ABSTRACT
We consider in this chapter some statistical methods that are a little more specialised. In Section 4.2 we present a discussion of regression analysis when the response vector is compositional in nature and describe a methodology for modelling such data. Following up on the material on binary logistic regression contained in Chapter 3, we then consider in Section 4.3 a Bayesian solution which overcomes the problem of complete separation. In Section 4.4 we discuss the challenge of statistical diagnosis when the types are naturally tree-structured. In our applications we have used mixed-effects models, which are briefly introduced in Section 4.5, and also Gibbs sampling, which is discussed in Section 4.6. Biplots often provide a useful summary of multivariate data and we discuss them in Section 4.7 in the contexts of unconstrained and compositional multivariate data. Finally in Section 4.8 we consider some kernel methods which are useful in non-parametric modelling.
