Zero-Inflated Poisson Regression with PROC HPFMM

This script demonstrates several facets of PROC HPFMM. It begins by creating a 'catch' data table containing demographic variables and a 'count' variable. Then, it progressively applies more complex models: a basic Poisson model, a 'zero-inflated' Poisson mixture model to account for an excess of zeros, and finally a Bayesian analysis of this last model. The script also shows how to optimize execution (nthreads) and generate specific graphs (ODS Graphics).

Data Analysis

Type : CREATION_INTERNE

The data is entirely generated and contained within the script via a DATA step with a DATALINES statement.

1 Code Block

DATA STEP Data

Explanation :
This block creates the 'catch' table from internal data. The 'input' statement reads the 'gender', 'age', and 'count' variables. The double 'at' ( @code_sas_json/8_SAS_Intro_ReadFile_MultiCol_@@.json) instructs SAS to read multiple observations from the same data line.

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1	DATA catch;
2	INPUT gender $ age count @code_sas_json/8_SAS_Intro_ReadFile_MultiCol_@@.json;
3	DATALINES;
4	F 54 18 M 37 0 F 48 12 M 27 0
5	M 55 0 M 32 0 F 49 12 F 45 11
6	M 39 0 F 34 1 F 50 0 M 52 4
7	M 33 0 M 32 0 F 23 1 F 17 0
8	F 44 5 M 44 0 F 26 0 F 30 0
9	F 38 0 F 38 0 F 52 18 M 23 1
10	F 23 0 M 32 0 F 33 3 M 26 0
11	F 46 8 M 45 5 M 51 10 F 48 5
12	F 31 2 F 25 1 M 22 0 M 41 0
13	M 19 0 M 23 0 M 31 1 M 17 0
14	F 21 0 F 44 7 M 28 0 M 47 3
15	M 23 0 F 29 3 F 24 0 M 34 1
16	F 19 0 F 35 2 M 39 0 M 43 6
17	;

2 Code Block

PROC HPFMM

Explanation :
This block executes a first simple Poisson regression model. The 'count' variable is modeled as a function of the interaction between 'gender' and 'age'.

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1	PROC HPFMM DATA=catch;
2	class gender;
3	model count = gender*age / dist=Poisson;
4	RUN;

3 Code Block

PROC HPFMM

Explanation :
This block fits a two-component mixture model, known as a 'zero-inflated' (ZI) Poisson model. The first MODEL statement specifies the Poisson component, and the second MODEL with 'dist=Constant' adds a component that models the excess of zeros.

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1	PROC HPFMM DATA=catch;
2	class gender;
3	model count = gender*age / dist=Poisson ;
4	model + / dist=Constant;
5	RUN;

4 Code Block

PROC HPFMM

Explanation :
This block performs a Bayesian analysis of the 'zero-inflated' Poisson model. The 'BAYES' statement requests Bayesian inference for the model parameters. 'PERFORMANCE NTHREADS=2' is used to accelerate the computation by using two threads.

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1	PROC HPFMM DATA=catch seed=12345;
2	class gender;
3	model count = gender*age / dist=Poisson;
4	model + / dist=constant;
5	performance nthreads=2;
6	bayes;
7	RUN;

5 Code Block

PROC HPFMM

Explanation :
This last block re-executes the Bayesian analysis, but by activating graph generation via 'ODS GRAPHICS ON'. 'ODS SELECT TADPanel' filters the output to display only the Bayesian diagnostic graphics panel (Trace, Autocorrelation, Density).

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1	ods graphics on;
2	ods select TADPanel;
3	PROC HPFMM DATA=catch seed=12345;
4	class gender;
5	model count = gender*age / dist=Poisson;
6	model + / dist=constant;
7	performance nthreads=2;
8	bayes;
9	RUN;
10	ods graphics off;

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