Table of Contents

1 Theory and Practice

• 1.1 The likelihood maximization problem
• 1.2 Likelihood theory
  • 1.2.1 All results are asymptotic
  • 1.2.2 Variance estimates and hypothesis tests
  • 1.2.3 Likelihood-ratio tests and Wald tests
  • 1.2.4 The outer product of gradients variance estimator
  • 1.2.5 Robust variance estimates
• 1.3 The maximization problem
  • 1.3.1 Numerical root finding
  • Newton's methods
  • The Newton–Raphson algorithm
  • 1.3.2 Quasi-Newton methods
  • The BHHH algorithm
  • The DFP and BFGS algorithm
  • 1.3.3 Numerical maximization
  • 1.3.4 Numerical derivatives
  • 1.3.5 Numerical second derivatives
• 1.4 Monitoring convergence
  
  

2 Overview of ml

• 2.1 The jargon of ml
• 2.2 Equations in ml
• 2.3 Likelihood-evaluator methods
• 2.4 Tools for the ml programmer
• 2.5 Common ml options
  • 2.5.1 Subsamples
  • 2.5.2 Weights
  • 2.5.3 OPG estimates of variance
  • 2.5.4 Robust estimates of variance
  • 2.5.5 Survey data
  • 2.5.6 Constraints
  • 2.5.7 Choosing among the optimization algorithms
• 2.6 Maximizing your own likelihood function
  
  

3 Method lf

• 3.1 The linear-form restrictions
• 3.2 Examples
  • 3.2.1 The probit model
  • 3.2.2 The normal model: linear regression
  • 3.2.3 The Weibull model
• 3.3 The importance of generating temporary variables as doubles
• 3.4 Problems you can safely ignore
• 3.5 Nonlinear specifications
• 3.6 The advantages of lf in terms of execution speed
• 3.7 The advantages of lf in terms of accuracy
  
  

4 Methods d0, d1, and d2

• 4.1 Comparing these methods
• 4.2 Outline of method d0, d1, and d2 evaluators
  • 4.2.1 The todo argument
  • 4.2.2 The b argument
    Using mleval to obtain values from each equation
  • 4.2.3 The lnf argument
    Using lnf to indicate that the likelihood cannot be calculated
    Using mlsum to define lnf
  • 4.2.4 The g argument
    Using mlvecsum to define g
    Scores for robust and OPG variance estimates (optional)
  • 4.2.5 The negH argument
    Using mlmatsum to define negH
  • 4.2.6 Aside: Stata's scalars
• 4.3 Summary of methods d0, d1, and d2
  • 4.3.1 Method d0
  • 4.3.2 Method d1
  • 4.3.3 Method d2
• 4.4 Linear-form examples
  • 4.4.1 The probit model
  • 4.4.2 The normal model: linear regression
  • 4.4.3 The Weibull model
• 4.5 Panel-data likelihoods
  • 4.5.1 Calculating lnf
  • 4.5.2 Calculating g
  • 4.5.3 Calculating negH
    Using mlmatbysum to help define negH
    Likelihoods other than linear form
    
    

5 Debugging likelihood evaluators

• 5.1 ml check
• 5.2 Using methods d1debug and d2debug
  • 5.2.1 Method d1debug
  • 5.2.2 Method d2debug
• 5.3 ml trace
  
  

6 Setting initial values

• 6.1 ml search
• 6.2 ml plot
• 6.3 ml init
  
  

7 Interactive maximization

• 7.1 The iteration log
• 7.2 Pressing the Break key
• 7.3 Maximizing difficult likelihood functions
  
  

8 Final results

• 8.1 Graphing convergence
• 8.2 Redisplaying output
  
  

9 Writing do-files to maximize likelihoods

• 9.1 The structure of a do-file
• 9.2 Putting the do-file into production
  
  

10 Writing ado-files to maximize likelihoods

• 10.1 Writing estimation commands
• 10.2 The standard estimation-command outline
• 10.3 Outline for estimation commands using ml
• 10.4 Using ml in noninteractive mode
• 10.5 Advice
  • 10.5.1 Syntax
  • 10.5.2 Estimation subsample
  • 10.5.3 Parsing with help from mlopts
  • 10.5.4 Weights
  • 10.5.5 Constant-only model
  • 10.5.6 Initial values
  • 10.5.7 Saving results in e()
  • 10.5.8 Displaying ancillary parameters
  • 10.5.9 Exponentiated coefficients
  • 10.5.10 Offsetting linear equations
  • 10.5.11 Program properties
    
    

11 Writing ado-files for survey data analysis

• 11.1 Program properties
• 11.2 Writing your own predict command
  
  

12 Other examples

• 12.1 The logit model
• 12.2 The probit model
• 12.3 The normal model: linear regression
• 12.4 The Weibull model
• 12.5 The Cox proportional hazards model
• 12.6 The random-effects regression model
• 12.7 The seemingly unrelated regression model
  
  

A Syntax of ml

B Likelihood evaluator checklists

• B.1 Method lf
• B.2 Method d0
• B.3 Method d1
• B.4 Method d2
  
  

C Listing of estimation commands

• C.1 The logit model
• C.2 The probit model
• C.3 The normal model
• C.4 The Weibull model
• C.5 The Cox proportional hazards model
• C.6 The random-effects regression model
• C.7 The seemingly unrelated regression model
  
  

References