When using Bayesian methods to estimate mixture models, such as latent class analysis (LCA) and growth mixture models (GMMs), researchers seem to use common priors for class-specific parameters. Of course, this makes sense when using so-called "noninformative" priors, yet Monte carlo studies often indicate that such priors provide biased and variable estimates, even with relatively large samples.
Confirmatory approaches to mixture modeling, using (weakly) informative priors, performs much better than "noninformative" priors. However, care must be taken when selecting prior distributions (e.g., through careful elicitation from experts or previous research findings).
But consider a scenario in which latent classes are unbalanced (e.g., a two-class model with .80/.20 class proportions). To my knowledge, most researchers use the same priors for parameters in each class, regardless of differences in relative class size. Does anybody know of research in which priors for class-specific parameters have been adjusted to equate their informativeness, dependent on the number of observations in each class? I would be happy to hear of any research where such an approach has been used.
Hi,
I wouldn't call this approach as 'weakly informative'. It only applies to the case that the number of states is known. In addition, it imposes the explicit assumption that the latent states are identifiable: The term 'component k-th' of the mixture is rarely a defined object, at least a priori. But I agree, that if these restrictions are indeed true, then the specific prior choice would perform reasonably well.
However, there are some studies that use similar prior set up. For example Diebolt and Robert (1994) place a prior ordering on the mixture weights (and this is actually a generalization of the scenario mentioned above). Richardson and Green (1997) consider a prior ordering of the means. It is well known that in general cases these assumptions lead to serious biases in the resulting estimates, therefore it is advised to avoid them and to use flat priors with common prior parameters (see papers related to the label switching problem beginning from Stephens, 2000)
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