Find definitions and interpretation guidance for the model summary statistics.

Deviance R^{2} is usually considered the proportion of the deviance in the response variable that the model explains.

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 to assess how well the model fits the data.

You can use a fitted line plot to graphically illustrate different deviance R^{2} values. The first plot illustrates a model that explains approximately 96% of the deviance in the response. The second plot illustrates a model that explains about 60% of the deviance in the response. The more deviance that a model explains, the closer the data points fall to the curve. Theoretically, if a model could explain 100% of the deviance, the fitted values would always equal the observed values and all of the data points would fall on the curve.

Adjusted deviance R^{2} is the proportion of deviance in the response that is explained by the model, adjusted for the number of predictors in the model relative to the number of observations.

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.

For example, you work for a potato chip company that examines factors that affect crumbled potato chips. You receive the following results as you add predictors:

Step | % Potato | Cooling rate | Cooking temp | Deviance R^{2} |
Adjusted Deviance R^{2} |
P-value |
---|---|---|---|---|---|---|

1 | X | 52% | 51% | 0.000 | ||

2 | X | X | 63% | 62% | 0.000 | |

3 | X | X | X | 65% | 62% | 0.000 |

The first step yields a statistically significant regression model. The second step, which adds cooling rate to the model, increases the adjusted deviance R^{2}, which indicates that cooling rate improves the model. The third step, which adds cooking temperature to the model, increases the deviance R^{2} but not the adjusted deviance R^{2}. These results indicate that cooking temperature does not improve the model. Based on these results, you consider removing cooking temperature from the model.

For binary logistic regression, the format of the data affects the adjusted deviance R^{2} value. For the same data, the adjusted deviance R^{2} is usually higher when the data are in Event/Trial format than when the data are in Binary Response/Frequency format. Use the adjusted deviance R^{2} only to compare the fit of models that have the same data format.

Akaike Information Criterion is a measure of the relative quality of a model that accounts for fit and the number of terms in the model. The statistic has no interpretation without a comparison value.

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.