ZIP and ZINB Models for Data Exhibiting Extra Zeros
/*--------------------------------------------------------------
SAS Sample Library
Name: cntex02.sas
Description: Example program from SAS/ETS User's Guide,
The COUNTREG Procedure
Title: ZIP and ZINB Models for Data Exhibiting Extra Zeros
Product: SAS/ETS Software
Keys: count data analysis
PROC: COUNTREG
Notes:
--------------------------------------------------------------*/
ods graphics on;
data long97data;
input fem ment phd mar kid5 art lnart;
datalines;
0 7.99999860 1.38000000 1 2 3 1.25276290
0 6.99999950 4.29000000 0 0 0 -0.69314720
0 47.00000760 3.84999990 0 0 4 1.50407740
0 19.00000190 3.58999990 1 1 1 0.40546510
0 0.00000000 1.80999990 1 0 1 0.40546510
0 6.00000050 3.58999990 1 1 1 0.40546510
0 9.99999900 2.11999990 1 1 0 -0.69314720
0 1.99999990 4.29000000 1 0 0 -0.69314720
0 1.99999990 2.57999990 1 2 3 1.25276290
0 3.99999900 1.80000000 1 1 3 1.25276290
0 0.00000000 4.29000000 1 2 1 0.40546510
0 3.00000000 2.76000000 1 1 0 -0.69314720
0 9.99999900 3.41000010 1 1 1 0.40546510
0 6.99999950 4.34000020 1 3 2 0.91629080
0 15.00000100 3.84999990 1 2 5 1.70474800
0 1.99999990 2.09999990 1 0 2 0.91629080
0 13.00000000 4.29000000 1 0 2 0.91629080
0 15.00000100 4.29000000 0 0 1 0.40546510
0 4.99999810 2.26000000 1 1 0 -0.69314720
0 6.00000050 2.09999990 0 0 0 -0.69314720
0 12.00000000 2.26000000 1 0 3 1.25276290
0 15.99999810 3.84999990 1 1 6 1.87180220
0 6.99999950 4.29000000 0 0 4 1.50407740
0 6.00000050 1.80000000 1 2 2 0.91629080
0 1.99999990 2.26000000 0 0 2 0.91629080
0 0.00000000 2.09999990 0 0 0 -0.69314720
0 30.00000190 4.29000000 1 0 4 1.50407740
0 9.99999900 4.29000000 1 2 1 0.40546510
0 1.99999990 2.09999990 1 0 1 0.40546510
0 0.99999990 3.58999990 1 0 7 2.01490310
0 3.00000000 3.42000010 1 1 2 0.91629080
0 9.99999900 4.29000000 1 2 2 0.91629080
0 9.99999900 4.29000000 0 0 2 0.91629080
0 0.99999990 3.33999990 1 2 0 -0.69314720
0 1.99999990 4.29000000 0 0 0 -0.69314720
0 10.99999710 4.29000000 1 0 1 0.40546510
0 4.99999810 3.61999990 1 0 4 1.50407740
0 0.00000000 4.29000000 1 3 1 0.40546510
0 3.99999900 4.34000020 1 1 1 0.40546510
0 1.99999990 1.25000000 1 1 2 0.91629080
0 19.00000190 4.34000020 0 0 7 2.01490310
0 3.00000000 1.67000000 1 3 1 0.40546510
0 0.00000000 3.47000000 0 0 0 -0.69314720
0 0.99999990 2.26000000 1 1 1 0.40546510
0 0.99999990 1.80000000 1 0 1 0.40546510
0 17.00000000 4.34000020 1 2 2 0.91629080
0 3.00000000 3.58999990 0 0 2 0.91629080
0 0.99999990 1.75000000 1 2 1 0.40546510
0 6.00000050 4.29000000 0 0 1 0.40546510
0 0.00000000 2.09999990 1 1 0 -0.69314720
0 15.00000100 4.29000000 1 2 0 -0.69314720
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0 6.99999950 3.41000010 0 0 4 1.50407740
