Everything we have discussed so far in class assumes that each replicate is independent. In ecology that assumption is often not met. Observations can be nested within sites or transects, and individuals can be sampled more than once.
In this week we will learn how to deal with non-independence using mixed effects models.
- The problem of non-independence
- Random vs. fixed effects
- Introducing the mixed effect model
- How to specify random effects in R
There will be a mixture of R code and lecture.
Much ink has been spilled on this topic. Some particularly useful lectures are:
- Schluter, D. Biology 501, University of British Columbia lecture on Mixed Effects Models
- PennState STAT 485: Intermediate Topics in R Statistical Language
There is also a brand new pre-print that looks to be an excellent resource on this topic:
- Harrison, X.A., et al. (Pre-print) A brief introduction to mixed effects modelling and multi-model inference in ecology. PeerJ Pre-prints
I cite this book a lot in this class, but where random effects are concerned their reference guide is especially useful:
- Zuur, A, Ieno, E.N., Walker, N.J., Saveliev, A.A., Smith, G.M. (2010) Mixed effects models and extensions in ecology with R. Springer
Bonus: Want to get an R squared value from your mixed effects model? See:
- Nakagawa, S., Schielzeth, H. (2012). A general and simple method for obtaining R2 from generalized linear mixed-effects models
Slides available on Speakerdeck