STAT 799
1
Welcome to STAT 799!
1.1
About this course:
1.1.1
Logistics
1.2
Learning goals
1.3
On notation
1.4
Semester project
1.5
Roadmap of this course
1.6
Getting started with statistical modeling
1.6.1
Writing a statistical model
1.6.2
What are linear models?
1.6.3
Vectorized notation
1.6.4
Vectorized notation - cont.
1.6.5
Continuous and categorical predictors
1.6.6
Three-step approach to writing a statistical model
1.7
Review
1.7.1
Probability distributions
1.7.2
Mean, Variance
1.7.3
Covariance
1.8
The most common statistical model
1.8.1
Properties of the general linear model
1.9
Uncertainty
1.9.1
Types of uncertainty
1.9.2
Types of uncertainty in the general linear model
1.9.3
Uncertainty - applied example
1.10
Coming up tomorrow:
2
Mixed models I
2.1
Recall the most common statistical model
2.1.1
Types of predictors
2.2
Variations to that very common statistical model
2.3
Relaxing the assumption of independence
2.4
Fixed effects and random effects
2.4.1
Going from fixed effects to fixed+random effects
2.5
Generalities on mixed models
2.5.1
Random effects
2.5.2
Estimation of parameters
2.5.3
Fixed effects versus random effects
2.6
Applied examples
2.6.1
Example A – independence holds
2.6.2
Example B – simple groups of similar observations
2.6.3
Example C – different groups of similar observations
2.7
Coming up tomorrow:
3
Mixed models II
3.1
Generalities of linear mixed models
3.2
Inference from linear mixed models
3.2.1
Balanced designs – blocks as fixed or as random?
3.2.2
Unbalanced designs
3.3
Coming up Monday:
4
Mixed models III – model checking, ANOVA, statistical inference
4.1
Review
4.2
Model checking and comparison
4.3
Model checking
4.4
Simulation-based model-checking
4.5
Some useful metrics to compare models
4.5.1
Root mean squared error
4.5.2
The coefficient of determination R
2
4.5.3
Adjusted R
2
4.5.4
Some issues with R
2
4.5.5
Akaike Information Criterion (AIC)
4.5.6
Bayesian Information Criterion (BIC)
4.6
Analysis of variance – ANOVA
4.6.1
This is how you build an ANOVA table
4.6.2
The elements of the ANOVA
4.7
Critiques of ANOVA over the years
4.8
A different take on ANOVA using multilevel modeling
4.8.1
An applied example
4.9
Coming up tomorrow:
5
Generalized linear mixed models
5.1
GLMMs
5.1.1
Review – building a statistical model
5.1.2
Generalities of GLMMs
5.1.3
Implications for model fitting
5.1.4
Model diagnostics
5.2
Applied example – picking distributions
5.3
Reading
6
Software implementation & troubleshooting
6.1
Software implementation
6.2
Troubleshooting
6.3
In-class example
6.4
Coming up tomorrow:
7
Non-linear mixed models
7.1
The general linear model
7.2
Revisiting linearity
7.3
Some benefits of non-linear models
7.4
Applied example
7.5
Numeric and categorical predictors
8
Statistical inference
8.1
What is statistical inference?
8.2
The components that go into interpreting results (in the context of LMMs)
8.2.1
Estimation
8.2.2
Prediction
8.3
On the use of R
2
for statistical inference
8.3.1
Bootstrapped R
2
8.3.2
Out-of-sample R
2
8.4
Next week
9
Communicating results
9.1
Scientific writing
9.1.1
Paragraphs
9.2
Communicating statistical analyses
9.3
Communicating results and uncertainty
9.3.1
Example
9.3.2
Hypothesis tests and p-values
9.3.3
Other results in mixed-effects models
9.4
Reading
10
Wrap-up
10.1
Announcements
10.2
From normal, iid data, to generalized mixed models
10.2.1
Independence
Mixed models!
10.2.2
Linearity
Non-linear models
10.2.3
Normality
Generalized linear models
10.2.4
Constant variance
two approaches
10.3
Applied wrap-up
10.4
Coming next
11
Semester Project
11.1
Learning objectives
11.2
Partial deadlines
11.2.1
Project proposal - Due Sunday February 1st at noon CT
11.2.2
Written report - Due Wednesday April 20 at 2pm CT for peer review
11.2.3
Oral presentation - Due May 9
11.2.4
Written report and reproducible tutorial - Due May 15
Published with bookdown
STAT 799 - Topics in Statistics: Applied linear mixed models in agriculture and life sciences
Day 6
Software implementation & troubleshooting
February 4th, 2026
6.1
Software implementation
Writing statistical models
Fitting linear mixed models using
lme4
6.2
Troubleshooting
lme4 convergence warnings: troubleshooting
lme4
’s own
troubleshooting
GLMM FAQ by Ben Bolker
WTF –
What They Forgot to Teach You About R
6.3
In-class example
get R code
6.4
Coming up tomorrow:
Non-linear mixed models