Various methods available

• Linear-form (lf) method; no need to code derivatives
• No derivative (d0) method; no need to code derivatives
• First derivative (d1) method; must code first derivative
• Second derivative (d2) method; must code first and second derivatives

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 for d1 and d2 methods

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