Exercise

 

Optional extension to Binomial (Bernoulli) GLM - dolphin behavioural plasticity

 

This extension to the dolphin data analysis is for those who may be a bit ahead and would like to :

• get some experience dealing with interactions between categorical predictors (valid with LMs or GLMs)
• test your understanding of the binomial GLMs for the analysis of Bernoulli data, by repeating the approach of the previous exercise with a slightly more advanced model:
  • model specification
  • model validation
  • interpreting a model graphically
• get more experience with model selection in GLMs (using AIC)

I recommend you continue with your previous R script for the GLM_2 exercise, in your RStudio Project.

 

13. To address the limitations of the previous analysis, fit a new model with categorical predictors only, and interactions between them, two by two: fTide4 + fMonth + fTime6 + fTide4:fMonth + fTide4:fTime6 + fMonth:fTime6. What hypotheses do these interactions correspond to?

 

 

14. Perform model selection “by hand” using the AIC, and construct an AIC table, using the example in the lecture. “By hand” means without using drop1 or step functions. You can get the AIC value from the model summary summary(YourModel) or by typing AIC(YourModel). There are 18 possible models in total, including the full model above. You can choose to evaluate all 18 models in a completely exploratory (the “ignorant and brave”) approach, or only a selection of models based on more specific research questions or predictions of your own (the “clear thinker” approach).

• Example: “We know/expect that dolphins are affected by A, B and C, but I suspect that the effect of B varies depending on the value of A whereas my colleague thinks that the effect of B depends on the value of C”, which would suggest comparing the following models to find out which hypothesis is best supported by the data:
  • A + B + C + A:B
  • A + B + C + B:C
  • A + B + C

 

 

15. Do the validation of your best model, using the approach taken in question 7.

 

 

16. Interpret the model, using plots of the predictions (use the approach taken in question 9) .

 

 

End of the optional extension to Binomial (Bernoulli) GLM exercise

 

For info, the publication here offers a different approach to analysing these data, using slightly fancier GLMs with smooth terms (called GAMs, for Generalized Additive Models), and a few additional refinements: [https://www.nature.com/articles/s41598-019-38900-4]. What assumptions differ between this and your approach?