lesson3.Rmd

---
title: "Lesson 3"
output: html_document
---

```{r setup}
library(dplyr)
library(magrittr)
library(ggplot2)
library(tidyr)
theme_set(theme_minimal())
```



## First, let's slow down a bit

Try to complete [Task 3 and 4](lesson3-tasks.html#task-3-detecting-overdispersion-with-a-posterior-predictive-check) from Lesson 2 (and possibly others from the previous lessons)

Pick projects!

## Note on models

- Reuse methodology slides: https://docs.google.com/presentation/d/1jkcKfTOupedZRoJZ9qSuGVDBjlzZFt6vOyEyN0pwduY/edit?usp=sharing

## Linear regression

- The most ubiquitous type of model --- see e.g. https://lindeloev.github.io/tests-as-linear/
- Taylor series
- Intercept, coefficients
- [Dummy coding](https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faqwhat-is-dummy-coding/)
  - There are other ways to code (e.g. [effect coding](https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faqwhat-is-effect-coding/))
  - `model.matrix` in `R` does the coding for you
- Linear predictors and matrix multiplication
  - Intercept in the matrix
- [Least squares](https://en.wikipedia.org/wiki/Least_squares) and  its relatio to normal distribution
  - Maximum likelihood estimator is equivalent to least-squares.
- [Generalized linear models](https://en.wikipedia.org/wiki/Generalized_linear_model) (GLM)
  - Link function, inverse link function
  - Most common link functions:
    - log for positive outcomes (i.e. exponentiate the predictors), 
    - logit (i.e. apply inverse logit to the predictor) for outcomes in [0, 1] - most notably for probabilities in logistic regression.
- Posterior predictive checks as a method to determine which predictors to add

Now, let's do some tasks. Note that they match workflow (simple stuff first, ...)