random factor structure for diversity surveys with repeat visits I’m involved in a project where we surveyed native insect communities across a large spatial gradient. Each site was surveyed twice over two summers for a total of 4 visits. We are hoping to analyze patterns in the abundance and richness of these communities across different land use types, regions, and management regimes. We are currently using both glmmPQL  and lmer depending on the distribution of each variable and are struggling to build an effective structure for our random effects.
Our data is currently structured such that each visit to a site is its own row, such that each site is listed multiple times.
We have two questions regarding how to structure our random effects.


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*First, do we need to include both SITE and VISIT as random effects to address the repeated measures, or is it sufficient to just include SITE?

*Secondly, if we have 1 predictor variable that was measured only once per year and another that was measured twice per year, how would this change our random effect structure?

 A: 
do we need to include both SITE and VISIT as random effects to address the repeated measures, or is it sufficient to just include SITE?

tl;dr use just 1|SITE for linear mixed models; 1|SITE/VISIT if you want to allow for overdispersion in GLMMs, otherwise 1|SITE.
Typically one would include this as 1|SITE/VISIT ("VISIT nested within SITE", equivalent to 1|SITE+SITE:VISIT or "main effect of SITE plus the interaction between 1|SITE and 1|VISIT") in the model, but since you have only a single observation at each VISIT for each SITE, the 1|SITE:VISIT term is an observation-level random effect. You definitely don't want to include it in your linear mixed models (i.e. lmer); if you include it in your generalized linear mixed models it will act as a model of overdispersion. If your data are not overdispersed (i.e. the conditional distribution of counts at a particular site has variance less than or equal to the mean), then you might not need the overdispersion term.

Secondly, if we have 1 predictor variable that was measured only once per year and another that was measured twice per year, how would this change our random effect structure?

In general, you don't have to worry about the levels at which fixed-effect predictors get measured; this gets handled automatically. I assume you're going to do something like assuming that the once-measured variable is constant across the two visits within a year?
In general I would recommend glmer over glmmPQL unless you have a particular reason to use the latter.
