GLM Part 2
Murray Logan
16 March 2019
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, statsScenario
Polis et al. (1998) were intested in modelling the presence/absence of lizards (Uta sp.) against the perimeter to area ratio of 19 islands in the Gulf of California.
Uta lizard
Format of polis.csv data file
| ISLAND | RATIO | PA |
|---|---|---|
| Bota | 15.41 | 1 |
| Cabeza | 5.63 | 1 |
| Cerraja | 25.92 | 1 |
| Coronadito | 15.17 | 0 |
| .. | .. | .. |
| ISLAND | Categorical listing of the name of the 19 islands used - variable not used in analysis. |
| RATIO | Ratio of perimeter to area of the island. |
| PA | Presence (1) or absence (0) of Uta lizards on island. |
The aim of the analysis is to investigate the relationship between island parimeter to area ratio and the presence/absence of Uta lizards.
Read in the data
polis = read_csv('data/polis.csv', trim_ws=TRUE)## Parsed with column specification:
## cols(
## ISLAND = col_character(),
## RATIO = col_double(),
## PA = col_integer()
## )glimpse(polis)## Observations: 19
## Variables: 3
## $ ISLAND <chr> "Bota", "Cabeza", "Cerraja", "Coronadito", "Flecha", "G...
## $ RATIO <dbl> 15.41, 5.63, 25.92, 15.17, 13.04, 18.85, 30.95, 22.87, ...
## $ PA <int> 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1Exploratory data analysis
Model formula: \[ y_i \sim{} \mathcal{Bin}(n, p_i)\\ ln\left(\frac{p_i}{1-p_i}\right) = \beta_0 + \beta_1 ln(x_i) \]
Fit the model
Model validation
Model investigation / hypothesis testing
Predictions
Summary figures
References
Polis, G. A., S. D. Hurd, C. D. Jackson, and F. Sanchez-Piñero. 1998. “Multifactor Population Limitation: Variable Spatial and Temporal Control of Spiders on Gulf of California Islands.” Ecology 79: 490–502.