Regression and Other Stories Book Club
Welcome
Book club meetings
Pace
Resources
1
Introduction
Three Challenges of Statistics
Regression Example
What’s it good for?
Causual Inference
Adjust for pretreatment differences
Examples of challenges
Statistical Analysis Cycle
Classical and Bayesian Inference
Computing least squares and Bayesian regression
Meeting Videos
1.0.1
Cohort 1
1.0.2
Cohort 2
2
Data and measurement
2.1
SLIDE 1
2.2
Meeting Videos
2.2.1
Cohort 1
2.2.2
Cohort 2
3
Some basic methods in mathematics and probability
3.1
SLIDE 1
3.2
Meeting Videos
3.2.1
Cohort 1
3.2.2
Cohort 2
4
Statistical inference
4.1
Inference and Sampling Distributions
Role of inference
Sampling distribution
4.2
Estimates, standard errors, and confidence intervals
Jargon
Confidence Interval Simulation
Degrees of Freedom, t-distribution
4.3
Bias and unmodeled uncertainty
Example
4.4
Statistical significance, hypothesis testing, and statistical errors
4.4.1
Type 1 and Type 2 errors vs. Type M and Type S errors
4.5
Problems with the concept of statistical significance
4.6
Moving beyond hypothesis testing
4.7
Meeting Videos
4.7.1
Cohort 1
4.7.2
Cohort 2
5
Simulation
5.1
SLIDE 1
5.2
Meeting Videos
5.2.1
Cohort 1
5.2.2
Cohort 2
6
Background on regression modeling
6.1
SLIDE 1
6.2
Meeting Videos
6.2.1
Cohort 1
6.2.2
Cohort 2
7
Linear regression with a single predictor
7.1
Example data
Fit the data
Examine the fit
Using the model to predict
7.2
Checking the procedure with fake-data simulation
Fake Data Loop
7.3
Comparisons as Regression
Estimating the mean = regression on constant term
Estimating a difference = regressing on an indicator variable
7.4
Meeting Videos
7.4.1
Cohort 1
7.4.2
Cohort 2
8
Fitting regression models
8.1
SLIDE 1
8.2
Meeting Videos
8.2.1
Cohort 1
8.2.2
Cohort 2
9
Prediction and Bayesian inference
9.1
SLIDE 1
9.2
Meeting Videos
9.2.1
Cohort 1
9.2.2
Cohort 2
10
Linear regression with multiple predictors
10.1
SLIDE 1
10.2
Meeting Videos
10.2.1
Cohort 1
10.2.2
Cohort 2
11
Assumptions, diagnostics, and model evaluation
11.1
Assumptions of Regression Analysis
How to Deal With Failures of Assumptions
Causal Inference
11.2
Plotting the data and fitted model
Example: Forming a linear predictor from a multiple regression
11.3
Residual plots
Using fake data simulation to understand residual plots
Understanding the choice using fake-data
11.4
Comparing data to replications from a fitted model
Speed of light example
Fit data to model (fit to constant term)
Compare simulated with observed
11.5
Example: predictive simulation to check the fit of a time-series model
11.6
Residual standard deviation
\(\sigma\)
and explained variance
\(R^2\)
11.6.1
Bayesian
\(R^2\)
11.7
External validation
11.8
Cross Validation
Leave-one-out cross validation
K-fold cross validation
Chat GPT Poem
11.9
Meeting Videos
11.9.1
Cohort 1
11.9.2
Cohort 2
12
Transformations
12.1
SLIDE 1
12.2
Meeting Videos
12.2.1
Cohort 1
12.2.2
Cohort 2
13
Logistic regression
13.1
Logistic regression with a single predictor
Example
Comparison to actual fraction
13.2
Intepreting regression coefficients
13.3
Predictions and Comparisons
13.4
Latent-data formulation
13.5
Maximum likelihood and Bayesian inference
Example comparing maximum likelihood and Bayesian inference
13.6
Cross validation and log score for logistic regression
13.7
Building a logisic regression model
13.8
Meeting Videos
13.8.1
Cohort 2
14
Working with logistic regression
14.1
SLIDE 1
14.2
Meeting Videos
14.2.1
Cohort 2
15
Other generalized linear models
15.1
SLIDE 1
15.2
Meeting Videos
15.2.1
Cohort 2
16
Design and sample size decisions
16.1
Statistical Power
16.2
General Principles of design (proportions)
16.3
Sample size and design for continuous outcomes
Regression predictors
16.4
Interactions
Example in R
16.5
Design calculations after the data have been collected
16.6
Design analysis using fake-data simulation
16.7
Meeting Videos
16.7.1
Cohort 2
17
Poststratification and missing-data imputation
17.1
SLIDE 1
17.2
Meeting Videos
17.2.1
Cohort 2
18
Causal inference basics and randomized experiments
18.1
Basics of causal inference
18.2
Average Causal Effects
18.3
Randomized experiments
Complete Randomization example
18.4
Other randomizations
18.5
Properties of randomized experiments
Returning to the example
18.5.1
Block Randomization
18.6
Assumptions and Limitations of randomized experiments
18.7
Meeting Videos
18.7.1
Cohort 2
19
Causal inference using regression on the treatment variable
19.1
SLIDE 1
19.2
Meeting Videos
19.2.1
Cohort 2
20
Observational studies assuming all confounders measured
20.1
SLIDE 1
20.2
Meeting Videos
20.2.1
Cohort 2
21
More advanced topics in causal inference
21.1
SLIDE 1
21.2
Meeting Videos
21.2.1
Cohort 2
22
Advanced regression and multilevel models
22.1
Expressing the models so far in a common framework
22.2
Incomplete data
22.3
Correlated errors
22.4
Many Predictors
22.5
Multilevel or hierachical models
22.6
Nonlinear models
22.7
Nonparametric regression and machine learning
Machine learning meta-algorithms
22.8
Computational efficency in Stan
22.9
The End
22.10
Meeting Videos
22.10.1
Cohort 2
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Regression and Other Stories Book Club
Chapter 8
Fitting regression models
Learning objectives:
THESE ARE NICE TO HAVE BUT NOT ABSOLUTELY NECESSARY