The deviance R^{2} indicates how much variation in the response is explained by the model. The higher the R^{2}, the better the model fits your data. The formula is:
Notation
Term
Description
D_{E}
Error Deviance
D_{T}
Total Deviance
Adjusted Deviance R^{2}
The adjusted deviance R^{2} 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
R^{2}
the deviance R^{2}
p
the regression degrees of freedom
Φ
1, for binomial and Poisson models
D_{T}
the total deviance
While the calculations for adjusted deviance R^{2} 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 specific form of the individual contributions depends on the model.
Model
l_{i}
Binomial
Poisson
Notation
Term
Description
p
the regression degrees of freedom
L_{c}
the log-likelihood of the current model
y_{i}
the number of events for the i^{th} row
m_{i}
the number of trials for the i^{th} row
the estimated mean response of the i^{th} 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
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