What is the difference between mixture and hierarchical models?

Are they of the same nature with different names or they are totally different things?

If there are any references, I will be happy to know.

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#### Best Answer

Terminology is not as standardized as one may whish, so what I understand under these terms may not be what others understand under these terms.

I understand under a mixture model a model that posits that posits a mixture of "brand name distributions" for the dependent variable. For example a discrete mixture of normals assumes that a person is drawn with a to be estimated probability from one normal distribution and with another probability form another normal distribution, etc., for a given number of groups. Notice that in this model we do not know which person belongs to which group

Under a hierarchical model I understand that we have observations that are nested in groups. For example: students are nested in classrooms, which are nested in schools, which are nested in countries. Here membership of the groups is known and part of the data.

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