Deviance at each iterative step for Fit Binary Logistic Model, Binary Logistic Regression, and Fit Poisson Model

To estimate the coefficients for a model, the analysis uses an iteratively reweighted least squares algorithm. The algorithm tries to maximize the log-likelihood of the model. This maximization is equivalent to minimization of the deviance of the model. The algorithm tries to maximize the log-likelihood by refining the estimates of the coefficients using the reweighted least squares method. The deviance of a model is twice the discrepancy between the log-likelihood of the saturated model and the log-likelihood of the model. The saturated model is the model with a parameter for every observation, which has the largest possible log-likelihood value.

The table displays the deviance of the model at each iteration. Usually, an increase in the log-likelihood for the model from one step to the next step indicates improvement in the estimates of the coefficients for the model. An increase in the log-likelihood is equivalent to a decrease in the deviance.

The algorithm uses the difference between deviances at successive steps to decide when the estimates of the coefficients are good enough. When the difference between the deviances becomes smaller than a threshold, the algorithm stops. By default, the threshold is 1E−8. Use session commands for Minitab Statistical Software to adjust the threshold.

Sometimes, the estimates do not converge after the maximum number of iterations in the specifications for the analysis. Failure to converge is usually due to some specific configuration of the data. For example, in binary logistic regression a complete separation of the data is known to prevent the fitting algorithm from full convergence regardless of the maximum number of iterations.