I am trying to specify a model for split plot design that acknowledges nested sub-sampling. Split plot designs are a little bit tricky to analyze, and I am new to R, so I provide my dataset along with instructions at the bottom in case anyone can solve this challenge.
THE CONTEXT: In my MSc thesis, I am using a split plot design to test the effect of forest type ("Riparian" vs "sloped") and forest age (250 years/"old" vs 35 years/"young") on the biomass of salal, an understory plant of economic interest. The experimental design is similar to a two way factorial ANOVA. However, each old forest site is paired with a young forest site; before logging occurred they were within the same patch of forest or "historicstand". This pairing means that it is a split plot design (see figure). It took me some effort to learn how to analyze this split plot design, but now I understand it, and I can run this simple model fine in R base stats.
This model in R is:
aov(salalbio ~ foresttype + Error(historicstand/foresttype) + forestage+ forestage*foresttype, data = antfp)
THE CHALLENGE:The problem with the above model is that it does not recognize that within each site I have two measurements: At each site there are two sampling plots "sample_plots" where we measured salal biomass. These measurements are not replicates so I need to acknowledge that they are nested within site, or I risk a Type I error. How do I rewrite the model so that it acknowledges that sample plot is nested within Siteid? In base R[stats] would be easiest for me to comprehend, but any package would do.
fyi, I could just average the two measures by site and analyze it this way but my sample size is very small (n = 3 sites per each experimental level). When biomass is averaged I do not detect the effect. Analyzing the nested sub samples maybe, just maybe, will reveal an effect.
Here is the data:
saldata <- structure(list(Site.id = structure(c(1L, 1L, 4L, 4L, 2L, 2L, 5L, 5L, 3L, 3L, 6L, 6L, 7L, 7L, 10L, 10L, 8L, 8L, 11L, 11L, 9L, 9L, 12L, 12L), .Label = c("ABOG1", "ABOG3", "ABOG4", "ABSG1", "ABSG3", "ABSG4", "ROG1", "ROG2", "ROG3", "RSG1", "RSG2", "RSG3" ), class = "factor"), foresttype = structure(c(2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L), .Label = c("riparian", "sloped"), class = "factor"), forestage = structure(c(1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L ), .Label = c("old", "young"), class = "factor"), historicstand = c(1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 3L, 3L, 3L, 3L, 4L, 4L, 4L, 4L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L), sample_plot = structure(c(1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L), .Label = c("a", "b"), class = "factor"), salalbio = c(26.7, 177, 100, 210, 240, 296.7, 410, 71.7, 253.3, 256.7, 93.3, 233.3, 106.7, 36.7, 0, 0, 86.7, 0, 20, 0, 233.3, 206.7, 115, 0)), .Names = c("Site.id", "foresttype", "forestage", "historicstand", "sample_plot", "salalbio"), class = "data.frame", row.names = c(NA, -24L))
The below model (for split plot) needs to be modified so that sample plot "a" and "b" are recognized as coming from the same Siteid:
M1 <- aov(salalbio ~ foresttype + Error(historicstand/foresttype) + forestage+ forestage*foresttype, data = saldata)