0 0.00000000 4.29000000 1 0 1 0.40546510
0 10.99999710 3.19000010 1 0 2 0.91629080
0 13.00000000 4.29000000 1 0 2 0.91629080
0 3.99999900 1.74000000 1 2 1 0.40546510
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0 9.99999900 1.80999990 1 0 4 1.50407740
0 13.00000000 4.29000000 1 1 2 0.91629080
0 0.99999990 4.29000000 1 1 1 0.40546510
0 6.00000050 2.76000000 0 0 1 0.40546510
0 6.00000050 3.47000000 0 0 6 1.87180220
0 4.99999810 2.50000000 1 2 2 0.91629080
0 1.99999990 1.25000000 1 0 5 1.70474800
0 13.99999710 3.58999990 1 1 3 1.25276290
0 0.00000000 2.09999990 1 1 0 -0.69314720
0 12.00000000 3.58999990 1 0 1 0.40546510
0 6.99999950 3.58999990 1 3 0 -0.69314720
0 3.00000000 1.75000000 1 0 1 0.40546510
0 1.99999990 1.75000000 1 2 1 0.40546510
0 1.99999990 3.58999990 1 1 1 0.40546510
0 1.99999990 4.29000000 0 0 1 0.40546510
0 0.00000000 4.29000000 0 0 0 -0.69314720
0 0.00000000 2.09999990 1 1 0 -0.69314720
0 0.00000000 2.60999990 1 0 3 1.25276290
0 30.00000190 4.29000000 1 0 5 1.70474800
0 21.00000000 1.74000000 1 0 16 2.80336050
0 4.99999810 2.76000000 1 0 1 0.40546510
0 9.00000000 4.29000000 0 0 0 -0.69314720
0 7.99999860 2.76000000 1 2 1 0.40546510
0 25.00000000 4.29000000 1 2 3 1.25276290
0 0.00000000 3.47000000 1 1 5 1.70474800
0 4.99999810 2.57999990 1 2 0 -0.69314720
0 0.99999990 2.14000010 1 0 0 -0.69314720
0 4.99999810 2.26000000 0 0 0 -0.69314720
0 0.00000000 4.29000000 1 2 3 1.25276290
0 15.00000100 4.29000000 1 0 3 1.25276290
0 30.00000190 4.29000000 0 0 3 1.25276290
0 1.99999990 2.20000000 1 0 0 -0.69314720
0 6.00000050 1.80000000 1 2 3 1.25276290
0 0.00000000 2.09999990 1 2 1 0.40546510
0 13.00000000 4.29000000 1 1 1 0.40546510
0 0.00000000 4.29000000 0 0 0 -0.69314720
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0 4.99999810 4.29000000 1 1 0 -0.69314720
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0 6.00000050 3.15000010 1 2 0 -0.69314720
0 21.00000000 2.55000000 1 1 4 1.50407740
0 3.99999900 1.52000000 1 0 0 -0.69314720
0 1.99999990 1.72000000 1 2 4 1.50407740
0 0.99999990 1.78000000 1 1 2 0.91629080
0 17.00000000 2.85999990 1 1 1 0.40546510
0 30.00000190 4.61999990 1 2 0 -0.69314720
0 4.99999810 4.13999990 0 0 1 0.40546510
0 13.00000000 2.96000000 1 1 6 1.87180220
0 10.99999710 2.55000000 1 0 1 0.40546510
0 19.00000190 2.21000000 1 1 0 -0.69314720
0 4.99999810 3.08999990 1 0 3 1.25276290
0 66.00000760 4.54000000 1 2 4 1.50407740
0 0.00000000 1.78000000 1 0 3 1.25276290
0 3.00000000 2.21000000 1 3 0 -0.69314720
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0 0.00000000 2.96000000 1 0 0 -0.69314720
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0 4.99999810 4.13999990 0 0 0 -0.69314720
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0 10.99999710 2.85999990 1 2 0 -0.69314720
