I have a question concerning the evaluation of mixture models. Is there a gold standard to compute the goodness of a fit for a mixture model?
What I am concerned about is how one would evaluate if one, two or three gaussians fit a given distribution better. Truly, one could visually inspect that but I am looking for an automated way that has a statistical meaning.
My initial idea was to measure the KS statistic between the observed distribution and sampled distributions by the estimated mean and variance for each model. Admittedly, I am not an expert for mixture models so I might miss something obvious here.
So I guess, what I am looking for is some kind of likelihood ratio test than gives me the best performing model for one, two or three overlapping distributions.
I am very thankful for any keywords and links that I can look up!