Maximum Likelihood Estimation with Stata, Fifth Edition

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.

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