4th Edition

# Maximum Likelihood Estimation with Stata, Fourth Edition

By

,

,

## Brian Poi

ISBN 9781597180788
Published October 27, 2010 by Stata Press
352 Pages

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## Book Description

Maximum Likelihood Estimation with Stata, Fourth Edition is written for researchers in all disciplines who need to compute maximum likelihood estimators that are not available as prepackaged routines. Readers are presumed to be familiar with Stata, but no special programming skills are assumed except in the last few chapters, which detail how to add a new estimation command to Stata. The book begins with an introduction to the theory of maximum likelihood estimation with particular attention on the practical implications for applied work. Individual chapters then describe in detail each of the four types of likelihood evaluator programs and provide numerous examples, such as logit and probit regression, Weibull regression, random-effects linear regression, and the Cox proportional hazards model. Later chapters and appendixes provide additional details about the ml command, provide checklists to follow when writing evaluators, and show how to write your own estimation commands.

THEORY AND PRACTICE
The likelihood-maximization problem
Likelihood theory
The maximization problem
Monitoring convergence

INTRODUCTION TO ml
The probit model
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

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
The advantages of lf in terms of accuracy

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

MATA-BASED LIKELIHOOD EVALUATORS
Introductory examples
Evaluator function prototypes
Utilities
Random-effects linear regression

WRITING DO-FILES TO MAXIMIZE LIKELIHOODS
The structure of a do-file
Putting the do-file into production

Writing estimation commands
The standard estimation-command outline
Outline for estimation commands using ml
Using ml in noninteractive mode

WRITING ADO-FILES FOR SURVEY DATA ANALYSIS
Program properties

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

APPENDIX A: Syntax of ml
APPENDIX B: Likelihood-evaluator checklists
APPENDIX C: Listing of estimation commands

References
Author Index
Subject Index

...

## Author(s)

### Biography

William Gould is president of StataCorp and heads the technical development of Stata. He is also the architect of Mata, Stata’s matrix programming language.

Jeff Pitblado is associate director of statistical software at StataCorp. He has played a leading role in the development of ml through adding the ability of ml to work with survey data and writing the current implementation of ml in Mata.

Brian Poi is senior economist at StataCorp. On the software development side, he has written a variety of econometric estimators in Stata.