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0 7.99999860 4.61999990 1 1 6 1.87180220
0 4.99999810 3.69000010 1 2 0 -0.69314720
0 0.99999990 3.15000010 1 1 0 -0.69314720
0 9.00000000 4.61999990 0 0 2 0.91629080
0 1.99999990 3.35999990 1 0 0 -0.69314720
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0 21.00000000 4.54000000 1 2 4 1.50407740
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0 19.00000190 2.21000000 1 0 0 -0.69314720
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0 3.00000000 1.17999990 1 1 0 -0.69314720
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1 21.00000000 4.29000000 0 0 2 0.91629080
1 3.99999900 4.29000000 1 1 0 -0.69314720
1 0.00000000 2.96000000 1 0 0 -0.69314720
1 0.99999990 1.78000000 1 0 0 -0.69314720
1 17.00000000 3.54000000 1 2 1 0.40546510
1 3.00000000 3.69000010 1 0 0 -0.69314720
1 1.99999990 3.35999990 0 0 3 1.25276290
1 1.99999990 3.54000000 1 0 0 -0.69314720
1 0.99999990 3.54000000 1 1 0 -0.69314720
1 3.00000000 1.22000000 1 1 3 1.25276290
1 3.99999900 3.35999990 0 0 1 0.40546510
1 1.99999990 2.21000000 0 0 1 0.40546510
1 3.99999900 2.25000000 0 0 1 0.40546510
1 17.00000000 4.61999990 1 1 2 0.91629080
1 4.99999810 3.58999990 1 0 1 0.40546510
1 0.99999990 4.29000000 1 0 0 -0.69314720
1 1.99999990 2.11999990 0 0 2 0.91629080
1 3.00000000 2.26000000 0 0 2 0.91629080
1 3.00000000 2.26000000 1 0 4 1.50407740
1 4.99999810 4.29000000 0 0 0 -0.69314720
1 3.00000000 3.58999990 1 1 3 1.25276290
1 13.00000000 4.29000000 1 2 1 0.40546510
1 1.99999990 2.00000000 0 0 1 0.40546510
1 0.00000000 1.97000000 1 2 0 -0.69314720
1 7.99999860 3.92000010 1 0 0 -0.69314720
1 39.00000000 2.85999990 0 0 4 1.50407740
1 26.00000000 2.82999990 0 0 2 0.91629080
1 3.00000000 3.35999990 1 1 3 1.25276290
1 22.99999620 2.55999990 0 0 4 1.50407740
1 7.99999860 1.63000000 0 0 1 0.40546510
1 22.00000000 4.61999990 0 0 3 1.25276290
1 4.99999810 4.61999990 0 0 1 0.40546510
1 21.00000000 4.29000000 1 0 3 1.25276290
1 6.00000050 4.29000000 1 1 0 -0.69314720
1 3.99999900 4.29000000 1 1 2 0.91629080
1 24.00000190 4.29000000 1 0 6 1.87180220
1 6.00000050 4.29000000 1 0 1 0.40546510
1 33.99999240 3.35999990 0 0 1 0.40546510
1 0.00000000 3.21000000 0 0 2 0.91629080
1 9.99999900 2.00000000 0 0 1 0.40546510
1 1.99999990 3.21000000 1 2 2 0.91629080
1 3.00000000 2.57999990 1 2 2 0.91629080
1 3.00000000 2.57999990 1 0 0 -0.69314720
1 0.99999990 2.82999990 0 0 0 -0.69314720
1 6.00000050 3.19000010 0 0 1 0.40546510
1 3.00000000 3.47000000 0 0 1 0.40546510
1 22.99999620 4.61999990 1 0 2 0.91629080
1 13.00000000 4.25000000 1 0 4 1.50407740
1 4.99999810 1.86000000 1 0 2 0.91629080
1 9.00000000 4.29000000 1 1 0 -0.69314720
1 9.00000000 3.35999990 0 0 0 -0.69314720
