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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?

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The main difference is that in PROC NLMIXED you are introducing a random-effect term ($u$) which is specific for each individual (ID). Depending on your data, this can significantly change coefficients.

You can try removing the random statement (and $u$ in $ell$ specification) in PROC NLMIXED to see if this is true.

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  • $\begingroup$ So the random effect $u$ is trying to capture partial uncertainty of residual? Which does not mean to replace error term, am I correct? $\endgroup$
    – illudian
    Mar 26, 2015 at 21:57
  • $\begingroup$ Random effect $u$ is capturing specific components for each individual. You can understand it as a different constant for each individual in ell specification. If you write random u ~ normal(0,S) subject=ID out=TABLE_U;, you will see all these constants per individual. $\endgroup$
    – cgonagu
    Mar 27, 2015 at 7:22

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