*** Logistic regression for ordinal factors;
*** Concept of saturated model;
*** Table 4.2 (Categorical Data Analysis by Agresti, 2nd edition);

data snoring;
input snore $ hd $ count;
datalines;
N YES 24
N NO 1355
O YES 35
O NO 603
AD YES 21
AD NO 192
D YES 30
D NO 224
;

** Assign scores to the response categories;
data snoring1;
set snoring;
if snore='N' then score=0;
if snore='O' then score=2;
if snore='AD' then score=4;
if snore='D' then score=5;
run;

** Fit different links;
proc genmod data=snoring1 descending;
freq count; ** Saturated model fits each individual person;
model hd=score/ dist=bin link=idenity p r obstats;
run;

proc genmod data=snoring1 descending;
freq count;
model hd=score/ dist=bin link=logit p r obstats;
run;

proc genmod data=snoring1 descending;
freq count;
model hd=score/ dist=bin link=probit p r obstats;
run;

data snoring2;
input snore $ no_hd total;
datalines;
N 24 1379
O 35 638
AD 21 213
D 30 254
;

data snoring2;
set snoring2;
if snore='N' then score=0;
if snore='O' then score=2;
if snore='AD' then score=4;
if snore='D' then score=5;
run;

** Saturated model fits each cell frequency;
proc genmod data=snoring2 descending;
class snore;
model no_hd/total=snore/ dist=bin link=logit;
run;

** linear association;
proc genmod data=snoring2 descending;
class snore;
model no_hd/total=score/ dist=bin link=logit;
run;

** no assoication or say independent;
proc genmod data=snoring2 descending;
class snore;
model no_hd/total= / dist=bin link=logit;
run;