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I want to know if a treatment effectively reduces the abundance of a particular species in some location. For that, I trapped the animals and identified each individual captured, releasing the animals after that. I trapped the animals 20 days with the treatment OFF and 20 days with the treatment ON. I captured 13 individuals within the experiment, but many individuals were captured only once. I had a total of 65 captures. Then, I performed a generalized linear mixed model in R using the lme4 package (glmer() function):

Capture ~ Treatment + (1 | Trap) + (1 | ID)

The factor Capture is 0 (no capture) or 1 (capture) and Treatment is ON or OFF. The Trap is the trap code, from 1 to 100. The ID is the individual identity, from 1 to 13. Is it correct to include the individual identity as a random effect? I am confused about what to include in the ID field for the absences. For the presences, I include the individual code, but for the absences should, I leave the random effect with no data?

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    $\begingroup$ Instead of a glmm, you may be better off analysing the data using some form of spatially explicit mark-recapture methodology such as cran.r-project.org/web/packages/secr/index.html $\endgroup$ Jan 6, 2020 at 15:09
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    $\begingroup$ Hmm... this is a really broad subject. Look at Hiearchical Models, look at books of Marc Kery and Andrew Royle. $\endgroup$
    – Tomas
    Jan 7, 2020 at 9:52

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Mixed models are used to account for correlations within the levels of a grouping factor. Hence, the model

Capture ~ Treatment + (1 | Trap)

postulates that Capture repeated measurements from the same trap are correlated. Likewise, the model

Capture ~ Treatment + (1 | Trap) + (1 | ID)

postulates that Capture repeated measurements from the same trap are correlated, and Capture repeated measurements from the same ID are correlated.

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