I have a dataset with counts of birds in two locations over time, and am interested in describing the difference in trends in bird counts between these locations. The counts are conducted by multiple observers, which are included as a random effect. The data is best modelled using generalised poisson or negative binomial distribution (differs per species), and zero-inflation added where indicated by tests using the DHARMa package. Basic model:
glmmTMB(total ~ year * location + (1 | observer), family=genpois, data=tmp)
When plotted next to the original data, the model fits poorly – with models (strongly) overestimating trend for some species and underestimating for others, compared with the observed data. When fitting the model without the random effect, the model fits well - however, we are interested in the trend over time. The discrepancy appears to be caused by the variance that is attributed to the observer random effect, which perhaps absorbs too much of the time trend information?
We know that there are differences in the quality of the counts between observers and would like to account for this (e.g. not all observers hear the calls of species with higher pitch calls). We do not expect a difference in the trend per observer over time and while there were a few observers that counted birds over two or more periods, most observers only counted one period. Therefore I think we cannot justify using partial pooling by including a random slope per observer. However, including this in the model does seem to reduce (but not eliminate) the bias and improve the fit for some species.
How can I attribute more of the variance currently ascribed to the observer random effect to the fixed effect of interest (trend over time)? Or in what other ways may I be able to reduce the bias in the model fit?
