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Course
Outline
1. Main ideas in
Statistics
2. Technical
Details
- a. Notation conventions for parameters, random
variables, realized values
- b. Need to be clear about meaning of subscripts
- c. Issues of notation and meaning for realized unit,
versus enumerated unit
- d. Simultaneous representation of equations for
multiple responses
- e. Parameter definitions
- f. Expectation (sampling, response error), and
variances/covariances
- g. Double expectation, and conditional variance
expansions
3. Representations using
Matrix Algebra
- a. Models
- b. Estimates, covariance matrices, linear
combinations
- c. LS estimates
- d. Two factor models
- e. Kronecker products
- f. Use of IML
4. Examples
- a. Season's study on serum cholesterol
- b. Yield based on cover crop and nitrogen
- c. Soil ingestion studies
5. Types of Random
error
- a. Cluster
- b. Time/distance models
- c. Variograms for spacial models
6. Basic results and
Context for Cluster Settings
- a. Terminology- spherical, compound symmetry
- b. Ignoring clustering (too small variances)
- c. Greehouse Geisser, Huynh Feld corrections
- d. Pretest-posttest- difference analysis vs posttest
analysis
- e. Lord's Paradox
- f. Multivariate analysis
7. General Issues in
Mixed Models
- a. Local, intermediate, and broad inference
- b. Population average, and subject specific
models
- c. Latent values vs linear predictors
8. Estimation
approaches
- a. Bayes Box and Bayesian estimates
- b. Likelihood Based Estimates
- c. Minimum MSE methods
- d. Unbiased Estimators (LS, or WLS)
9. ML Equations and
Estimates for Simple Mixed Model
- a. Development
- b. Implementation in IML
10.
Henderson's/Goldbergers/Scott and Smith's Mixed model
Equations
- a. Different Frameworks for development
- b. Superpopulation/Bayesian, Frequentist
interpretations
- c. EM algorithm for fitting.
11. Mixed models for
Categorical Data
- a. Parameter definitions
- b. Liang-Zeger GEE model
- c. Wolfinger mixed model
- d. Other models
12. Other
Topics
- a. Growth curve models
- b. Random coefficient models
- c. Time series models
- d. Cross-over designs
Last Update: 1/26/99
Comments: Ed Stanek
Email:
stanek@schoolph.umass.edu
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