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I have a dataset of fish species from different sites within a harbour collected over 17 years. The dataset consists of 1,042 sampling transects collected at 6 specific locations where fish were captured and identified to species. There are two sites in the east, two in the west and two in the south which are suspected to have slightly different communities. I want to analyze the community structure and see if it has changed at the sites where artificial reefs were constructed part way through the study.

To analyze this I'm pooling my catches across year and running a PERMANOVA with location (East, West, South) and presence of a reef (Yes, No) and the interaction effect included as fixed effects. What I'm wondering is how I should include the sampling year to account for all of the repeated sampling. My first impulse was to include it as a mixed effect to control for the repeated samples which wouldn't be independent from each other; but then I thought that including it as a factor would allow me to determine its effect and see if there were any interesting interactions. But then I thought that including it as a covariate would be more powerful, as it would preserve the order of the years which would potentially be more powerful.

My question is: If I include Year as a fixed effect versus a random effect versus a covariate what does that mean about my conclusions? My understanding is that if I include it as a fixed effect I can only draw inferences about the years included in my dataset and I can't extrapolate the effect of the reef construction itself; if I include it as a random effect I control for the multiple repeated samples; and I'm unsure what it means if I include it as a covariate as I haven't encountered anyone who's done that.

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  • $\begingroup$ From your question, I understand that when you say 'include year as a co-variate' you mean include year as a linear fixed effect (meaning you are interested in the change in species over time); whereas when you talk about 'fixed effect' you actually mean include year as a factor fixed effect. Correct? $\endgroup$ – Tilt Jan 18 at 14:21
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First note that including a variable as a covariate and as a fixed effect means exactly the same thing to the model.

So the question is about whether to include year as a fixed or a random effect. I would suggest doing both (seperate models of course). As you correctly point out, there are trade-offs in fitting a variable as fixed vs random and often there is no clear cut answer as to which to use.

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  • $\begingroup$ I get very different results when I include year as a fixed effect versus when I include it as a covariate (Pseudo-F stat = 23.2 versus 6.6; degrees of freedom = 1 versus 16 for the year effect respectively) so I don't think they're equivalent. My reading of this is that when I include year as a fixed effect the PERMANOVA treats it like a categorical variable where there is no relationship between year 1, 2, or 3 versus when I include it as a covariate it preserves the relationship between years and assess whether there is a linear change over time. Does that sound correct? $\endgroup$ – Dugan Jan 11 at 15:11
  • $\begingroup$ I have a similar question. I wonder whether including year as a linear fixed-effect would appropriately take into account the repeated yearly measures? (Which is part of what the OP is asking if I understand correctly) $\endgroup$ – Tilt Jan 18 at 14:23

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