Find maximum likelihood estimates

[osorensen]

Overview

Given a model set up according to #6 and methods for computing the loglikelihood according to #11, in this step we should maximize that function. We should compare automatic differentiation and numeric differentiation. The fill-reducing permutation found in #11 should be retained in each step of the algorithm, although the values of the lambda parameters differ. This means that the mapping for the lambda parametes should comply with the permutation.

Intended outcome

Based on model input in R, the maximum likelihood estimates should be computed in C++ and returned to R.

Things to do

• Compute derivatives using automatic differentiation
• Compute derivatives using numerical differentiation
• Optimization algorithms #18
• Line search #19
• Stage 2 optimization for GLMs #20
• Sensible initial values #21
• Stepsize selection for conditional modes, inner step #22