Latent Normal Models for Multivariate Data
Harvey Goldstein · Wiley series in probability and statistics · 2010
This chapter talks about the multilevel multivariate normal model with responses at several levels. In particular, it considers only responses at level 1 and generalizes it to the case where responses can be mixtures of different types. The chapter shows how responses of various different types can be incorporated within a multivariate normal framework. This is referred to as a ‘latent normal model’, where the observed non-normal responses plus the observed normal responses are mapped onto an underlying multivariate normal distribution. The chapter starts by considering binary responses. Next, it focuses on sampling ordered categorical responses and unordered categorical responses. This is followed by a discussion on sampling count data and continuous non-normal data. Sampling the level 1 and level 2 covariance matrices is also explained. The chapter concludes with a discussion on hybrid normal/ordered variables. Controlled Vocabulary Terms count data; multivariate statistics