Poisson Regression with PROC MCMC

This script illustrates how to perform Poisson regression in a Bayesian framework. It starts by creating an 'insure' dataset containing insurance claims. It then uses PROC TRANSREG to create a design matrix for categorical variables. The main analysis is performed with PROC MCMC to estimate model parameters. Finally, a comparative validation is performed using PROC GENMOD with the BAYES statement.

Data Analysis

Type : CREATION_INTERNE

Data is generated directly within the script via a DATA step using 'datalines'.

1 Code Block

DATA STEP Data

Explanation :
Creation of the 'insure' dataset containing information on the number of policies (n), the number of claims (c), the car type (car), and age. A logarithmic offset variable 'ln' is calculated.

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1	title 'Poisson Regression';
2	DATA insure;
3	INPUT n c car $ age;
4	ln = log(n);
5	DATALINES;
6	500 42 small 0
7	1200 37 medium 0
8	100 1 large 0
9	400 101 small 1
10	500 73 medium 1
11	300 14 large 1
12	;

2 Code Block

PROC TRANSREG Data

Explanation :
Use of PROC TRANSREG to generate dummy variables for the categorical variable 'car', thus preparing the data for PROC MCMC.

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1	PROC TRANSREG DATA=insure design;
2	model class(car / zero=last);
3	id n c age ln;
4	OUTPUT out=input_insure(drop=_: Int:);
5	RUN;

3 Code Block

PROC MCMC

Explanation :
Execution of the Bayesian analysis with PROC MCMC. The model specifies a Poisson distribution for the response variable 'c', with a log link function and an 'ln' offset. Priors are defined as normal.

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1	PROC MCMC DATA=input_insure outpost=insureout nmc=5000 propcov=quanew
2	maxtune=0 seed=7;
3	ods select PostSumInt;
4	array DATA[4] 1 &_trgind age;
5	array beta[4] alpha beta_car1 beta_car2 beta_age;
6	parms alpha beta:;
7	prior alpha beta: ~ normal(0, prec = 1e-6);
8	call mult(DATA, beta, mu);
9	model c ~ poisson(exp(mu+ln));
10	RUN;

4 Code Block

PROC GENMOD

Explanation :
Use of PROC GENMOD with the BAYES statement to fit the same Poisson regression model. This serves as a comparison point to validate the results obtained with PROC MCMC.

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1	PROC GENMOD DATA=insure;
2	ods select PostSummaries PostIntervals;
3	class car age(descending);
4	model c = car age / dist=poisson link=log offset=ln;
5	bayes seed=17 nmc=5000 coeffprior=normal;
6	RUN;

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