Various methods available
Linear-form methods; no need to code derivatives
No-derivative methods; no need to code derivatives
First-derivative methods; must code first derivative
Second-derivative methods; must code first and second derivatives
Write code in ado or Mata
Debugging
Utility to verify that the log likelihood works
Ability to trace the execution of the log-likelihood evaluator
Comparison of numerical and analytic derivatives
Techniques
Modified Newton–Raphson
Davidon–Fletcher–Powell (DFP)
Broyden–Fletcher–Goldfarb–Shanno (BFGS)
Berndt–Hall–Hall–Hausman (BHHH)
Variance matrix estimators
Observed information matrix (Hessian matrix)
Outer product of the gradients (OPG)
Huber/White/robust and cluster–robust
Bootstrap
Jackknife
Survey design, including multistage and stratified designs
Built-in features
Calculate robust standard errors
Include weights
Include linear constraints
Use clustered data
Calculate scores
Automatic support for survey data
Graph convergence path
Redisplay results
Specify initial values
Maximize difficult functions
Control convergence criteria
Use standard output or create your own
Maximum likelihood estimation example
Additional resource
Maximum Likelihood Estimation With Stata, Fourth Edition