Deviance measures the discrepancy between the current model and the full model. The full model is the model that has n parameters, one parameter per observation. The full model maximizes the log-likelihood function. The full model provides a point of comparison for models with fewer than n parameters. Comparisons to the full model use the scaled deviance.
The contribution to the scaled deviance from each individual data point depends on the model.
The degrees of freedom for the test depend on the sample size and the number of terms in the model:
the log-likelihood for the full model
the log-likelihood of the model with a subset of terms from the full model
the number of events for the ith row in the data
the estimated mean response for the ith row in the data
the number of trials for the ith row in the data
the number of rows in the data
the regression degrees of freedom
Elements of the Pearson chi-square that can be used to detect ill-fitted factor/covariate patterns. Minitab stores the Pearson residual for the ith factor/covariate pattern. The formula is:
the response value for the ith factor/covariate pattern
the fitted value for the ith factor/covariate pattern
the variance function for the model at
The variance function depends on the model:
A goodness-of-fit test for models with binary responses based on grouping data based on the estimated probabilities. It is the chi-square statistic from a 2 × g table of observed and estimated expected frequencies, where g is the number of groups. The degrees of freedom for the test is g − 2.
The formula is:
To form the groups, Minitab orders the estimated probabilities and then attempts to create 10 groups of equal size.
The expected number of events in a group is:
expected events =
The expected value for the number of nonevents is:
expected nonevents =
The number of trials in the kth group
The number of events among the factor/covariate patterns
The average estimated probability for each group
The fitted probabilities for the factor/covariate patterns in a group