The COUNTREG Procedure

DISPMODEL Statement

DISPMODEL dependent-variable $\sim$ <dispersion-related regressors> ;

The DISPMODEL statement names the variables that are used to model dispersion. This statement is ignored unless you specify DIST=CMPOISSON in the MODEL statement. The dependent-variable in the DISPMODEL statement must be the same as the dependent-variable in the MODEL statement.

The dependent-variables that appear in the DISPMODEL statement are directly used to model dispersion. Each of these $q$ variables has a parameter to be estimated in the regression. For example, let $\mathbf{g}_{i}’$ be the $i$ th observation’s $1 \times (q+1)$ vector of values of the $q$ dispersion explanatory variables ( $q_0$ is set to 1 for the intercept term). Then the dispersion is a function of $\mathbf{g}_{i}’\bdelta$ , where $\bdelta$ is the $(q+1) \times 1$ vector of parameters to be estimated, the dispersion model intercept is $\delta _0$ , and the coefficients for the $q$ dispersion covariates are $\delta _1, \ldots , \delta _ q$ . If you specify DISP=CMPOISSON in the MODEL statement but do not include a DISPMODEL statement, then only the intercept term $\delta _0$ is estimated. The “Parameter Estimates” table in the displayed output shows the estimates for the dispersion intercept and dispersion explanatory variables; they are labeled with the prefix “Disp_”. For example, the dispersion intercept is labeled “Disp_Intercept”. If you specify Age (a variable in your data set) as a dispersion explanatory variable, then the “Parameter Estimates” table labels the corresponding parameter estimate “Disp_Age”. The following statements fit a Conway-Maxwell-Poisson model by using the covariates SEX, ILLNESS, and INCOME and by using AGE as a dispersion covariate:

   proc countreg data=docvisit;
      model doctorvisits=sex illness income / dist=cmpoisson;
      dispmodel doctorvisits ~ age;
   run;