/* Hypothetical example on sampling zeros from Fienberg (1980)*/

options ls=90 nocenter nodate;

/* non-zero margin, bad patter of zeros */
data zeros;
input X $ Y $ Z $ count @@;
datalines;
x1 y1 z1 0 x1 y1 z2 6 x1 y2 z1 5 x1 y2 z2 9
x2 y1 z1 16 x2 y1 z2 5 x2 y2 z1 7 x2 y2 z2 0
;
 
 proc freq;
 weight count;
 tables Z*X*Y / chisq nocol nopct;
 run;
 
 proc sort; by X;

 /*saturated model */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z X*Y X*Z Y*Z X*Y*Z /link=log dist=poi obstats;
 title 'Yaturated model:  (XYZ)';
run;
 
 /* complete independence */
 proc genmod order=data;
 class X Y Z;
 model count = X Y Z /link=log dist=poi obstats;
 title 'Complete independence model:  (X,Y,Z)';
run;


/* joint independence of (XY,Z) */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z X*Y /link=log dist=poi obstats;
 title 'Joint Independence:  (XY,Z)';
run;

/* joint independence of (XZ,Y) */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z X*Z /link=log dist=poi obstats;
 title 'Joint Independence:  (XZ,Y)';
run;

/* joint independence of (YZ,X) */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z Y*Z /link=log dist=poi obstats;
 title 'Joint Independence:  (YZ,X)';
run;


 /* conditional independence (XY,XZ) */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z X*Y X*Z /link=log dist=poi obstats;
 title 'Conditional Independence:  (XY,XZ)';
run;

/* conditional independence (XY,YZ) */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z X*Y Y*Z /link=log dist=poi obstats;
 title 'Conditional Independence:  (XY,YZ)';
run;

/* conditional independence (XZ, YZ) */
proc genmod order=data;
 class X Y Z;
 model count = X Y Z X*Z Y*Z /link=log dist=poi obstats;
 title 'Conditional Independence:  (XZ, YZ)';
run;

/* homogeneous associations */ 
proc genmod order=data ;
class X Y Z;
model count = X Y Z  X*Y X*Z Z*Y /link=log dist=poi obstats;
title 'Homogeneous Association':  (XY,XZ,YZ);
run;

/*zero margin, bad patter of zeros */
data zeros;
input X $ Y $ Z $ count @@;
datalines;
x1 y1 z1 0 x1 y1 z2 6 x1 y2 z1 5 x1 y2 z2 9
x2 y1 z1 0 x2 y1 z2 5 x2 y2 z1 16 x2 y2 z2 7
;

/* homogeneous associations */ 
proc genmod order=data ;
class X Y Z;
model count = X Y Z  X*Y X*Z Z*Y /link=log dist=poi obstats;
title 'Homogeneous Association with zero margin':  (XY,XZ,YZ);
run;

/*delete zero values*/
data zeros1;
set zeros;
if count=0 then delete;
run;

/* homogeneous associations */ 
proc genmod order=data ;
class X Y Z;
model count = X Y Z  X*Y X*Z Z*Y /link=log dist=poi obstats;
title 'Homogeneous Association with zero margin':  (XY,XZ,YZ);
run;

;