Goodness of Fit

Deviance

The deviance goodness of fit test is based on the likelihood ratio test of the current model against a full or saturated model. The statistic has an asymptotic distribution with degrees of freedom equal to the number of observations minus the number of parameters estimated.

Scaled Deviance

The scaled deviance statistic is the respective statistic divided by the current estimate of the dispersion parameter. The statistic has an asymptotic distribution with degrees of freedom equal to the number of observations minus the number of parameters estimated.

For a review of how the dispersion parameter is estimated see Dispersion.

Pearson

The Pearson statistic has an asymptotic distribution with degrees of freedom equal to the number of observations minus the number of parameters estimated.

Scaled Pearson

The scaled Pearson statistic is the respective statistic divided by the current estimate of the dispersion parameter. The statistic has an asymptotic distribution with degrees of freedom equal to the number of observations minus the number of parameters estimated.

For a review of how the dispersion parameter is estimated see Dispersion.

Akaike Information Criterion (AIC)

Bayesian Information Criterion (BIC)

Cox-Snell R²

In linear regression using ordinary least squares, a measure of goodness of fit is R², which represents the proportion of variance explained by the model. Using logistic regression, an equivalent statistic does not exist, and therefore several pseudo-R² statistics have been developed. The Cox-Snell R² is a pseudo-R² statistic, and the ratio of the likelihoods reflects the improvement of the full model over the intercept only model with a smaller ratio reflecting greater improvement. It is given by:

Nagelkerke R²

The Nagelkerke R² adjusts the Cox-Snell R² so the range of possible values extends to one.

Log-Likelihood

The first spreadsheet generated from Statistica® when clicking the Goodness of fit button from the GLZ Results dialog contains, in addition to the above, the Log-likelihood statistic as shown in the Overview.