# The HPNLMOD Procedure

### Binomial Model

In Example 69.3 in SAS/STAT 13.2 User's Guide cancer remission is modeled by expressing the maximum likelihood function for a binary distribution as a nonlinear least squares optimization. The following statements show an equivalent formulation of this model that uses PROC HPNLMOD and specifies the binary distribution explicitly:

```proc hpnlmod data=remiss corr;
parms int=-10 a=-2 b=-1 c=6;
linp = int + a*cell + b*li + c*temp;
p = probnorm(linp);
model remiss ~ binary(1-p);
run;
```

This binary distribution model displays information about the quality of the estimation that is different from the information displayed in the section Least Squares Model. No analysis of variance table is produced for this model; fit statistics that are based on the value of the likelihood function are displayed in Figure 10.3.

Figure 10.3: Nonlinear Likelihood Function Statistics

The HPNLMOD Procedure

Fit Statistics
-2 Log Likelihood 21.9002
AIC (smaller is better) 29.9002
AICC (smaller is better) 31.7183
BIC (smaller is better) 35.0835

Parameter estimates for the binary distribution model that uses the same quantities as are used in the section Least Squares Model are displayed in Figure 10.4.

Figure 10.4: Parameter Estimates and Approximate 95% Confidence Intervals

Parameter Estimates
Parameter Estimate Standard
Error
DF t Value Approx
Pr > |t|
Approximate 95% Confidence
Limits
int -36.7548 32.3607 1 -1.14 0.2660 -103.2 29.6439
a -5.6298 4.6376 1 -1.21 0.2353 -15.1454 3.8858
b -2.2513 0.9790 1 -2.30 0.0294 -4.2599 -0.2426
c 45.1815 34.9095 1 1.29 0.2065 -26.4469 116.8