GLM Part 4
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
Loyn (1987) modeled the abundance of forest birds with six predictor variables (patch area, distance to nearest patch, distance to nearest larger patch, grazing intensity, altitude and years since the patch had been isolated).
Regent honeyeater
Format of loyn.csv data file
| ABUND | DIST | LDIST | AREA | GRAZE | ALT | YR.ISOL |
|---|---|---|---|---|---|---|
| .. | .. | .. | .. | .. | .. | .. |
| ABUND | Abundance of forest birds in patch- response variable |
| DIST | Distance to nearest patch - predictor variable |
| LDIST | Distance to nearest larger patch - predictor variable |
| AREA | Size of the patch - predictor variable |
| GRAZE | Grazing intensity (1 to 5, representing light to heavy) - predictor variable |
| ALT | Altitude - predictor variable |
| YR.ISOL | Number of years since the patch was isolated - predictor variable |
The aim of the analysis is to investigate the effects of a range of predictors on the abundance of forest birds.
Read in the data
loyn = read_csv('data/loyn.csv', trim_ws=TRUE)## Parsed with column specification:
## cols(
## ABUND = col_double(),
## AREA = col_double(),
## YR.ISOL = col_integer(),
## DIST = col_integer(),
## LDIST = col_integer(),
## GRAZE = col_integer(),
## ALT = col_integer()
## )glimpse(loyn)## Observations: 56
## Variables: 7
## $ ABUND <dbl> 5.3, 2.0, 1.5, 17.1, 13.8, 14.1, 3.8, 2.2, 3.3, 3.0, 2...
## $ AREA <dbl> 0.1, 0.5, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 2.0,...
## $ YR.ISOL <int> 1968, 1920, 1900, 1966, 1918, 1965, 1955, 1920, 1965, ...
## $ DIST <int> 39, 234, 104, 66, 246, 234, 467, 284, 156, 311, 66, 93...
## $ LDIST <int> 39, 234, 311, 66, 246, 285, 467, 1829, 156, 571, 332, ...
## $ GRAZE <int> 2, 5, 5, 3, 5, 3, 5, 5, 4, 5, 3, 5, 2, 1, 5, 5, 3, 3, ...
## $ ALT <int> 160, 60, 140, 160, 140, 130, 90, 60, 130, 130, 210, 16...Exploratory data analysis
Model formula: \[ y_i \sim{} \mathcal{N}(\mu_i, \sigma^2)\\ \mu_i = \boldsymbol{\beta} \bf{X_i} \]
where \(\boldsymbol{\beta}\) is a vector of effects parameters and \(\bf{X}\) is a model matrix representing the additive effects of the scaled versions of distance (ln), distance to the nearest large patch (ln), patch area (ln), grazing intensity, year of isolation and altitude on the abundance of forest birds.
Fit the model
Model validation
Model investigation / hypothesis testing
Predictions
Summary figures
References
Loyn, R. H. 1987. “Nature Conservation: The Role of Remnants of Native Vegetation.” In, edited by D. A. Saunders, G. W. Arnold, A. A. Burbridge, and A. J. M. Hopkins. Chipping Norton, NSW: Surrey Beatty & Sons.