ABSTRACT
The original three mixed membership models all analyze categorical data. In this special case there are two equivalent interpretations of what it means for an observation to have mixed membership. Individuals with mixed membership in multiple profiles may be considered to be ‘between’ the profiles, or they can be interpreted as ‘switching’ between the profiles. In other variations of mixed membership, the between interpretation is inappropriate. This chapter clarifies the distinction between the two interpretations and characterizes the conditions for each interpretation. I present a series of examples that illustrate each interpretation and demonstrate the implications for model fit. The most counterintuitive result may be that no change in the distribution of the membership parameter will allow for a between interpretation.
