Non-repeated measures ANOVA of time series with different subjects per treatment in R?

Question

I have the following experimental layout:

1. five different treatments - harvesting rates, ranging from 0 to 1, indicating proportion of branches per plant harvested

2. 75 plants, randomly assigned plants to each treatment, resulting in 15 plants per treatment

3. followed over 5 years, resulting in five data points per individual plant

Now I want to analyse the data and see if the treatment (harvesting rate) has an impact on different measured variables (e.g., height of plant, cumulative number of stems harvested), and preferably also in which years they differ.

Initially I thought using a repeated-measures ANOVA, but the subjects per treatment are different, but they are followed over time, which violates independence assumptions of normal ANOVAs. So which statistical test can I use here?

I use R, so an example in R would be nice.

Answer 1

How about something like

library(nlme)
lme(height~treatment*year,
     random=~year|plant,
     correlation=corAR1(form=~year|plant))

? It would be interesting to do this as a multi-trait analysis (i.e include all of your measured variables as a single multivariate response), but that would be considerably more complicated to set up ...

Answer 2

I think you do want a repeated-measures ANOVA, and to try different variance-covariance structures. You may want to try AR(1) for the repeated measures effects and to model the between-subjects random effects separately (this last part is according to Littell et al. 2006, SAS for Mixed Models, 2nd edition).