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 more likely at level A. Odds ratios that are less than 1 indicate that the event is less likely at level A. For information on coding categorical predictors, go to Coding schemes for categorical predictors.
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.
Many of the model summary and goodness-of-fit statistics are affected by how the data are arranged in the worksheet and whether there is one trial per row or multiple trials per row. The Hosmer-Lemeshow test is unaffected by the data format and is 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.
Goodness-of-fit statistics are just one measure of how well the model fits the data. Even when a model has a desirable value, 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, AICc, and BIC to compare different models. For each statistic, smaller values are desirable. However, the model with the smallest value 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.
The area under the ROC curve values range from 0.5 to 1. When the binary model can perfectly separate the classes, then the area under the curve is 1. When the binary model cannot separate the classes better than a random assignment, then the area under the curve is 0.5.
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.