I'm working with psychophysiological data--specifically, tonic electrodermal activity (EDA). Tonic EDA is commonly accepted as an indicator of arousal. Simply put, I sample tonic EDA over time as subjects listen to different selections of music. Using OLS, I fit a line to the tonic EDA signal for each recording, and take the slope of this line to be indicative of the general trajectory of arousal over the course of the music selection. So, while I'm using regression, I'm really only using it to 'simplify' a time series.

What I'd like to do is to compare these trajectories between music selections for within subjects, and to generally compare the trajectories between selections between subjects. In other words, I'd like to ask questions like these:

  • Between subjects, what pairs of songs are related with the largest contrasts in arousal trajectories (e.g., sharp declines in arousal for one song followed by steep increases in arousal for the following song)?
  • Within subjects, what pair of songs are related with the largest contrasts? (If these are significantly different than the results between subjects, I'd look to other variables to see if they might explain these differences.)
  • Between subjects, what individual songs are related with the steepest arousal trajectories (in either direction)? (And a similar follow-up investigation within subjects, as above.)

So, I'm fairly certain what I'm most interested in comparing is these regression slopes, but I'm not exactly sure where to start. Can someone point me in the right direction? Thank you!

Edit: Per the comments, here is a plot of a typical time series with fitted line.

Tonic EDA Signal with Fitted Line

So, each subject in the study listens to several selections of music. During each, EDA is recorded. In the example I've shown arousal generally increased over the course of the recording, and this increase is summarized in the slope of the fitted line. I'm interested in comparing these slopes in all of the questions I addressed above. I hope this helps, but am happy to address any confusion in further edits.

Edit 2: Let me also clarify the study design a bit. Every subject listens to three selections. These selections are drawn randomly from a larger pool of selections. I'm fitting a line like this to the tonic EDA signal for every subject for every recording. For every subject then, I have two pairs of recordings: first/second selection, and second/third selection. This is a large study, so there are large groups of subjects who hear the same two selections in succession.

With this in mind I'm asking what is the best way to identify the pairs of selections that correspond to the most drastic changes in slopes of the fitted lines? And, what is the best way to identify the individual songs that across subjects have the most extreme slopes?

  • $\begingroup$ How much data do you have per person per song? Are the measurements originally continuous, but discretized into mean values over consecutive, say, 1 second intervals, or something like that? $\endgroup$ – gung - Reinstate Monica Jan 25 '16 at 20:51
  • $\begingroup$ For each song/listen, I have on the order of 90 seconds of data sampled at 50Hz: a time series of approximately 4,500 samples. $\endgroup$ – Brennon Bortz Jan 25 '16 at 20:55
  • $\begingroup$ Your question seems to be broad (and a bit vague) -- aside from some statements about what questions you want to be able to answer and your uncertainty over where to start, your question is "Can someone point me in the right direction" which could be hard to answer given there's not a lot of information about direction there to point you toward. Do you have some specific questions? Note that the usual forms of regression inference assumes independence. You don't have that. Would it be possible to show some pictures of the sort of data you're talking about (e.g. time series plots) ... (ctd) $\endgroup$ – Glen_b -Reinstate Monica Jan 25 '16 at 23:36
  • $\begingroup$ (ctd) .. perhaps with some indication of what intervals you're fitting lines over? $\endgroup$ – Glen_b -Reinstate Monica Jan 25 '16 at 23:37
  • $\begingroup$ Glen_b, I'm sorry for the vagueness. I'm having trouble articulating my questions well. But, those questions I listed are the specific questions I'm looking to answer. Also, note that this isn't regression in the usual sense. All I'm really doing is finding the best fit straight line to a time series. Will add a plot. $\endgroup$ – Brennon Bortz Jan 26 '16 at 0:19

Just taking a stab at this, I think that you need to understand the answer to this question first

  • Between subjects, what individual songs are related with the steepest arousal trajectories (in either direction)

To answer this, I would split every time series up into the songs that were in each segment and label them. I would then find the beginning y and ending y of the signal for each song which would give some indicator of positive or negative change.

Once you calculate this change for ever instance of the song. Then just sort them by the positive or negative change. This might not give you a perfect answer but it would probably point you in a good direction.

For pairwise questions you would probably want to write some code that takes in the two song segments and compares them. You could then create a probability out of the pairwise comparisons. For example, when A and B are together 50% of the time there is an increase.

  • $\begingroup$ I'm not sure why this delta in $y$ is any better than the slope of the line I'm fitting. In fact, there is the potential for a very few spurious extrema at the beginning of signals due to filter transients, etc. Taking the beginning $y$ in these cases would be a mistake. Also, every time series is an individual song listen—no splitting necessary. With respect to your analysis suggestions, is there really no more rigorous way to compare these deltas (or slopes) than sorting them and taking the top x entries in said list? For pairs, is there no way to quantify significant changes? $\endgroup$ – Brennon Bortz Jan 26 '16 at 11:20
  • $\begingroup$ For instance, searching for 'comparing regression slopes' yields plenty of results (e.g., stats.stackexchange.com/questions/55501/…), but I'm not certain that these approaches are applicable for what I'm asking. $\endgroup$ – Brennon Bortz Jan 26 '16 at 11:21
  • $\begingroup$ Alright. Well good luck then! $\endgroup$ – jpotts18 Jan 27 '16 at 5:08
  • $\begingroup$ Do you have any insights about my questions? $\endgroup$ – Brennon Bortz Jan 27 '16 at 11:10

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