1 9.99999900 1.80000000 1 0 2 0.91629080
1 0.00000000 1.65500000 0 0 1 0.40546510
1 6.00000050 2.85999990 0 0 0 -0.69314720
1 13.99999710 4.61999990 0 0 2 0.91629080
1 3.00000000 4.29000000 0 0 0 -0.69314720
1 4.99999810 2.35999990 1 0 4 1.50407740
1 10.99999710 1.80999990 1 0 1 0.40546510
1 32.00001140 3.58999990 1 0 1 0.40546510
1 9.99999900 1.76000000 0 0 0 -0.69314720
1 4.99999810 2.00000000 1 0 1 0.40546510
1 13.99999710 3.58999990 0 0 5 1.70474800
1 6.00000050 2.26000000 1 0 3 1.25276290
1 3.99999900 2.26000000 0 0 1 0.40546510
1 3.99999900 1.76000000 1 1 1 0.40546510
1 0.99999990 3.58999990 1 0 1 0.40546510
1 0.99999990 3.58999990 1 0 0 -0.69314720
1 4.99999810 2.82999990 1 1 1 0.40546510
1 1.99999990 2.57999990 0 0 1 0.40546510
1 17.99999810 4.61999990 1 0 1 0.40546510
1 15.00000100 2.31999990 0 0 1 0.40546510
1 0.00000000 2.39000010 1 0 0 -0.69314720
1 22.00000000 2.96000000 1 0 3 1.25276290
1 10.99999710 2.11999990 0 0 0 -0.69314720
1 17.99999810 4.61999990 1 0 1 0.40546510
1 3.00000000 2.25000000 1 0 1 0.40546510
1 7.99999860 1.76000000 1 0 1 0.40546510
1 12.00000000 4.54000000 0 0 6 1.87180220
1 9.99999900 3.69000010 1 1 2 0.91629080
1 1.99999990 1.25000000 0 0 0 -0.69314720
1 4.99999810 1.25000000 1 0 1 0.40546510
1 3.99999900 3.19000010 1 0 0 -0.69314720
1 0.00000000 2.57999990 1 2 0 -0.69314720
1 6.99999950 2.00000000 1 1 2 0.91629080
1 0.99999990 2.76000000 0 0 0 -0.69314720
1 3.99999900 2.54000000 0 0 2 0.91629080
1 0.00000000 3.19000010 0 0 0 -0.69314720
1 9.00000000 3.08999990 1 2 1 0.40546510
1 3.99999900 3.19000010 0 0 2 0.91629080
1 0.00000000 3.08999990 0 0 0 -0.69314720
1 7.99999860 2.26000000 0 0 2 0.91629080
1 9.00000000 2.26000000 1 1 1 0.40546510
1 7.99999860 3.35999990 1 0 2 0.91629080
1 9.00000000 3.15000010 1 0 1 0.40546510
1 3.99999900 4.54000000 1 0 0 -0.69314720
1 0.00000000 3.58999990 1 0 2 0.91629080
1 3.00000000 3.47000000 1 0 1 0.40546510
1 1.99999990 2.85999990 1 1 1 0.40546510
1 6.00000050 2.26000000 1 0 0 -0.69314720
1 3.99999900 3.47000000 1 1 2 0.91629080
1 0.00000000 2.76000000 1 0 0 -0.69314720
1 1.99999990 3.58999990 1 2 0 -0.69314720
1 13.00000000 3.75000000 0 0 5 1.70474800
1 1.99999990 2.57999990 1 2 1 0.40546510
1 1.99999990 3.58999990 1 1 2 0.91629080
1 15.99999810 1.89000000 1 2 3 1.25276290
1 9.00000000 3.15000010 0 0 7 2.01490310
1 12.00000000 2.86999990 0 0 5 1.70474800
1 0.99999990 2.11999990 1 2 0 -0.69314720
1 3.99999900 4.61999990 1 0 1 0.40546510
1 0.00000000 2.39000010 0 0 0 -0.69314720
1 10.99999710 2.11999990 0 0 0 -0.69314720
1 4.99999810 1.80999990 1 0 0 -0.69314720
1 7.99999860 2.31999990 0 0 4 1.50407740
1 15.00000100 2.39000010 0 0 0 -0.69314720
1 6.00000050 3.75000000 1 0 3 1.25276290
