I was hoping someone could help me understand more about the use of the Observation-Level Random Effect. Basically, I want to look at individual animals as a random effect in a GLMM and I want to account for between-individual and within-individual variation in a behaviour (the response variable). By including individual as a random effect (as far as I understand it) that accounts for the between-individual variance. Previous posts have discussed the Observation-Level Random Effect (OLRE), which would appear to be a random variable that can be included into a model to account for the within individual variance. 


There is an example of the model summary (only for the random effects) from the best model from my data where:
 (1| FINAL_ID_FAC) = Between Individual variation 

 (1| OBS_INDEX) = Within Individual variation


##~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Generalized linear mixed model fit by the Laplace approximation

Formula: cbind(A_C_T, A_C_F) ~ ACT_PUP_PROP + YEAR_FAC + (1 | FINAL_ID_FAC) + (1 | OBS_INDEX)

   Data: A_DATA

  AIC  BIC logLik deviance

 7156 7311  -3555     7110

Random effects:

 Groups       Name        Variance Std.Dev.

 OBS_INDEX    (Intercept) 0.580827 0.76212

 FINAL_ID_FAC (Intercept) 0.053969 0.23231

Number of obs: 6094, groups: OBS_INDEX, 6094; FINAL_ID_FAC, 54

##~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The OLRE explains a significant amount of the variation in the random effects (0.580827). Also, by comparing the AIC to the same model without OLRE the model presented above is far better (7156 compared to 7440). So based on this it seems I should include the OLRE in the model? If this is the correct approach then would I be right in interpreting the output to mean that there is a lot of variation within individuals’ behaviour? And by looking at the other random effect (FINAL_ID), which explains 0.053969 of the variance that there is little evidence for variation between individuals? So these results basically suggest that individuals are plastic in their behaviour? 

What I am not sure about is whether the OLRE takes in to account the variation in the explanatory variables, for example an individual may experience particularly extreme environmental conditions that other individuals did not experience due to temporal variation in their presence or absence at the study site, as a result there may be a greater (or lesser) variation within individual behaviour during such events. Is anyone aware of a reference that has used this approach in a paper and/or has explained what the OLRE is exactly doing - so that I can ease my mind on this approach? 

Many thanks for your time, any help or advice would be greatly appreciated,

Best wishes,

Ross


Ross Culloch
PhD Candidate
School of Biological & Biomedical Sciences
University of Durham
South Road
Durham
DH1 3LE





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