Generalized Linear Models

Course overview

Filippo Gambarota

University of Padova

2023

Last Update: 2023-11-29

Material

Github

The material is available on Github You can find the slides, code, datasets and other stuff.

stat-teaching.github.io/GLMphd

Getting started

  1. Download the repository from Github
  2. Unzip the folder
  3. Open the GLMphd.Rproj file

R

R style

I use sometimes a coding style that is not common. I try to stay as close as possible to base R. But here some general patterns that you will see:

Accessing functions within a package, if I don’t want to load it:

MASS::mvrnorm()

R style

Especially in slides or quick exploratory analysis, extensive use of pipes |> or %>%

as.character(round(mean(iris$Sepal.Length)))

# equivalent but more clear
iris$Sepal.Length |> 
  mean() |> 
  round() |> 
  as.character()

R style

Use of the tidyverse package for data-manipulation using dplyr, tidyr, etc. Sometimes you will se a tibble object. It is only a dataframe with some extra features.

iris |> 
  group_by(Species) |> 
  summarise(Sepal.Length = mean(Sepal.Length))
# A tibble: 3 × 2
  Species    Sepal.Length
  <fct>             <dbl>
1 setosa             5.01
2 versicolor         5.94
3 virginica          6.59
# in base R
aggregate(Sepal.Length ~ Species, iris, mean)
     Species Sepal.Length
1     setosa        5.006
2 versicolor        5.936
3  virginica        6.588

R style

Extensive use of *apply like function (functional programming) to make iterations. In the examples I use for loops because because is more transparent.

means <- vector(mode = "numeric", length = ncol(mtcars))
for(i in 1:length(means)){
  means[i] <- mean(mtcars[[i]])
}
means
 [1]  20.090625   6.187500 230.721875 146.687500   3.596563   3.217250
 [7]  17.848750   0.437500   0.406250   3.687500   2.812500
# equivalent to
sapply(mtcars, mean)
       mpg        cyl       disp         hp       drat         wt       qsec 
 20.090625   6.187500 230.721875 146.687500   3.596563   3.217250  17.848750 
        vs         am       gear       carb 
  0.437500   0.406250   3.687500   2.812500

R style

For plotting I use ggplot2. Is not super easy at the beginning but it pays off.

iris |> 
  ggplot(aes(x = Sepal.Length, y = Petal.Width, color = Species)) +
  geom_point() +
  geom_smooth(method = "lm")

R Studio projects

If you have trouble understanding and using the working directory and setwd() I highly suggest you to use the R Studio projects.

The *.Rproj can be created in a folder and when you open the file R Studio will open an R session setting the working directory automatically.

All the paths will be relative to the *.Rproj file. You can move the folder or share it with other people without worrying about file location.

Contents

  • Overview about GLM and why they are useful
  • Binomial, Poisson and Gamma GLM
    • Fitting the model
    • Parameters interpretation
    • Diagnostic
  • Simulating data
    • Understanding the data generation process
    • Power analysis
    • (for fun 😁)
    • …