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

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.

• Of course it is a RM-ANOVA! More specifically, your treatment is a between-subject factor, and your year is within-subject (aka RM) factor (subjects are plants), so what you have is a mixed ANOVA with one RM factor. You can use aov to specify it in R: aov(height ~ treatment*year + Error(plant/year)). Of course you can also use a mixed model approach as suggested by @BenBolker. – amoeba Nov 3 '17 at 7:49

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 ...

• nlme is mixed effects models - correct? I read that these can be used somewhere else and the R code makes understanding it easier - I will look into it and give feedback. – Rainer Aug 3 '12 at 9:42

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).

• I don't think that I can use a repeated-measures ANOVA, as the treatments are based on different samples, i.e. the subjects are not the same for the different treatments. – Rainer Aug 3 '12 at 9:40