## RP with reaction times: Dimension and delay

General discussions and questions about recurrence plot related methods.

### RP with reaction times: Dimension and delay

Hi,

I was wondering if it makes sense to use RP for the analysis of reaction times? The idea behind this is that some cognitive system generates a time series of reaction times and that I can reconstruct the attractor in phase space.

Three questions arise:

1. The minimal number of data points I have is 80 reaction times (the maximal number of data points I have is 200). I'm not sure if 80 data points are enough. I used the crqa-function and it seems to work (see attachment reactiontimes1), but is it theoretically sound?

2. For the above calculation of the 80 reaction times I used dimension 1 and delay 1. I'm not sure, if this is correct. In other words: Which dimension and delay to choose?

3. When I use a higher dimension the RP Quantification measures become flat or are not computed (see attachment reactiontimes2). So the only dimension where I get some useful measure is 1.

Attachments
Calculation fo reaction times with 80 data points with delay 1 and dimension 3
reactiontimes2.png (55.53 KiB) Viewed 3080 times
Calculation of reaction times with 80 data points with delay and dimension of 1
reactiontimes1.png (62.09 KiB) Viewed 3080 times
holistic
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Joined: Wed Feb 19, 2014 09:53

### Re: RP with reaction times: Dimension and delay

Hi,

I think an answer depends on your research question. For example, do you need a time resolved RQA? From your plots I can see that you divided your very short time series again in smaller chunks of length 40. This is really very short. You should know that then the statistical reliability of the RQA measures decreases very fast.

In principle, you can apply the method on such short data, but you cannot interpret the results with much confidence. It would then good to perform a significance test. The results would give you an idea how much confident you can be with the RQA results.

Embedding for such short data is not to be recommended.

You should have a look in to the literature for the significance test.

Best
Norbert

Norbert
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Joined: Wed Jan 4, 2006 11:03
Location: Potsdam Institute for Climate Impact Research, Germany

### Re: RP with reaction times: Dimension and delay

Norbert wrote:I think an answer depends on your research question. For example, do you need a time resolved RQA? From your plots I can see that you divided your very short time series again in smaller chunks of length 40. This is really very short. You should know that then the statistical reliability of the RQA measures decreases very fast.

I want as many RQA measures as possible. I chose a time window of 40 arbitrarily in this pictures, but my idea is to use the smallest value possible to get more measures. I'm not sure if I understood you correctly, is a smaller time window (e.g. 25) better or worse than a greater one?

In principle, you can apply the method on such short data, but you cannot interpret the results with much confidence. It would then good to perform a significance test. The results would give you an idea how much confident you can be with the RQA results.

Do you mean some permutation tests to test if a specific value is at the edge of the, e.g. DET-distribution indicating a "real" chaos-order transition?

Embedding for such short data is not to be recommended.

At what length of a time series would you recommend using an embedding dimension higher than 1?

You should have a look in to the literature for the significance test.

Can you maybe recommend a paper?
holistic
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Posts: 16
Joined: Wed Feb 19, 2014 09:53