Iteration History for Parameter Estimates

If you specify the ITPRINT or PRINTALL options in the PROC COUNTREG statement, PROC COUNTREG displays a table that contains the following information for each iteration. Note that some information is specific to the model-fitting procedure chosen (for example, Newton-Raphson, trust region, quasi-Newton).

• iteration number

• number of restarts since the fitting began

• number of function calls

• number of active constraints at the current solution

• value of the objective function (–1 times the log-likelihood value) at the current solution

• change in the objective function from previous iteration

• value of the maximum absolute gradient element

• step size (for Newton-Raphson and quasi-Newton methods)

• slope of the current search direction (for Newton-Raphson and quasi-Newton methods)

• lambda (for trust region method)

• radius value at current iteration (for trust region method)

Model Fit Summary

The "Model Fit Summary" table contains the following information:

• dependent (count) variable name

• number of observations used

• number of missing values in data set, if any

• data set name

• type of model that was fit

• offset variable name, if any

• zero-inflated link function, if any

• zero-inflated offset variable name, if any

• log-likelihood value at solution

• maximum absolute gradient at solution

• number of iterations

• AIC value at solution (a smaller value indicates better fit)

• SBC value at solution (a smaller value indicates better fit)

Under the "Model Fit Summary" is a statement about whether the algorithm successfully converged.

Parameter Estimates

The “Parameter Estimates” table gives the estimates of the model parameters. In zero-inflated (ZI) models, estimates are also given for the ZI intercept and ZI regressor parameters labeled with the prefix "Inf_". For example, the ZI intercept is labeled "Inf_intercept". If you specify "Age" as a ZI regressor, then the “Parameter Estimates” table labels the corresponding parameter estimate "Inf_Age". If you do not list any ZI regressors, then only the ZI intercept term is estimated.

"_Alpha" is the negative binomial dispersion parameter. The statistic given for "_Alpha" is a test of overdispersion.

Last Evaluation of the Gradient

If you specify the model option ITPRINT, the COUNTREG procedure displays the last evaluation of the gradient vector.

Covariance of Parameter Estimates

If you specify the COVB option in the MODEL statement or in the PROC COUNTREG statement, the COUNTREG procedure displays the estimated covariance matrix, defined as the inverse of the information matrix at the final iteration.

Correlation of Parameter Estimates

If you specify the CORRB option in the MODEL statement or in the PROC COUNTREG statement, PROC COUNTREG displays the estimated correlation matrix. It is based on the Hessian matrix used at the final iteration.