Hi everyone,

I have been struggling with analysis of a dataset I am working with, but I believe I may have thought of a possible solution. But after a bit of searching I have not been able to see any published research using a similar analysis method, so I would appreciate your input on whether this is valid or not.

I am studying a species of frog that calls in bouts; the frogs call a number of times before falling silent, and then after a certain amount of time starts calling again (i.e. starts a new bout). I want to investigate whether characteristics of their calls change throughout bouts, and what factors influence this. E.g. does call loudness decrease during bouts, and is this effect more pronounced in longer bouts (bouts containing a greater number of calls)?

Unfortunately, I only have 1 bout per male (the dataset is old, and even getting/transcribing 1 bout per male was a laborious task back before digital recorders, or so I'm told), giving me 25 bouts/males in total. I had initially just thought I would include characteristics of all calls from each bout as a dependent variable in an LMM, and include an interaction term between my variable of interest and bout progress (representing the percentage of the way through the whole bout that each call occurred) to see if this interaction was significant. To avoid pseudo-replication (due to many calls from each male within their single bout), I had wanted to include male ID as a random effect, but I came to realize that because each male only has a single bout in the dataset, this is also, in effect, including factors I'm interested in looking at (e.g. bout length) as random effects too. Thus, I thought of the following solution:

For each bout, I could do a simple LM of e.g. call loudness vs progress through the bout, and then store each male's individual beta in a dataframe, thus compressing the change in each males calls over a bout into a single value. I could then use these betas as a dependent variable in a LM, and include the variables I am interested in as independent vars. Thus, if loudness decreases at a greater or lesser rate in longer bouts, I would be able to see this by a significant relationship between that males' betas and their bout length (e.g. if longer bouts correspond significantly to more strongly negative betas). Obviously, only having 1 bout per male is not ideal as you can't be certain that idiosyncrasies among males are driving differences, but by including factors known to influence male calling as covariates, I think this could still be a decent preliminary analysis.

Is this valid? Mainly: does it make sense to have a correlation coefficient as a dependent variable? I get that all of my individual LMs that generate betas for each male would have to meet assumptions etc. Would just regular correlation coefficients (from a pearson or spearman correlation) be better than betas from an LM?

If you have seen similar analysis elsewhere, I'd appreciate the references.

Thanks for reading this, and thanks any info you can provide!