# SAS NLMIXED proc and LOGISTIC proc results different

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?

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.
• So the random effect $u$ is trying to capture partial uncertainty of residual? Which does not mean to replace error term, am I correct? – illudian Mar 26 '15 at 21:57
• 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. – cgonagu Mar 27 '15 at 7:22