Random effect or not?

Question

My intent is to model plant growth with a generalised linear mixed model. Let's say I sampled growth of 10 plants each on 10 plots in five different (non-consecutive) years. In order to find out which factors influence growth I have several variables which characterise the plots (e. g. elevation, soil) and several variables which characterise the conditions in the year in which sampling took place (e. g. maximum temperature, length of vegetation period). My model now looks like this:

Growth ~ elevation + soil + maximum temperature + length of vegetation period + (1|Plant ID)

Plant ID is a unique ID across all plot (i. e. A_1, A_2, .., B_2, B_2, ...).

Would I still have to include plot and year of sampling as (nested?) random effects, even though they are (indirectly, i. e. as their characteristics) included as fixed effects?

Answer 1

In the first instance you should include random effects for plot. As for year, it depends whether you are interested in a possible fixed effect of time. If not, then, since you have coded the plant IDs uniquely you can specify the model as

Growth ~ elevation + soil + maximum temperature + length of vegetation period + (1|PlantID) + (1|PlotID) + (1|YearID)

This will account for non-independence of observations in each plant, each plot, and also each year.

It may be the case that there is so little variation at the plot and year level, or that what variation there is is accounted for by the fixed effects that vary at these levels. In that case you may decide to drop one or more of these random effects, but a priori there is clustering at the plot at year level which needs to be accounted for.

If you are interested in the effect of time, then you can simply fit YearID as a fixed effect and not a random effect.