In Example 67.3 in SAS/STAT 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(1p); 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
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 