I used Raven Pro and obtained 7 song parameters from the whole song selection tables. The objective is to see whether variation exists between the 3 subspecies. There's a common song motif/bout between the three but the sample size is so small (only 4 for each subspecies). Can I use PCA to analyze this dataset? Can I use PCA to analyze all songs from each subspecies despite not having common structures?
Thank you!
Perhaps helpful - a related methods paper on this was released just this week, on a framework for analysis and reporting of songs/rhythms - check out Hersh et al.
Hersh, T. A., Ravignani, A., & Burchardt, L. S. (2023) Robust rhythm reporting will advance ecological and evolutionary research. Methods in Ecology and Evolution, n/a(n/a). doi: https://doi.org/10.1111/2041-210X.14118
(Also see her for the first author's sci-comm/twitter thread breakdown of their findings).
PCA is a type of dimension-reduction that helps to find consistent patterns of variation in multidimensional data. Your dataset has 12 items and 7 dimensions. Technically, it is possible to apply PCA to any dataset where the number of items is greater than the number of dimensions. The important question is, what benefit do you get from it?
In my opinion, 7 dimensions is small enough that you don't really need PCA. You can simply use a Parallel coordinates plot or a Facets plot to directly inspect the differences. And since you only have 12 items, you should think carefully about whether your 4 items per class are really enough to be representative of the generality - this depends on how stereotyped your data are.
You also ask whether you can analyse "all songs from each subspecies despite not having common structures". This part of your question is not really about PCA - it's about whether the 7 features you are extracting are appropriate for analysing all songs despite not having common substructures. I don't know your song parameters, but I would advise you to be cautious and to think it through: for example, "average frequency" is a useful measurement, but when your songs contain multiple syllables which span varying ranges, what does that average frequency really represent? You are right to ask the question, because a general value such as that is not always meaningful, but perhaps it is, given your study species and your research goal.
You ask "What method is typically used" - indeed these general features are often used, but I would suggest to try and extract them either from individual syllables (song units), or from larger+longer datasets for each species. In the latter case, the analysis would be about the species' capabilities or tendencies rather than about a specific song phrase type.
