Maximum Likelihood Estimation with Stata, Fourth Edition is the essential reference and guide for researchers in all disciplines who wish to write maximum likelihood (ML) estimators in Stata. Beyond providing comprehensive coverage of Stata’s ml command for writing ML estimators, the book presents an overview of the underpinnings of maximum likelihood and how to think about ML estimation.
The book shows you how to take full advantage of the ml command’s noteworthy features:
linear constraints
four optimization algorithms (Newton–Raphson, DFP, BFGS, and BHHH)
observed information matrix (OIM) variance estimator
outer product of gradients (OPG) variance estimator
Huber/White/sandwich robust variance estimator
cluster–robust variance estimator
complete and automatic support for survey data analysis
direct support of evaluator functions written in Mata
When appropriate options are used, many of these features are provided automatically by ml and require no special programming or intervention by the researcher writing the estimator.
The fourth edition has been updated to include new features introduced in recent versions of Stata. Such features include new methods for handling scores, more consistent arguments for likelihood-evaluator programs, and support for likelihood evaluators written in Mata (Stata’s matrix programming language). The authors illustrate how to write your estimation command so that it fully supports factor-variable notation and the svy prefix for estimation with survey data. They have also restructured the chapters that introduce ml in a way that allows you to begin working with ml faster. This edition is essential for anyone using Stata 11.
In the final chapter, the authors illustrate the major steps required to get from log-likelihood function to fully operational estimation command. This is done using several different models: logit and probit, linear regression, Weibull regression, the Cox proportional hazards model, random-effects regression, and seemingly unrelated regression.
The authors provide extensive advice for developing your own estimation commands. With a little care and the help of this book, users will be able to write their own estimation commands—commands that look and behave just like the official estimation commands in Stata.
Whether you want to fit a special ML estimator for your own research or wish to write a general-purpose ML estimator for others to use, you need this book.
List of Tables
List of Figures
Preface to the fourth edition
Notation and typography
Versions of Stata
1. THEORY AND PRACTICE
The likelihood maximization problem
Likelihood theory
All results are asymptotic
Variance estimates and hypothesis tests
Likelihood-ratio tests and Wald tests
The outer product of gradients variance estimator
Robust variance estimates
The maximization problem
Numerical root finding
Newton’s method
The Newton-Raphson algorithm
Quasi-Newton methods
The BHHH algorithm
The DFP and BFGS algorithms
Numerical maximization
Numerical derivatives
Numerical second derivatives
Monitoring convergence
2. INTRODUCTION TO OF ml
The probit model
Normal linear regression
Robust standard errors
Weighted estimation
Other features of method-gf0 evaluators
Limitations
3. OVERVIEW OF ml
The terminology of ml
Equations in ml
Likelihood-evaluator methods
Tools for the ml programmer
Common ml options
Subsamples
Weights
OPG estimates of variance
Robust estimates of variance
Survey data
Constraints
Choosing among the optimization algorithms
Maximizing your own likelihood functions
4. METHODS lf
The linear-form restrictions
Examples
The probit model
Normal linear regression
The Weibull model
The importance of generating temporary variables as doubles
Problems you can safely ignore
Nonlinear specifications
The advantages of lf in terms of execution speed
5. METHODS lf0, lf1, AND lf2
Comparing these methods
Outline of evaluators of methods lf0, lf1, and lf2
The todo argument
The b argument
Using mleval to obtain values from each equation
The lnfj argument
Arguments for scores
The H argument
Using mlmatsum to define H
Aside: Stata’s scalars
Summary of methods lf0, lf1, and lf2
Method lf0
Method lf1
Method lf2
Examples
The probit model
Normal linear regression
The Weibull model
6. METHODS d0, d1, AND d2
Comparing these methods
Outline of method d0, d1, and d2 evaluators
The todo argument
The b argument
The lnf argument
Using lnf to indicate that the likelihood cannot be calculated
Using mlsum to define lnf
The g argument
Using mlvecsum to define g
The H argument
Summary of methods d0, d1, and d2
Method d0
Method d1
Method d2
Panel-data likelihoods
Calculating lnf
Calculating g
Calculating H
Using mlmatbysum to help define H
Other models that do not meet the linear-form restrictions
7. DEBUGGING LIKELIHOOD EVALUATORS
ml check
Using the debug methods
First derivatives
Second derivatives
ml trace
8. SETTING INITIAL VALUES
ml search
ml plot
ml init
9. INTERACTIVE MAXIMIZATION
The iteration log
Pressing the Break key
Maximizing difficult likelihood functions
10. FINAL RESULTS
Graphing convergence
Redisplaying output
11. MATA-BASED LIKELIHOOD EVALUATORS
Introductory examples
The probit model
The Weibull model
Evaluator function prototypes
Method-lf evaluators
lf-family evaluators
d-family evaluators
Utilities
Dependent variables
Obtaining model parameters
Summing individual or group-level log likelihoods
Calculating the gradient vector
Calculating the Hessian
Random-effects linear regression
Calculating lnf
Calculating g
Calculating H
Results at last
12. WRITING DO-FILES TO MAXIMIZE LIKELIHOODS
The structure of a do-file
Putting the do-file into production
13. WRITING ADO-FILES TO MAXIMIZE LIKELIHOODS
Writing estimation commands
The standard estimation-command outline
Outline for estimation commands using ml
Using ml in noninteractive mode
Advice
Syntax
Estimation subsample
Parsing with help from mlopts
Weights
Constant-only model
Initial values
Saving results in e()
Displaying ancillary parameters
Exponentiated coefficients
Offsetting linear equations
Program properties
14. WRITING ADO-FILES FOR SURVEY DATA ANALYSIS
Program properties
Writing your own predict command
15. OTHER EXAMPLES
The logit model
The probit model
Normal linear regression
The Weibull model
The Cox proportional hazards model
The random-effects regression model
The seemingly unrelated regression model
A. SYNTAX OF ML
B. LIKELIHOOD-EVALUATOR CHECKLISTS
Method lf
Method d0
Method d1
Method d2
Method lf0
Method lf1
Method lf2
C. LISTING OF ESTIMATION COMMANDS
The logit model
The probit model
The normal model
The Weibull model
The Cox proportional hazards model
The random-effects regression model
The seemingly unrelated regression model
