[R] Time-series analysis with treatment effects - statistical approach

[Ravi Varadhan]

If you have any specific features of the time series of soil moisture, you could either model that or directly estimate it and test for differences in the 4 treatments.  If you do not have any such specific considerations, you might want to consider some nonparametric approaches such as functional data analysis, in particular  functional principal components analysis (fPCA) might be relevant.  You could also consider semiparametric methods. For example, take a look at the "SemiPar" package.  

Ravi.
________________________________________
From: r-help-bounces at r-project.org [r-help-bounces at r-project.org] on behalf of Mike Marchywka [marchywka at hotmail.com]
Sent: Wednesday, June 22, 2011 9:31 PM
To: jmo101 at student.canterbury.ac.nz; r-help at r-project.org
Subject: Re: [R] Time-series analysis with treatment effects - statistical approach

> Date: Wed, 22 Jun 2011 17:21:52 -0700
> From: jmo101 at student.canterbury.ac.nz
> To: r-help at r-project.org
> Subject: Re: [R] Time-series analysis with treatment effects - statistical approach
>
> Hi Mike, here's a sample of my data so that you get an idea what I'm working
> with.

Thanks, data helps make statements easier to test :)  I'm quite
busy at moment but I will try to look during dead time.

>
> http://r.789695.n4.nabble.com/file/n3618615/SampleDataSet.txt
> SampleDataSet.txt
>
> Also, I've uploaded an image showing a sample graph of daily soil moisture
> by treatment. The legend shows IP, IP+, PP, PP+ which are the 4 treatments.
> Also, I've included precipitation to show the soil moisture response to
> precip.

Personally I'd try to write a simple physical model or two and see which one(s)
fit best. It shouldn't be too hard to find sources and sinks of water and write
a differential equation with a few parameters.  There are probably online
lecture notes that cover this or related examples. You probably suspect a
mode of action for the treatments, see if that is consistent with observed dyanmics.
You may need to go get temperature and cloud data but it may or may not
be worth it.

>
> http://r.789695.n4.nabble.com/file/n3618615/MeanWaterPrecipColour2ndSeasonOnly.jpeg
>
> I have used ANOVA previously, but I don't like it for 2 reasons. The first
> is that I have to average away all of the interesting variation. But mainly,

There are  a number of assumptions that go into that to make it useful. If
you are just drawing samples from populations of identical independent things
great but here I would look at things related to non-stationary statistics of
time series.

> it becomes quite cumbersome to do a separate ANOVA for each day (700+ days)
> or even each week (104 weeks).

I discovered a way to do repetitive tasks that can be concisely specified using
something called a computer.  Writing loops is pretty easy, don't give up
due to cumbersomeness. Also, you could try a few simple things like plotting
difference charts ( plot treatment minus control for example).

If you approach this purely empirically, there are time series packages
and maybe the econ/quant financial analysts would have some thoughts
that wouldn't be well known in your field.


>
> Thanks for your help,
> -Justin
>
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