# a covariate versus a random effect [duplicate]

I have looked around on cross validated as well as other places but can't seem to find an answer. I'm running a generalized linear mixed-effects model.

Y~initial abundance + Treatment + (1|Month)

Where Y is count data (abundance of prey) Initial abundance is a covariate of initial abundances before any treatments Treatment is a factor of two levels (control and treated) Month is a random intercept due to repeat sampling

The context of this model is an experiment where I reduced a predator in "treated plots" and left the other plots as "controls". Prior to the start of this experiment baseline sampling was done in all plots. I realized some plots natural had higher abundances of prey than other plots. So I decided to use these initial abundances as a covariate to control for the natural unequal abundances between plots. Here is the question: Should this covariate be included as a random effect versus a covariate that's a fixed effect? My understanding is that it could be technically be used as either.

I used it as a covariate because I know that if more prey are abundant than the effects of reducing a predator would most likely be higher than in a poorly abundant plot. It was something that I knew would have an effect on my response of prey abundance. However, I don't know if this reasoning is justified. Any info or opinions would be welcomed!

Thanks

• Random effects are for categorical variables that have non-independent data, like plots that are measured repeatedly, or are nested (subplots within plots within regions, etc). It makes no sense to have a continuous variable like initial abundance as a random variable. Whether you want to mode the initial abundance as an offset or a covariate is covered in the linked thread. Jun 20, 2019 at 3:37
• The design of your study is not entirely clear. How many treated and untreated 'plots' do you have? I would imagine that you would want to allow random effects for these 'plots' if possible. Within each plot, you likely have multiple months worth of Y values (?) and within each month, you may have multiple Y values. Initial abundance can be viewed as a characteristic of the 'plot', hence included as what you term a "covariate". But your model may have to include a random effect for month, say, depending on the design of your study. Jun 20, 2019 at 8:37