In the Logistic platform, the Whole Model Test report shows whether the model fits better than simply using a constant for all of the response probabilities. This report is analogous to the Analysis of Variance report for a continuous response model. The test shown in this report is a likelihood ratio chi-square test that evaluates how well the logistic regression model fits the data.
The negative sum of natural logs of the observed probabilities is called the negative log-likelihood (–LogLikelihood). The negative log-likelihood for categorical data is similar to the sums of squares for continuous data. Twice the difference in the negative log-likelihood between the model fitted to the data and the model with equal probabilities for each level is a chi-square statistic. This test statistic is for the hypothesis that the value of the X variable has no association with the levels of the Y variable.
Values of RSquare (U) (sometimes denoted as R2) range from 0 to 1. Higher R2 values are indicative of a better model fit. Note that high values of R2 are rare in categorical models.
The Whole Model Test report contains the following columns:
Model
The label of the sources of variation.
Difference
The difference between the Full model and the Reduced model. This model is used to measure the significance that the X variable contributes to the fit.
Full
The complete model that includes the intercepts and the X variable.
Reduced
The model that includes only the intercept parameters.
–LogLikelihood
The negative log-likelihood, which measures variation, for the respective models. See “Likelihood, AICc, and BIC” in Fitting Linear Models.
DF
The degrees of freedom (DF) for the Difference between the Full and Reduced model.
Chi-Square
The likelihood ratio chi-square test statistic for the hypothesis that the model fits no better than fixed response rates across the whole sample. The test statistic is computed by taking twice the difference in negative log-likelihoods between the fitted model and the reduced model that has only intercepts. See Statistical Details for the Logistic Platform.
Prob>ChiSq
The probability of obtaining a greater chi-square value if the specified model fits no better than the model that includes only intercepts. Models are often judged significant if this probability is below 0.05.
RSquare (U)
The proportion of the total uncertainty that is attributed to the model fit, defined as the Difference negative log-likelihood value divided by the Reduced negative log-likelihood value. An RSquare (U) value of 1 indicates that the predicted probabilities for events that occur are equal to one: There is no uncertainty in predicted probabilities. Because certainty in the predicted probabilities is rare for logistic models, RSquare (U) tends to be small. See Statistical Details for the Logistic Platform.
RSquare (U) is sometimes referred to as U, the uncertainty coefficient, or as McFadden’s pseudo R2.
AICc
The corrected Akaike Information Criterion. See “Likelihood, AICc, and BIC” in Fitting Linear Models.
BIC
The Bayesian Information Criterion. See “Likelihood, AICc, and BIC” in Fitting Linear Models.
Observations (or Sum Weights)
Total number of observations in the sample. If a Freq or Weight column is specified in the Fit Model window, this value is the sum of the values of a column assigned to the Freq or Weight role.