Hello!

I am interested in fitting multivariate mixture model, defined as follow :

Where i stands for individuals and p for an experimental unit. For simplicity, the variance-covariance matrix is common to every observation.

The obvious way to identify the model is to put an ordering constraints on \boldsymbol{\mu}, such as \mu_{j1} < \mu_{j2} < \mu_{jk} for any variable j. This approach works wonderfully in my case, and give well-explored posteriors.

However, some of the variables j are negatively correlated. In that case, it makes no sense to define a component which would have the greater mean in every variable, because components with the greater mean in some variables are expected to have the lower in some other.

Is there another way to identify this model without the mean ordering constraints? I tried to order the intercepts of component weights, but it results in degenerate posteriors, with exchangeable means, even with only two components.

Or is there any other idea I am missing?

Thank you very much!

Lucas

EDIT : for information, my data look generally like this :