Comparing regression slopes

Question

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 throughout the music selection. So, while I'm using regression, I'm only using it to 'simplify' a time series.

What I'd like to do is to compare these trajectories between music selections 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 to 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 a 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 throughout 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 have the most extreme slopes across subjects?

Answer 1

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.