Consider a dataset $Z$ with $S\in \{0,1\}$ as binary response variable and 2 predictors $\{x_1, x_2\}$.
The logistic regression model
proc logistic data=Z;
model S=x1 x2;
run;
and consider an aggregate dataset $A$ with $Y$ as the response varible "1" counts and $N$ as total variable counts for each predictor $x_1$ and $x_2$ the nonlinear Mixed model
proc nlmixed data=A;
parms A=1 B=1 C=1 S=0.1;
ell= A + B*x1 + C*x2 + u;
p= exp(ell)/(1+exp(ell));
model Y ~ binomial(N,p);
random u ~ normal(0,S) subject=ID;
run;
These two procs should return similar coefficient estimation. However I observed big gap between the coefficient estimated mean and confident interval for my data. What is the possible cause to this difference?