Preparations

Load the necessary libraries

library(tidyverse)

## Loading tidyverse: ggplot2
## Loading tidyverse: tibble
## Loading tidyverse: tidyr
## Loading tidyverse: readr
## Loading tidyverse: purrr
## Loading tidyverse: dplyr

## Conflicts with tidy packages ----------------------------------------------

## filter(): dplyr, stats
## lag():    dplyr, stats

Scenario

Here is a modified example from Quinn and Keough (2002). Day and Quinn (1989) described an experiment that examined how rock surface type affected the recruitment of barnacles to a rocky shore. The experiment had a single factor, surface type, with 4 treatments or levels: algal species 1 (ALG1), algal species 2 (ALG2), naturally bare surfaces (NB) and artificially scraped bare surfaces (S). There were 5 replicate plots for each surface type and the response (dependent) variable was the number of newly recruited barnacles on each plot after 4 weeks.

Six-plated barnacle

Format of day.csv data files

Read in the data

day = read_csv('data/day.csv', trim_ws=TRUE)

## Parsed with column specification:
## cols(
##   TREAT = col_character(),
##   BARNACLE = col_integer()
## )

glimpse(day)

## Observations: 20
## Variables: 2
## $ TREAT    <chr> "ALG1", "ALG1", "ALG1", "ALG1", "ALG1", "ALG2", "ALG2...
## $ BARNACLE <int> 27, 19, 18, 23, 25, 24, 33, 27, 26, 32, 9, 13, 17, 14...

Exploratory data analysis

Model formula: \[ y_i \sim{} \mathcal{Pois}(\lambda_i)\\ \mu_i = \boldsymbol{\beta} \bf{X_i} \]

where \(\boldsymbol{\beta}\) is a vector of effects parameters and \(\bf{X}\) is a model matrix representing the intercept and treatment contrasts for the effects of Treatment on barnacle recruitment.

Fit the model

Model validation

Model investigation / hypothesis testing

Predictions

Summary figures