Chapter 6 Fixed vs. random effects

We frequently encounter the terms ‘fixed’ and ‘random’ effects in the LMM literature.

There are also many possible definitions, and we chose to present those we think are easier to apply when doing your analyses.

6.1 Fixed effects: deterministic processes

Data comes from:

  • all possible levels of a factor (qualitative variable)
  • a predictor (quantitative variable)

We wish to make conclusions about the levels of the factor or about the relationship between the response variable and the predictor.

Example: If you are comparing mercury concentration in fish from three different habitats. Habitat has a fixed effect as we sampled in each 3 habitats and we are interested in making conclusions about these specific habitats.

6.2 Random effects: stochastic processes

Variables with a random effect are also called random factors, as they are only qualitative variables (categorical, not continuous).

A random effect is observed when the data only includes a random sample of the factor’s many possible levels, which are all of interest.

They usually are grouping factors for which you want to control the effect in your model, but are not interested in their specific effect on the response variable. Therefore they enable us to structure the error process.

Example: If you are studying mercury contamination in fish in Ugandan crater lakes. For logistical reasons, you can’t sample all the crater lakes, so you sample only 8 of them. However, fish from a given lake might have some sort of correlation between themselves (auto-correlation) since they experience the same environmental conditions. Even though you’re not interested in the effect of each lake specifically, you should account for this potential correlation with a random factor (crater lake) in order to make conclusions about crater lakes in general.