5th Edition
Maximum Likelihood Estimation with Stata, Fifth Edition
Maximum Likelihood Estimation with Stata, Fifth 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 commands for writing ML estimators, the book presents an overview of the underpinnings of maximum likelihood and how to think about ML estimation.
The fifth edition includes a new second chapter that demonstrates the easy-to-use mlexp command. This command allows you to directly specify a likelihood function and perform estimation without any programming.
The core of the book focuses on Stata's ml command. It shows you how to take full advantage of ml’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.
In later chapters, you will learn how to take advantage of Mata, Stata's matrix programming language. For ease of programming and potential speed improvements, you can write your likelihood-evaluator program in Mata and continue to use ml to control the maximization process. A new chapter in the fifth edition shows how you can use the moptimize() suite of Mata functions if you want to implement your maximum likelihood estimator entirely within Mata.
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. This edition adds a new example of a bivariate Poisson model, a model that is not available otherwise in Stata.
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.
Theory and practice
The likelihood-maximization problem
Likelihood theory
The maximization problem
Estimation with mlexp
Syntax
Normal linear regression
Initial values
Restricted parameters
Robust standard errors
The probit model
Specifying derivatives
Additional estimation features
Wrapping up
Introduction to ml
The probit mode
Normal linear regression
Robust standard errors
Weighted estimation
Other features of method-gf0 evaluators
Limitations
Overview of ml
The terminology of ml
Equations in ml
Likelihood-evaluator methods
Tools for the ml programmer
Common ml options
Maximizing your own likelihood functions
Appendix: More about scalar parameters
Method lf
The linear-form restrictions
Examples
The importance of generating temporary variables as doubles
Problems you can safely ignore
Nonlinear specifications
The advantages of lf in terms of execution speed
Methods lf0, lf1, and lf2
Comparing these methods
Outline of evaluators of methods lf0, lf1, and lf2
Summary of methods lf0, lf1, and lf2
Examples
Methods d0, d1, and d2
Comparing these methods
Outline of method d0, d1, and d2 evaluators
Summary of methods d0, d1, and d2
Panel-data likelihoods
Other models that do not meet the linear-form restrictions
Debugging likelihood evaluators
ml check
Using the debug methods
ml trace
Setting initial values
ml search
ml plot
ml init
Interactive maximization
The iteration log
Pressing the Break key
Maximizing difficult likelihood functions
Final results
Graphing convergence
Redisplaying output
Writing do-files to maximize likelihoods
The structure of a do-file
Putting the do-file into production
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
Writing ado-files for survey data analysis
Program properties
Writing your own predict command
Mata-based likelihood evaluators
Introductory examples
Evaluator function prototypes
Utilities
Random-effects linear regression
Ado-file considerations
Mata’s moptimize() function
Introductory examples
Restricting the estimation sample
Estimation preliminaries
Estimation
Results
Estimation commands
Regression redux
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 bivariate Poisson regression model
Epilogue
Syntax of mlexp
Syntax of ml
Syntax of moptimize()
Likelihood-evaluator checklists
Method lf
Method d0
Method d1
Method d2
Method lf0
Method lf1
Method lf2
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
A bivariate Poisson regression model
References
Biography
Jeff Pitblado is Executive Director, Statistical Software at StataCorp. Pitblado has played a leading role in the development of ml: he added the ability of ml to work with survey data, and he wrote the current implementation of ml in Mata.
Brian Poi previously worked as a developer at StataCorp and wrote many popular econometric estimators in Stata. Since then, he has applied his knowledge of econometrics and statistical programming in several areas, including macroeconomic forecasting, credit analytics, and bank stress testing.
William Gould is President Emeritus of StataCorp and headed the development of Stata for over 30 years. Gould is also the architect of Mata.
