Optimization in multivariate analysis

Abstract

Multivariate analysis deals with data where there are observations on more than one variable for each subject or object under investigation, and where there is some inherent interdependence between the variables. Many of the techniques of multivariate analysis involve large amounts of arithmetic, often in an attempt to maximize a likelihood function or minimize some goodness-of-fit measure, and several methods, originally suggested several decades ago, have only become of practical significance with the advent of computers and improved optimization algorithms. An outstanding example is the use of maximum likelihood methods for factor analysis, which will be described in the next section. Other techniques which will be discussed in this chapter include the estimation of the parameters in finite mixtures of multivariate normal densities, latent class analysis and multidimensional scaling.