1 0.00000000 2.00000000 0 0 0 -0.69314720
1 13.99999710 3.58999990 1 1 0 -0.69314720
1 4.99999810 4.29000000 0 0 2 0.91629080
1 0.00000000 2.57999990 1 0 0 -0.69314720
1 4.99999810 4.61999990 1 0 0 -0.69314720
1 3.00000000 1.50500000 0 0 0 -0.69314720
1 3.99999900 3.75000000 1 0 2 0.91629080
1 3.99999900 3.75000000 1 2 0 -0.69314720
1 0.00000000 1.75000000 1 0 1 0.40546510
1 0.00000000 2.11999990 1 0 1 0.40546510
1 4.99999810 3.75000000 0 0 2 0.91629080
1 0.00000000 0.75500000 0 0 0 -0.69314720
1 6.99999950 2.25000000 0 0 1 0.40546510
1 3.00000000 3.19000010 0 0 1 0.40546510
;
proc freq data=long97data;
table art / out=obs;
run;
/*-- Poisson Model with Output Statement--*/
proc countreg data=long97data;
model art=fem mar kid5 phd ment / dist=poisson;
output out=predpoi probcount(0 to 10);
run;
proc means mean data=predpoi;
var p_0;
run;
/*-- Negative Binomial Model with Output Statement--*/
proc countreg data=long97data plots(only)=profilelike;
model art=fem mar kid5 phd ment / dist=negbin(p=2) method=qn;
output out=prednb probcount(0 to 10);
run;
proc means mean data=prednb;
var p_0;
run;
/*-- ZIP Model with Output Statement--*/
proc countreg data=long97data;
model art = fem mar kid5 phd ment / dist=zip;
zeromodel art ~ fem mar kid5 phd ment;
output out=predzip probcount(0 to 10);
run;
proc means data=predzip mean;
var p_0;
run;
/*-- ZINB Model with Output Statement--*/
proc countreg data=long97data;
model art=fem mar kid5 phd ment / dist=zinb method=qn;
zeromodel art ~ fem mar kid5 phd ment;
output out=predzinb probcount(0 to 10);
run;
proc means data=predzinb mean;
var p_0;
run;
proc summary data=predpoi;
var p_0-p_10;
output out=mnpoi mean(p_0-p_10)=mn0-mn10;
run;
proc summary data=prednb;
var p_0-p_10;
output out=mnnb mean(p_0-p_10)=mn0-mn10;
run;
proc summary data=predzip;
var p_0-p_10;
output out=mnzip mean(p_0-p_10)=mn0-mn10;
run;
proc summary data=predzinb;
var p_0-p_10;
output out=mnzinb mean(p_0-p_10)=mn0-mn10;
run;
data means;
set mnpoi mnnb mnzip mnzinb;
drop _type_ _freq_;
run;
proc transpose data=means out=tmeans;
run;
data allpred;
merge obs(where=(art<=10)) tmeans;
obs=percent/100;
run;
proc sgplot;
yaxis label='Probability';
xaxis label='Number of Articles';
series y=obs x=art / name='obs' legendlabel='Observed'
lineattrs=(color=black thickness=4px);
series y=col1 x=art / name='poi' legendlabel='Poisson'
lineattrs=(color=blue);
series y=col2 x=art/ name='nb' legendlabel='Negative Binomial'
lineattrs=(color=red);
series y=col3 x=art/ name='zip' legendlabel='ZIP'
lineattrs=(color=blue pattern=2);
series y=col4 x=art/ name='zinb' legendlabel='ZINB'
lineattrs=(color=red pattern=2);
discretelegend 'poi' 'zip' 'nb' 'zinb' 'obs' / title='Models:'
location=inside position=ne across=2 down=3;
run;
