Repeated measures ANOVA of time series with different subjects per treatment

[rogerchl]

Hello everyone.

I have the following experimental design:

1. 3 treatments - control, sodium and potassium fertilization.

2. 27 plants, randomly assigned to each treatment, resulting in 9 plants per each treatment.

3. Growth measurements were assessement over time, resulting in more than 60 data points per individual plant.

Now I want to analyse the data and see if the treatments has an impact on different measured variables (e.g., height, basal area, wood anatomical features, etc), and also in which periods they differ as well as if the effects change over time.

Initially I thought using a classical repeated-measures ANOVA, but the subjects per treatment are different.

After, I found on the web an extension of repeated-measures that could be adequate for my data, total variance is partitioned in: Between subjects (Treatment, Error due to Subjects Within Treatment), Within subjects (Time, Treatment*Time, Error)

But I dont sure about it. So which statistical test can I use?

An example code would be nice.

Thank.

[sld]

I would use GLIMMIX.

60 repeated measurements on each plant is a lot. You could specify an ANOVA model for repeated measures in time, but interpretation of the interaction of treatment and time will be challenging. I suggest that you give some thought to what you want to learn about the response over time--in other words, why did you take 60+ observations on each plant? You might be able to reduce the number of time levels (for example, you mention period as a factor). Or, a better idea of your research questions about response over time might suggest alternatives for a statistical model, for example, incorporating a regression on time (e.g., an ANCOVA type of approach).

This book would be an excellent resource.

I hope this helps.

[rogerchl]

Thank you for your suggestions. Actually my data are time series (during almost 3 years) of growth under differents treatments. I have 27 time series (one for each tree). I want to know the effects of treatments over the different periods. As you said, is a lot of measures, so now, I think I can reduce the number of time levels, analyzing at monthly intervals (34 time levels). However I still have doubts about which model would be the most correct for the anova?.

[sld]

(For those of you who saw my prior post: I misunderstood the OP's reply, so I have edited. Use this one instead.)

I also have doubts about the correct model, and I do not have enough information about your research questions to do much speculation.

The dilemma of collapsing observations within each year to months is that a monthly basis is arguably arbitrary. How do you justify collapsing to a month level? How do you justify the date cutpoints that determine "month"? Trees do not recognize the human concept of "June" versus "July", for example. Is "June" in year 1 equivalent to "June" in year 2 equivalent to "June" in year 3? In the field, this is not usually the case because of annual variability in weather. Should year be a factor that is separate from month?

When in doubt, go back to your research questions. Why did you measure over 3 years? What did you expect to learn from the temporal observations within each year? What did you expect to learn from the observations over multiple years? What aspect of these temporal observations is fundamental to your research questions? For example, perhaps you are primarily interested in annual growth and care less about the growth within each year.

34 observations per tree (= 3 x 11 plus an extra? = 3 x 12 minus 2?) is still a lot for an interpretable ANOVA. I'd give it more thought. If you have statistical consultation available to you at your institution, take advantage of it, particularly if the consultant has some familiarity with your discipline.

I hope this helps.