# 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

## marked as duplicate by gung♦ regression StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jun 20 at 3:33

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 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. – gung Jun 20 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. – Isabella Ghement Jun 20 at 8:37

## 1 Answer

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

• I used a negative binomial model because of overdispersion but what do you mean by an offset? – Leo Ohyama Jun 20 at 0:56
• 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 – pankaj negi Jun 20 at 1:00
• 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? – Leo Ohyama Jun 20 at 1:04
• 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. – pankaj negi Jun 20 at 1:16
• 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. – Leo Ohyama Jun 20 at 1:31