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This program illustrates the use of the GENMOD procedure to analyze data following a Tweedie distribution. First, it simulates a dataset of 250 observations via a DATA step, constructing the response variable as a Poisson sum of Gamma variables (mathematical representation of the Tweedie distribution). Then, it fits two models: the first estimates parameters with the default Tweedie distribution, and the second fixes the power parameter p to 1.5.

Data Analysis

Type : CREATION_INTERNE

Data is entirely generated in the 'tmp1' DATA step using random functions (ranuni, ranpoi, rangam) based on parameters defined by macro variables.

1 Code Block

DATA STEP Data

Explanation :
Initialization of configuration macro-variables. Creation of the 'tmp1' table containing categorical (c1-c5) and continuous (d1, d2) explanatory variables, as well as a target variable 'yTweedie' simulated according to a compound Poisson-Gamma process.

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1	%let nObs = 250;
2	%let nClass = 5;
3	%let nLevs = 4;
4	%let seed = 100;
5
6	DATA tmp1;
7	array c{&nClass};
8
9	keep c1-c&nClass yTweedie d1 d2;
10
11	/* Tweedie parms */
12	phi=0.5;
13	p=1.5;
14
15	DO i=1 to &nObs;
16
17	DO j=1 to &nClass;
18	c{j} = int(ranuni(1)*&nLevs);
19	END;
20
21	d1 = ranuni(&seed);
22	d2 = ranuni(&seed);
23
24	xBeta = 0.5((c2<2) - 2(c1=1) + 0.5c&nClass + 0.05d1);
25	mu = exp(xBeta);
26
27	/* Poisson distributions parms */
28	lambda = mu*(2-p)/(phi(2-p));
29	/* Gamma distribution parms */
30	alpha = (2-p)/(p-1);
31	gamma = phi(p-1)(mu**(p-1));
32
33	rpoi = ranpoi(&seed,lambda);
34	IF rpoi=0 THEN yTweedie=0;
35	ELSE DO;
36	yTweedie=0;
37	DO j=1 to rpoi;
38	yTweedie = yTweedie + rangam(&seed,alpha);
39	END;
40	yTweedie = yTweedie * gamma;
41	END;
42	OUTPUT;
43	END;
44	RUN;

2 Code Block

PROC GENMOD

Explanation :
Execution of the GENMOD procedure to fit a generalized linear model on the simulated data, specifying a Tweedie distribution. The type3 option requests type 3 statistics.

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1	PROC GENMOD DATA=tmp1;
2	class C1-C5;
3	model yTweedie = C1-C5 D1 D2 / dist=Tweedie type3;
4	RUN;

3 Code Block

PROC GENMOD

Explanation :
Second execution of PROC GENMOD with a simplified model (fewer explanatory variables) and explicitly setting the Tweedie distribution's power parameter to 1.5.

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1	PROC GENMOD DATA=tmp1;
2	class C1 C2;
3	model yTweedie = C1 C2 D1 / dist=Tweedie(p=1.5) type3;
4	RUN;

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