Item Response Theory: It's factor analysis for categorical variables.

AnnMaria frets over the large number of useless academic articles and how this might relate to the general backlash against academia.  I think it depends on your field, or subfield.  Fifteen years ago, most of the Bayesian statistics articles I read were about trying to solve problems.  They generally began with a clear description of the model and the process used to estimate the model.  They had to, because it was all so new.  By contrast, the articles concerning extensions of traditional statistical methods seemed to assume you already knew everything about the method from prior articles.  It's one thing to follow a hyperlink to get to that information, but having to look up another article (which in turn might point to another article) just to figure out what the current article is talking about is a bit of a drag.  Maybe Bayesian statistics articles have this problem today.  At any rate, back in the day I did some work with Bayesian item response models, so here's my short description:

Item Response Theory: It's factor analysis for categorical variables.

There's even a journal article on it.  I think that's easier to understand than the description of the parallel analysis criterion.