Background and Problem
I recently ran a Bayesian multivariate epidemiological meta-analysis on prevalence estimates for several disorders. This analysis included a probit-based model to deal with the individual patient data (N ~ 1600) I was able to dig up. In addition to providing an estimate of the individual prevalences for each of the 8 disorders included in my model, I also end up with an 8 x 8 tetrachoric correlation matrix between the latent variables representing the disorders in probit-space. One of my collaborators pointed out that it would be interesting to use this correlation matrix to conduct a cluster analysis on the disorders themselves, to see which disorders clustered together. I am (vaguely) familiar with approaches like the hclust(), factanal() or principal() functions in the R programming language (or similar approaches in Python, etc.) that can take correlation matrices (or derivations thereof) and use them to estimate clusters, factors or components. However, a unique challenge posed by my data is that – being a Bayesian correlation matrix – I do not have a single estimate for the matrix, but rather 2000 correlation matrices representing the posterior distribution of that matrix. As such, I am unsure how best to proceed.
I was hoping that someone could suggest a clustering approach that:
- is easily fit using a correlation matrix (or variation thereof);
- produces output that can somehow be combined across fits (in this case combining estimates across posterior samples);
If such a thing exists. I must admit, I am not even sure how to approach this one, so any advice concerning the situation would be most welcome. I am leaning towards saying it is simply not tenable.