Dear List;
I am analyzing a large data set on lemon shark detection/nondetection on a sonic telemetry array. The response variable is binomial and I am using a GLMM to account for the effects of individual shark (49 levels) and month nested within year (over 4 years). We considered several a priori structures for the fixed effects and model selection based on AIC showed a clear winner among the a priori models:

glmer(detect ~ dalCat +  dtemp3d + daylength + (1|shark) + (1|Year/month), family = binomial, data = Lemon3)
However, the detection/nondetection was measured daily and using acf() on the residuals of the best GLMM, there is evidence of correlation over the range of 1-4 days for many of the sharks. To remedy this I thought of creating a set of variables which code the detection/nondetection for the previous 1-7 days and including them among the fixed effects. I created these variables, then compared AIC of models with all the fixed effects in the previous best model, plus none, 1, 2,..etc. of these autocorrelation variables. The model with autocorrelation variables for previous 1-4 days was best, and all models with these variables outperformed the models without them (based on AIC). The effect sizes for the fixed effects from the previously considered best model are all reduced but still significant (they have decent SE). I don't think that this approach is correcting for the autocorrelation in regards to the variance, but perhaps they give more reliable estimates of effect size and SE.

My questions are: does this approach make sense, and does anyone know of any references that used this approach?
Thanks,
Eric


Eric D. Stolen, Ph.D.
Mail Code: IHA-300
Kennedy Space Center, FL  32899
office: 321.861.6324  cell: 321.480.6799
eric.d.stolen@nasa.gov<mailto:eric.d.stolen@nasa.gov>

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