Introduction
Missingness mechanisms, identifiability, and the questions that come before choosing a method.
Missing Data:Foundations and Methods
Statistical inference when the data we observe are only part of the story.
- Assumptions: missingness mechanisms and identifiability.
- Algorithms: EM, Bayesian computation, and multiple imputation.
- Inference: connections between likelihood, weighting, and doubly robust estimating equations.
About the course
Originally taught in 2017, this course is intended for graduate students in statistics and biostatistics with a foundation in mathematical statistics. Familiarity with asymptotic theory and statistical programming is helpful.
A common thread
Beginning with missingness mechanisms and identifiability, we connect likelihood-based methods, including EM and imputation, with semiparametric methods based on weighting.
Chapters & lecture slides
01 — 07The EM algorithm
Build likelihood-based inference from the complete-data problem, one conditional expectation at a time.
Regression with missing covariates
Apply maximum likelihood and the method of weights to incomplete regression data.
Advanced topics in EM
Extend the algorithm to nonparametric estimation, information calculations, and conditional maximization.
Multiple imputation & Bayesian analysis
Represent uncertainty about missing values through posterior distributions and repeated completed datasets.
The estimating equation approach
Move from likelihoods to estimating equations, inverse probability weighting, and double robustness.
Conclusion
Reconnect the assumptions, algorithms, and inferential ideas developed throughout the course.
DISCUSSION
Comments and questions
Share questions, corrections, and suggestions about this chapter or the book.