# Repeated Measures - repeat measures at same site but at different distances

• I have a study where I have two stress zones (high and low stress).
• In each zone, I have 10 sites.
• Within each site, I am setting up traps at 1m, 2m, 3m, 4m, and 5m away from a focal plant.
• My response variable is number of insects caught per trap.

I am interested in if the response changes with distance away from the focal plant and if there is an interaction between distance x stress zone.

Would a repeated measures analysis be a appropriate way to analyze these data? I keep reading about repeated measures through time, but repeated measures through space at the same site might make sense. Like a two-factor experiment with repeated measures on one factor, I think I would use site nested within stress zone as the error term for the effect of stress zone. Is my logic correct?

Yes, it's generally no problem if the repetitons are through space and not time.

In a repeated measures layout, you have a number of independent replications (subjects, i.e. probands, in your case the sites, if I'm correct) and at each replication a number of measurements measuring the same scale (here: number of insects) just at different time points or places or both.

Repeated measures layouts are sometimes also called split-plot-layouts. The name split-plot comes from agriculture: Several (independent) plots have been split and each subplot has been treated e.g. with a different fertilizer. This is an example where the repetition is within space.

Modeling the error term, you are nearly right. As the results are (hopefully) independent from site to site but only within the stress/no stress groups identically distributed, you are right to estimate the error terms in both groups separately.

However, even the dependency between the traps will be different: Insects caught at trap 1 cannot be caught at the other traps. So there will be different dependency structures if an interaction exists. That's why I strongly recommend to use different "unstructured" covariance structures between the distances. In SAS proc mixed,

repeated distance / group=stress type=UN;

would do the trick.

Note by the way that if the total number of insects to catch is limited, it would be better to model the number of caught insects by a multinomial distribution.

• Thanks! That's really helpful- I didn't get around to thinking about the dependence between traps...I'm glad you saw that. – Jo Lewis Dec 5 '14 at 20:01