Using Principal Components in Multivariate Stratification Scheme
Apantaku Fadeke Sola

Abstract
In sample surveys more than one population characteristics are estimated and these characteristics may be of conflicting nature. Stratified sampling has been designed to ensure that all important views are represented in samples. In multivariate stratified sample design, correlation is considered among interest variables. A variation of one variable with lower correlation is more important than others. Optimal allocation in multi-item is developed as a multivariate optimization problem by finding the principal components. A search was made for a set of mutually uncorrelated variables, Y , Y ,....., Y p 1 2 each one being a linear combination of the original set of variables, p X , X ,....., X 1 2 . An empirical study from a household survey conducted in Abeokuta South and Ijebu North local government areas were used. The data about the households are available for four characteristics or variables that are related to the survey. These characteristics include occupation, income, number of dependants and the educational level. Each of the two local government areas with a sample size of 200 households each were randomly selected using simple random sampling technique making a total of 400 households. The heads of the households were interviewed. The study adopted an approach based on the fact that its methodology is more realistic under the ambit of multivariate analysis. Using Splus software, the variance- covariances matrices were computed. The principal component analysis ensured that the variance-covariance matrix was decomposed and the eigenvalues and eigenvectors calculated from the multivariate data representing information from the households were computed.

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