How many latent factors to use?

[tpbilton]

Also a follow up question. If I understand the methodology correctly, the multivariate LMM in MegaLMM is a reparametrization of the standard multivariate LMM when the number of factors (k) is sufficiently large. However, if the number of factors is not sufficiently large, then I'm guessing that the model fitted in MegaLMM is an approximation of the multivariate LMM model. With this in mind, is there any way of knowing how to set k as being as small as possible before the accuracy of the posterior distributions really start to deteriorate?

Thanks again,
Timothy