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

Debugger

• 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