How can I include repeated measures to my lmer correctly

Question

In my study I was sampling the same sites in different regions for many years. Each site has different properties in each year, which is important for my research question. I want to know, if the properties of the site affect biodiversity on the sites. And I am interested in the interaction of the propterties and the regions.

Overview:

• Biodiversity = response
• Site property = fixed factor, changes every year
• Region = fixed factor , same regions every year
• Site = random effect, is repeatedly sampled in the different sampling years
• Year = random effect, is the factor in which "site" is repeated

At the moment my model looks like this:

mod1 <- lmer(biodiversity~region*siteProperty+(1|Year)+(1|site))

I'm not sure if this accounts for the repeated measures. Alternatively I was thinking about this one, as it includes also the nestedness of the sites in the years, but maybe that is not necessary:

mod2 <- lmer(biodiversity~region*siteProperty+(1|Year)+(1|Year:site))

The problem with this approach is, that it only works if my site properties are not zero. But I have zeros in different properties and I need to analyse their effects as well.

If you need more information, just ask me for. Thanks for your help!

Answer 1

Your first example,

mod1 <- lmer(biodiversity~region*siteProperty+(1|Year)+(1|site))

should be fine (although I'd encourage you to use the data argument explicitly ...). If you have samples for "many years" for each site, you might want to consider

• including a trend model (i.e. include Year, as a numeric variable, in the fixed effects part of the model as well, either as a simple linear term or as part of an additive model, e.g. using splines::ns
• checking for/allowing for autocorrelation (although this is tricky in lme4; you can use lme, but then crossed random effects of Year and site become harder).

If you have one sample per site/year combination, you don't want (1|Site:year), because that will be the same as the residual variability term.

Your statement "only works if my site properties are not zero" doesn't make sense to me: in general, having zeros in predictor variables shouldn't cause any problems ... ?