List of tables
List of figures
Preface to the fourth edition (pdf)
Versions of Stata
Notation and typography

1 Theory and practice

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

2 Introduction to ml

• 2.1 The probit model
• 2.2 Normal linear regression
• 2.3 Robust standard errors
• 2.4 Weighted estimation
• 2.5 Other features of method-gf0 evaluators
• 2.6 Limitations

3 Overview of ml

• 3.1 The terminology of ml
• 3.2 Equations in ml
• 3.3 Likelihood-evaluator methods
• 3.4 Tools for the ml programmer
• 3.5 Common ml options
  • 3.5.1 Subsamples
  • 3.5.2 Weights
  • 3.5.3 OPG estimates of variance
  • 3.5.4 Robust estimates of variance
  • 3.5.5 Survey data
  • 3.5.6 Constraints
  • 3.5.7 Choosing among the optimization algorithms
• 3.6 Maximizing your own likelihood functions

4 Method lf

• 4.1 The linear-form restrictions
• 4.2 Examples
  • 4.2.1 The probit model
  • 4.2.2 Normal linear regression
  • 4.2.3 The Weibull model
• 4.3 The importance of generating temporary variables as doubles
• 4.4 Problems you can safely ignore
• 4.5 Nonlinear specifications
• 4.6 The advantages of lf in terms of execution speed

5 Methods lf0, lf1, and lf2

• 5.1 Comparing these methods
• 5.2 Outline of evaluators of methods lf0, lf1, and lf2
  • 5.2.1 The todo argument
  • 5.2.2 The b argument
    aaaaaUsing mleval to obtain values from each equation
  • 5.2.3 The lnfj argument
  • 5.2.4 Arguments for scores
  • 5.2.5 The H argument
    aaaaaUsing mlmatsum to define H
  • 5.2.6 Aside: Stata’s scalars
• 5.3 Summary of methods lf0, lf1, and lf2
  • 5.3.1 Method lf0
  • 5.3.2 Method lf1
  • 5.3.3 Method lf2
• 5.4 Examples
  • 5.4.1 The probit model
  • 5.4.2 Normal linear regression
  • 5.4.3 The Weibull model

6 Methods d0, d1, and d2

• 6.1 Comparing these methods
• 6.2 Outline of method d0, d1, and d2 evaluators
  • 6.2.1 The todo argument
  • 6.2.2 The b argument
  • 6.2.3 The lnf argument
    aaaaaUsing lnf to indicate that the likelihood cannot be calculated
    aaaaaUsing mlsum to define lnf
  • 6.2.4 The g argument
    aaaaaUsing mlvecsum to define g
  • 6.2.5 The H argument
• 6.3 Summary of methods d0, d1, and d2
  • 6.3.1 Method d0
  • 6.3.2 Method d1
  • 6.3.3 Method d2
• 6.4 Panel-data likelihoods
  • 6.4.1 Calculating lnf
  • 6.4.2 Calculating g
  • 6.4.3 Calculating H
    aaaaaUsing mlmatbysum to help define H
• 6.5 Other models that do not meet the linear-form restrictions

7 Debugging likelihood evaluators

• 7.1 ml check
• 7.2 Using the debug methods
  • 7.2.1 First derivatives
  • 7.2.2 Second derivatives
• 7.3 ml trace

8 Setting initial values

• 8.1 ml search
• 8.2 ml plot
• 8.3 ml init

9 Interactive maximization

• 9.1 The iteration log
• 9.2 Pressing the Break key
• 9.3 Maximizing difficult likelihood functions

10 Final results

• 10.1 Graphing convergence
• 10.2 Redisplaying output

11 Mata-based likelihood evaluators

• 11.1 Introductory examples
  • 11.1.1 The probit model
  • 11.1.2 The Weibull model
• 11.2 Evaluator function prototypes
  aaaaMethod-lf evaluators
  aaaalf-family evaluators
  aaaad-family evaluators
• 11.3 Utilities
  aaaaDependent variables
  aaaaObtaining model parameters
  aaaaSumming individual or group-level log likelihoods
  aaaaCalculating the gradient vector
  aaaaCalculating the Hessian
• 11.4 Random-effects linear regression
  • 11.4.1 Calculating lnf
  • 11.4.2 Calculating g
  • 11.4.3 Calculating H
  • 11.4.4 Results at last

12 Writing do-files to maximize likelihoods

• 12.1 The structure of a do-file
• 12.2 Putting the do-file into production

13 Writing ado-files to maximize likelihoods

• 13.1 Writing estimation commands
• 13.2 The standard estimation-command outline
• 13.3 Outline for estimation commands using ml
• 13.4 Using ml in noninteractive mode
• 13.5 Advice
  • 13.5.1 Syntax
  • 13.5.2 Estimation subsample
  • 13.5.3 Parsing with help from mlopts
  • 13.5.4 Weights
  • 13.5.5 Constant-only model
  • 13.5.6 Initial values
  • 13.5.7 Saving results in e()
  • 13.5.8 Displaying ancillary parameters
  • 13.5.9 Exponentiated coefficients
  • 13.5.10 Offsetting linear equations
  • 13.5.11 Program properties

14 Writing ado-files for survey data analysis

• 14.1 Program properties
• 14.2 Writing your own predict command

15 Other examples

• 15.1 The logit model
• 15.2 The probit model
• 15.3 Normal linear regression
• 15.4 The Weibull model
• 15.5 The Cox proportional hazards model
• 15.6 The random-effects regression model
• 15.7 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
• B.5 Method lf0
• B.6 Method lf1
• B.7 Method lf2

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
Author index (pdf)
Subject index (pdf)