The deviance R2 indicates how much variation in the response is explained by the model. The higher the R2, the better the model fits your data. The formula is:
Notation
Term
Description
DE
Error Deviance
DT
Total Deviance
Adjusted Deviance R2
The adjusted deviance R2 accounts for the number of predictors in your model and is useful for comparing models with different numbers of predictors. The formula is:
Notation
Term
Description
R2
the deviance R2
p
the regression degrees of freedom
Φ
1, for binomial models
DT
the total deviance
While the calculations for adjusted deviance R2 can produce negative values, Minitab displays zero for these cases.
Akaike Information Criterion (AIC)
Use this statistic to compare different models. The smaller AIC is, the better the model fits the data.
The log-likelihood functions are parameterized in terms of the means. The general form of the functions follow:
The general form of the individual contributions follows:
The following equation gives the form of the individual contributions for a binomial model:
Notation
Term
Description
p
the regression degrees of freedom
Lc
the log-likelihood of the current model
yi
the number of events for the ith row
mi
the number of trials for the ith row
the estimated mean response of the ith row
AICc (Akaike's Corrected Information Criterion)
AICc is not calculated when .
Notation
Term
Description
p
the number of coefficients in the model, including the constant
n
the number of rows in the data with no missing data
BIC (Bayesian Information Criterion)
Notation
Term
Description
p
the number of coefficients in the model, not counting the constant
n
the number of rows in the data with no missing data
.
