Newton-Raphson vs Nelder-Mead simplex method

Hi there,

I have a huge dataset (>60,000 data points) and I am writing my own
code to fit a GLMM to it. When I maximized the likelihood function, I
used Nelder-Mead simplex first to get some idea what the estimates
would be like and the algorithm converged with no problem. Then I use
Newton-Raphson but now it always diverges. Even I plugged in the result
from Nelder-Mead as initial value for N-R, the sum of score vector
(over all data points) was far from zero then it started to diverge
again (even though when I plot the histgram of score, then looked
centered around zero and each one of them is tiny). I did centering and
scaling on the independent variables and it helped a bit but not much.
My question is: in the model, 6 out 8 independent variables are binary
variables, will this affect Newton-Raphson's convergence? Also the
scores look skewed and I think that's why they don't sum to zeros.
Could anything be done to remedy this? When I plug the result from N-M
into the N-R, should I not expect a score vector that is close to zero?
Thanks for you attention and I appreciate your help.

Regards

Aaron

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