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Programmable maximum likelihood

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
  • 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

See New in Stata 18 to learn about what was added in Stata 18.