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



Utility to verify that the log likelihood works

Ability to trace the execution of the log-likelihood evaluator

Comparison of numerical and analytic derivatives



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



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