STAT 870
1
Welcome to STAT 870!
1.1
About this course:
1.1.1
Logistics
1.2
Learning goals
1.3
Overview of the course
1.4
What is messy data anyways?
1.5
Linear Models review
1.6
On notation
1.7
Homework & Announcements
2
Designed Experiments Review
2.1
Announcements
2.2
Designed experiments
2.2.1
Treatment structure
2.2.2
Design structure
2.3
Homework & Announcements
3
Designed Experiments Review
3.1
Announcements
3.2
Semester project
3.3
Designed experiments
3.3.1
Design structures
3.4
Applied example: fungicide effects on barley genotypes
3.5
Homework & Announcements
4
Linear mixed models
4.1
Announcements
4.2
Statistical models
4.3
The general linear model
4.3.1
Applied example
4.4
Linear mixed models applied to designed experiments
4.4.1
General notation for linear mixed models
4.4.2
Class discussion: Blocks - random or fixed?
4.5
Homework
5
Linear mixed models
5.1
Announcements
5.2
Linear mixed models
5.2.1
Why do we call these multi-level models?
5.2.2
Degrees of freedom in a mixed model
5.3
Next week
6
Linear Mixed Models
6.1
Announcements
6.2
Mixed Models Review
6.3
Estimation of parameters in Mixed Models
6.3.1
Analysis of variance (ANOVA)
6.3.2
Estimation of fixed effects
6.3.3
Estimation of variance components
6.3.4
Estimating random effects
6.3.5
Degrees of freedom in mixed models
6.4
R demo
7
Generalized Linear Mixed Models
7.1
Announcements
7.2
Review about the (general) linear mixed model
7.3
Generalized linear mixed models
7.3.1
Three steps to modeling data
7.3.2
Implications for model fitting
7.4
Reading
8
Inference – Estimability, degrees of freedom, hypothesis tests, contrasts
8.1
Announcements
8.2
Review: Hypothesis tests, t-tests, F tests
8.2.1
Hypothesis tests
8.2.2
On p-values
8.2.3
t-tests
8.2.4
F-tests are multivariate t-tests
8.3
Applied example
8.3.1
t-test
8.3.2
F-test
8.4
Estimability
8.4.1
Contrasts
8.4.2
Adjusting degrees of freedom for mixed models
8.5
Applied example II
8.6
Wednesday
9
Practice
9.1
Announcements
9.2
In-class activity
10
Repeated Measures, Practice II
10.1
Announcements
10.2
Repeated measures
10.2.1
Correlation functions
10.2.2
Deciding which covariance function for a given problem
10.3
Last week’s practice
10.3.1
Weight
10.3.2
Jaw deformity
10.4
Task for today
11
Repeated Measures II
11.1
Announcements
11.2
Linear mixed models review
11.3
Repeated measures
11.3.1
Correlation - G side (conditional) and R side (marginal)
11.3.2
Review – correlation functions
12
Repeated Measures III
12.1
Announcements
12.2
Where we’re standing in this course
12.3
Repeated measures
12.4
Correlation - G side (conditional) and R side (marginal)
12.5
Repeated measures in GLMMs
12.6
Appendix A: Common Response Variable (
\(y | b\)
) Distributions
12.7
Applied example using R
13
Modeling designed experiments in the presence of spatial variability
13.1
Announcements
13.2
Spatial variability
13.2.1
Spatial patterns
13.2.2
Applied example
14
Software Implementation of LMMs
14.1
Announcements
14.2
Model review
14.3
Computational tricks
14.3.1
Improving computational stability
14.3.2
Nonlinear optimizing algorithms
14.4
References
15
Software Implementation of LMMs
15.1
Announcements
15.2
Issues
15.3
References
16
Accounting for spatial effects
16.1
Announcements
16.2
Parametric tools
16.3
Non-parametric tools
16.3.1
Splines
16.4
B-splines
16.4.1
Illustrating splines
16.4.2
Penalized splines
16.4.3
Other types of splines
16.5
Final comments
16.6
Resources
17
Smoothing Splines
17.1
Announcements
17.2
Non-parametric tools
17.2.1
Splines
17.3
Thin-plate regression splines
17.4
Final comments
17.5
Resources
18
Applications of Smoothing Splines
18.1
Announcements
18.2
Splines review
18.3
Applications of splines
19
Miscellaneous
19.1
Announcements
19.2
Statistical models
19.2.1
General linear model
19.3
Illustrating this with a simulation
19.3.1
What is a simulation?
19.3.2
Simulation with 3 repetitions
19.3.3
Simulation with 5 repetitions
19.3.4
Demonstrating the bias-variance tradeoff
19.4
Wrap-up & Discussion
20
Zero-inflated models
20.1
Announcements
20.2
Zero-inflated models
20.3
Applied example
20.3.1
Poisson model
20.3.2
Zero-inflated Poisson model
20.3.3
Negative Binomial model
20.3.4
Zero-inflated NB model
20.3.5
Marginal means
20.4
Other related distributions
21
Zero-inflated models practice
21.1
Announcements
21.2
In-class activity
22
Missing values
22.1
Announcements
22.2
Missing data
22.2.1
Bayesian imputation - MCAR Example
22.2.2
Data missing in all observations & latent variables
22.3
References
23
Integrating multi-environment trials with weather data
23.1
Announcements
23.2
Opportunistic use of multi-environment trials
23.3
Power analyses
23.3.1
Power calculations
23.4
Precision analyses
24
Model selection
24.1
Announcements
24.2
Model selection
24.2.1
The coefficient of determination R
2
24.2.2
Adjusted R
2
24.2.3
Some issues with R
2
24.2.4
Akaike Information Criterion (AIC)
24.2.5
Bayesian Information Criterion (BIC)
24.3
Regularization
24.3.1
Ridge Regression
24.3.2
Lasso Regression
24.3.3
Elastic Net Regression
24.3.4
Some thoghts about regularization
24.4
A few thoughts
24.5
Applied examples
24.6
References
25
Model selection II
25.1
Announcements
25.2
Model selection
25.3
Applied examples
25.4
Next week
26
Planning designed experiments
26.1
Announcements
26.2
Designed experiments
26.2.1
Precision analysis
26.3
Bayesian analysis of designed experiments
26.4
Applied example
26.5
Resources
27
Bayesian analysis of data generated by designed experiments
27.1
Announcements
27.2
Applied example
28
Semester Project
28.1
Learning objectives
28.2
Partial deadlines
28.2.1
Project proposal - Due Friday September 24 at 11:59pm CT
28.2.2
Written report for peer review - Due Friday November 28 at 11:59pm CT for peer review
28.2.3
Peer review - Due Friday December 5 at 11:59pm
28.2.4
Oral presentation - Somewhere between December 3 - December 12
28.2.5
Written report - Due Friday December 19 at 11:59pm CT for peer review
Published with bookdown
STAT 870 - Analysis of Messy Data
Day 15
Software Implementation of LMMs
15.1
Announcements
Assignment 4 grades will be posted tonight
Projects
Download R script for implementing LMMs (from last Monday)
15.2
Issues
Optimizing algorithms
Convergence problems
Singularity and the meaning of zero/negative variance components
15.3
References
lme4 troubleshooting I
lme4 troubleshooting II
Anything by
Ben Bolker
GLMM FAQ
Fitting Linear Mixed-Effects Models Using lme4