Generalized Linear Models for count and proportion data

1 Lecture

Slides in full screen

2 Exercise 1

Revisit the example from the lecture on species richness depending on biomass and pH of a site in the dataset 08_species.csv.

In the lecture, the data and the model predictions were plotted on the scale of the response variable (see slide 25). Now, create a similar plot with data and predictions at the scale of the link function, or in other words at the scale of the linear predictor. That means the scaling of the y-axis has to be adjusted.

Discuss the pros and cons of the figure using the response-scale vs. the link-scale for the y axis.

For predictions on the link-scale use: predict(your_model, your_newdata, type = "link")

You also have to scale the data with an appropriate function. Which one? See slide 10!

You need to transform the data with the link-function, which is the log() function here.

An alternative solution is to keep data and predictions at the response scale and only use a log-scaled y-axis in the figure by adding + scale_y_log10() in the ggplot() call.

Solutions

3 Exercise 2

In this example, we investigate the occurrence of Odonata larvae (dragonflies and damselflies) in water-filled bromeliads, which are epiphytic tropical plants. The data were adopted from Petermann et al. 2015 and is provided in the dataset 08_bromeliads.csv.

The main research question is: “How does bromeliad size (measured by volume) influence the presence or absence of Odonata larvae?

  • Response variable: Odonatepresence (0 - absent, 1 - present)
  • Explanatory variable: logmaxvolume
  1. Plot the relationship between Odonata occurrence and bromeliad size!
  2. Which type of data do you have here? Which type of GLM do you need for the analysis?
  3. Fit a GLM with appropriate error distribution and link function!
  4. Test the effect of bromeliad volume on Odonata occurrence!
  5. Plot the data and the model predictions.
  6. Think about the question: “What exactly does the line with the model predictions show?”

3.1 Extra

  • Fit, analyse and visualise a more complex model with logmaxvolume and site as predictor variables!
  • Does the effect of bromeliad size on Odonata occurrence differ between sites?
  • What might to be the statistical problem in answering this question?

Solutions