The GENMOD Procedure

The following SAS statements simulate 250 observations, which are based on an underlying Tweedie generalized linear model (GLM) that exploits its connection with the compound Poisson distribution. A natural logarithm link function is assumed for modeling the response variable (yTweedie), and there are five categorical variables (C1–C5), each of which has four numerical levels and two continuous variables (D1 and D2). By design, two of the categorical variables, C3 and C4, and one of the two continuous variables, D2, have no effect on the response. The dispersion parameter is set to 0.5, and the power parameter is set to 1.5.

%let nObs = 250;
%let nClass = 5;
%let nLevs = 4;
%let seed = 100;

data tmp1;
   array c{&nClass};

   keep c1-c&nClass yTweedie d1 d2;

   /* Tweedie parms */
   phi=0.5;
   p=1.5;

   do i=1 to &nObs;

      do j=1 to &nClass;
         c{j} = int(ranuni(1)*&nLevs);
      end;

      d1 = ranuni(&seed);
      d2 = ranuni(&seed);

      xBeta   =  0.5*((c2<2) - 2*(c1=1) + 0.5*c&nClass + 0.05*d1); 
      mu      =  exp(xBeta);

      /* Poisson distributions parms */
      lambda = mu**(2-p)/(phi*(2-p));
      /* Gamma distribution parms */
      alpha = (2-p)/(p-1);
      gamma = phi*(p-1)*(mu**(p-1));

      rpoi = ranpoi(&seed,lambda);
      if rpoi=0 then yTweedie=0;
      else do;
         yTweedie=0;
         do j=1 to rpoi;
         yTweedie = yTweedie + rangam(&seed,alpha);
         end;
         yTweedie = yTweedie * gamma;
      end;
      output;
   end;
run;

The following SAS statements invoke PROC GENMOD to fit the Tweedie GLM with the log link using all of the categorical and continuous variables. A Type III analysis is requested by the TYPE3 option in the MODEL statement.

proc genmod data=tmp1;
   class C1-C5;
   model yTweedie = C1-C5 D1 D2 / dist=Tweedie type3;
run;

The “Criteria For Assessing Goodness Of Fit” table is displayed in Output 42.12.1. The scaled Pearson is close to 1, indicating that the specified model fits the data well.

The “LR Statistics For Type 3 Analysis” table is displayed in Output 42.12.2. As expected, the p-values for C3, C4, and d2 are not statistically significant at the level.

You can fix the power parameter for fitting the Tweedie GLM by using the P= option. The following SAS statements fit the model for C1, C2 and D1, while holding the power parameter at 1.5:

proc genmod data=tmp1;
   class C1 C2;
   model yTweedie = C1 C2 D1 / dist=Tweedie(p=1.5) type3;
run;

The parameter estimates are displayed in Output 42.12.3.