## Documentation Example 3 for PROC NLMIXED

```/****************************************************************/
/*          S A S   S A M P L E   L I B R A R Y                 */
/*                                                              */
/*    NAME: nlmex3                                              */
/*   TITLE: Documentation Example 3 for PROC NLMIXED            */
/*          Probit-Normal Model with Ordinal Data               */
/* PRODUCT: STAT                                                */
/*  SYSTEM: ALL                                                 */
/*    KEYS: Ordinal data                                        */
/*          Proportional odds model with random effects         */
/*   PROCS: NLMIXED                                             */
/*    DATA: Ezzet and Whitehead (1991)                          */
/*                                                              */
/* SUPPORT: Oliver Schabenberger                                */
/*     REF:                                                     */
/*    MISC:                                                     */
/****************************************************************/

data inhaler;
input clarity group time freq @@;
gt = group*time;
sub = floor((_n_+1)/2);
datalines;
1 0 0 59   1 0 1 59   1 0 0 35   2 0 1 35   1 0 0  3   3 0 1  3   1 0 0  2
4 0 1  2   2 0 0 11   1 0 1 11   2 0 0 27   2 0 1 27   2 0 0  2   3 0 1  2
2 0 0  1   4 0 1  1   4 0 0  1   1 0 1  1   4 0 0  1   2 0 1  1   1 1 0 63
1 1 1 63   1 1 0 13   2 1 1 13   2 1 0 40   1 1 1 40   2 1 0 15   2 1 1 15
3 1 0  7   1 1 1  7   3 1 0  2   2 1 1  2   3 1 0  1   3 1 1  1   4 1 0  2
1 1 1  2   4 1 0  1   3 1 1  1
;

proc nlmixed data=inhaler corr ecorr;
parms b0=0 b1=0 b2=0 b3=0 sd=1 i1=1 i2=1;
bounds i1 > 0, i2 > 0;
eta = b0 + b1*group + b2*time + b3*gt + u;
if (clarity=1) then p = probnorm(-eta);
else if (clarity=2) then
p = probnorm(i1-eta) - probnorm(-eta);
else if (clarity=3) then
p = probnorm(i1+i2-eta) - probnorm(i1-eta);
else p = 1 - probnorm(i1+i2-eta);
if (p > 1e-8) then ll = log(p);
else ll = -1e20;
model clarity ~ general(ll);
random u ~ normal(0,sd*sd) subject=sub;
replicate freq;
estimate 'thresh2' i1;
estimate 'thresh3' i1 + i2;
estimate 'icc' sd*sd/(1+sd*sd);
run;

```