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I have studied the effect of site, specific area and depth on amount of organisms on kelp blades. Each site had two different depth with three frames on each depth. From each site I have analysed a random set of plates (within each frame). Then I have analysed 10 points on each plate for organisms (so each plate could have 0-10 organisms registered).

I want to test whether there are different amount of organisms dependent on location, depth, and also where on the blade area the organisms occur (tips, middle, meristematic region). This was done through analysing 10 points on each section of the blade and if any organism covered that specific point it was counted as 1, and if not 0, so on each area it could have 0-10 points covered by organisms. Due to the nature of some colony forming organisms, the blade could be completely covered or completely free from organisms. Therefore, my data contains quite some 10's and many zeroes, and are not really normally distributed.

The hypothesises are that 1. different locations affect amount of organisms differently, 2. there are more fouling towards the tips of the blade compared to the meristematic regions, 3. There are less fouling at deeper waters.

I am uncertain whether i should have frames, individuals (as seaweed blades), and/or locations as the random factor/s.

I tried to run my data as a mixed model with lmer, here is one of the many versions I tried:

pc_model = lmer(Total ~ Depth + Bladearea + Location + 
                        (1+Depth|Frame) + (1+Depth|Individual), 
                data=PC, REML=FALSE)

One of the problems I encounter is when I run a residual plot:

residual plot from lmer()

One of the reasons for the plot looking like this is that I have "hard highs and lows" (due to the nature of the organisms, covering whole blades or not at all in many cases).

I tried to use glmer instead

mod.Blade = glmer(Respons~Bladearea+(1|Frame), data=data, family="binomial")

where the response is made from

data$Neg     = data$Total-data$PC
data$Pos     = data$PC
data$Respons = with(data, cbind(Neg,Pos))

The residual plot looks bad, but different.

residual plot from glmer

I would be very thankful for any input on how to find the appropriate model and if anyone could tell me what I am doing wrong.

EDIT 1:

After input from prof. Florian Hartig I used the DHARMa package simulating residuals. When I used the location as a random factor the residual plots looks ok, but I do want to use location as a predictor variable (to see the effect of location on fouling). So, when I use this model:

fittedModel = glmer(Respons~Bladearea+Location+(1|Frame), data=data, family="binomial"), I again get a residual plot with "stripes" (now vertically aligned).

Any ideas why this happens?

Residual plot from simulated residuals using the DHARMa package

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  • $\begingroup$ Can you say more about your situation, your data, & your goals? What is an "amount of organisms"? Are these counts of colony forming units on petri dishes, eg? Are you trying to test a particular hypothesis (what)? Etc. $\endgroup$ – gung - Reinstate Monica Aug 24 '18 at 14:34
  • $\begingroup$ Thanks for your input, I have now edited my question to make it more understandable (I hope). $\endgroup$ – sma Aug 25 '18 at 7:27
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    $\begingroup$ Check out cran.r-project.org/web/packages/DHARMa, the Vignette cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html explains all your questions about the residuals (disclaimer - I'm the developer) - and yes, you should use a GLMM. $\endgroup$ – Florian Hartig Aug 26 '18 at 14:16
  • $\begingroup$ Thank you so much prof. Hartig! I have still some troubles with the residual plot. I have edited my question above, including this graph as well. do you have any thoughts about this? $\endgroup$ – sma Aug 28 '18 at 8:47
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    $\begingroup$ The stripes are probably because the location variable has a strong influence, and all values with the same location get the same prediction. $\endgroup$ – Florian Hartig Aug 30 '18 at 15:14
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According to the developers. It is almost impossible:

https://cran.r-project.org/web/packages/DHARMa/vignettes/DHARMa.html#calculating-scaled-residuals

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