Longitudinal model appropriate?

[deleted_user]

Hi,

I have a basic question about a longitudinal experiment on bird abundance in forests receiving fuels reduction treatments. The treatments were implemented in stages, and my question is whether I can do 1 repeated measures analysis (SAS, mixed model, proc mixed) across all years, or if I need to break down the analysis for the different stages.

The basic model for each bird species is:

Bird abundance = treatment year treatment*year

The experiment ran 4 years, and in the first year no treatment groups were treated. Bird abundance was measured in the same replicate forest stands across all 4 years. The experimental treatment groups were as follows (3 replicates of each):

1. Controls (no treatment over the 4 years)
2. Prescribed fire (burned after 2nd year of sampling)
3. Thinning (thinned after year 1, thinned again after year 2)
4. Fire plus thinning (thinned after year 1, thinned and burned after year 2).

My understanding is the “treatment*year” effect tests for differences in treatments across the years. But examples on the web and books usually are on data where the treatment is applied at the beginning. In my case, there were treatments occurring after year 1 in some of the treatment groups. Thus I don’t know what the “treatment*year” interaction is really testing. It seems a significant treatment*year interaction could mean differences occurred anywhere in the 4 years, and if in year 1 or 2 would not really be directly related to the full treatment manipulations. I don’t know if a model for all 4 years is even appropriate or valid since some forest stands undergo different states (untouched, thinned, burned) across the years of the experiment.

If it is not appropriate, I could do simple ANOVA analyses for the stages by comparing year1 to year2, year 2 to year 3, etc. This, however, ignores the repeated measures.

Cheers

[Susan]

I probably would start with one analysis, using all 4 years in all 12 stands, and then “breakdown” the analysis subsequently.

You obviously want TREATMENT*YEAR to be significant (or you won’t have much to talk about). You are right that the overall test of TREATMENT*YEAR is not particularly informative, so you likely will need to follow up with additional testing. Ideally, you would follow up with comparisons identified, in advance, that capture predictions about how bird abundance will vary over time under the different treatments. Or you might do some post-hoc comparisons to sort out the nature of the interaction. These comparisons could be simple mean comparisons, or they might be more complex contrasts.

In particular, the effect of treatment over time has to be assessed relative to the temporal pattern of abundance in the control plots. You expect abundance to vary over time in the absence of any treatment; (simplistically) if there is no treatment effect, then the temporal treatment pattern would be parallel to the temporal control pattern. So I could see setting up a contrast to compare the temporal control pattern to the temporal pattern for each treatment (which would be a component of the overall TREATMENT*TIME effect).

You also have one pre-treatment observation on each stand. If these abundances are highly variable, you may want to consider various ways to control for “initial condition.” For example, the year_1 abundance could be subtracted from abundances for years 2, 3, and 4, and you could analyze these differences. Or you could analyze a ratio of year_i/year_1 for i=2, 3, 4. Or (year_i – year_1)/year_1. Or you could use year_1 as a continuous covariate.

Your study design is a form of BACI (Before and After/Control and Intervention) design. This link

http://www.stat.org.vt.edu/vining/smith/B001-_o.pdf

is a good entry point into the ecological literature on this design.

HTH,
Susan

[deleted_user]

Thank you for your detailed response! I figured all years might be best. I'll construct appropriate contrasts for the interaction that highlights the stages..