest AIC for a set of predictors does not necessarily fit the data well. Also use goodness-of-fit tests and residual plots to assess how well a model fits the data.
If the deviation is statistically significant, you can try a different link function or change the terms in the model.
For binary logistic regression, the format of the data affects the p-value because it changes the number of trials per row.