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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

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    $\begingroup$ 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. $\endgroup$
    – gung - Reinstate Monica
    Commented Jun 20, 2019 at 3:37
  • $\begingroup$ 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. $\endgroup$
    – Isabella Ghement
    Commented Jun 20, 2019 at 8:37

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I think you should use poisson random effect model and the initial abundance should be an offset.

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  • $\begingroup$ I used a negative binomial model because of overdispersion but what do you mean by an offset? $\endgroup$
    – antR
    Commented Jun 20, 2019 at 0:56
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    $\begingroup$ The offset formulates the problem as a rate. So you would be modeling the ratio of abundance of prey after experiment to before experiment. The offset variable would have a coefficient of 1 $\endgroup$
    – pankaj negi
    Commented Jun 20, 2019 at 1:00
  • $\begingroup$ Ah. I'm more keen on keeping inital sampling as a covariate or a random effect as the question I'm interested doesn't have anything to with rates. What are you opinions of using it as a covariate versus a random effect? $\endgroup$
    – antR
    Commented Jun 20, 2019 at 1:04
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    $\begingroup$ My understanding is that random effects are usually categorical variables with a different intercept and slope for each level. Also, it works best when they are many levels to the categorical variable. I would suggest briefly reading 'Data Analysis Using Regression and Multilevel/Hierarchical Models' by Andrew Gelman and co. It has a chapter on modelling count data. $\endgroup$
    – pankaj negi
    Commented Jun 20, 2019 at 1:16
  • $\begingroup$ Thanks for the tip. Unfortunately that none of this actually answers the question of whether or not initial sampling abundances should be used as a covariate or a random effect. $\endgroup$
    – antR
    Commented Jun 20, 2019 at 1:31

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