NetCourseTM 200: Maximum likelihood estimation with Stata
- Content:
- Estimation of user-defined models via maximum likelihood.
Includes overview of theory, explanation of how optimizers
work, and practical coding considerations.
- Course leaders:
- William Gould, President of StataCorp and Head of Development.
- Course length:
- 7 weeks (5 lectures)
- Price:
- $125
- Prerequisites:
- Stata 7, installed and working.
- Course content of
NetCourse 151 or equivalent knowledge.
- Editor or word processor with which you are familiar and
that can save and edit plain text files; if you have Stata for
Windows or Stata for Mac, these include an
editor.
- (Course is platform independent.)
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This syllabus is for the Stata 5.0 NetCourse 200 —
it will be rewritten when we offer the course for Stata 7.0.
Syllabus:
Lecture 1: Background on maximum likelihood estimators
- Maximum likelihood theory
- The likelihood function
- The rationale of ML estimates (consistency and asymptotic
normality)
- Why inverse of second derivatives gives the variances
- Why likelihood-ratio tests are better than Wald tests
- Robust variance estimates
- Numerical optimization
- How numerical optimizers work
- Why -g*inv(H) is a good direction to go
- Setting stepsize
- How numerical derivatives are calculated
- Declaring convergence
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Note:
Lecture 1 does not concern Stata per se. This lecture focuses on the
rationale of maximum likelihood estimation and the numerical issues
involved. Emphasis is on practice and providing the background to
knowledgeably discuss maximum likelihood estimates and variance
estimates, and how to diagnose problems.
Lectures 2 to 5 concern estimation with Stata.
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Lecture 2: Introduction to Stata's ml commands and how to program
the linear-form (lf) method
- Overview of Stata's maximizers
- The linear-form (lf) simplification
- Advantages of the lf method
- Practical programming of the lf method
- Multiple equations
- Ancillary parameters
- Specifying initial values
There is an additional one-week break between Lectures 2 and 3 in this
course to allow extra time for discussion.
Lecture 3: Maximization of general likelihood functions without
analytic derivatives (the deriv0 method)
- The deriv0 method
- Programming with scalars, vectors, and matrices in Stata
- The deriv0 likelihood-evaluation program
- Debugging
- Specifying initial values
- Panel-data estimators
- Complex likelihood functions
Lecture 4: Maximization with analytic derivatives (the deriv1 and
deriv2 methods)
- The deriv1 and deriv2 methods
- Using Stata's matrix programming language to calculate derivatives
- Establishing that the derivatives are right
- Ancillary parameters
- Comparison of deriv1 and deriv2 with deriv0 and lf
Lecture 5: Robust variance estimator
- Robust (Huber/White/sandwich/survey design-based) variance
estimates
- Sketch of the theory of the robust variance estimator
- Understanding the computation of the robust variance estimator
- Implementing the robust variance estimator using the _robust
command
- Robust variance estimates for clusters
- Pitfalls of the robust variance estimator for clusters: no
free lunch
- Complex survey data
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