Mixtures vs Multi-level models? I'm confused on how mixture models and multi-level models are different (if at all.) Are there general rules for when to use one and not the other, pros/cons, etc?
 A: Mutli-level models are used when you have grouping variables with multiple levels. For example, let's say you want to know the relationship between income and happiness in different counties then you can use a multi level model in which your model parameters can vary from county to county.
Mixture models are referred to models in which the distribution of the variable of interest is not a standard one that can be represented with a single distribution such as Gaussian. Then you can model the distribution of such a variable using a mixture of distributions. For example you can use a mixture of Gaussians with different means like below:
$p(y) = \omega_{1} N(\mu_{1}, \sigma^2) + (1-\omega_{1}) N(\mu_{2},\sigma^2) $
With mixture models you can be flexible in modelling various distributions. One common use case is zero inflated Guassian mixture models where you have a consentrated density on zero and then a Gaussian density on the side which could be used to model many real world scenarios where there are a lot of zero counts.
