Construction of Composite Index under Complex Surveys

Abstract

Principal component (PC) based index accounts for the effect of multicollinearity among the indicator variables through the eigen values and eigen vectors derived from the variance-covariance matrix using maximum likelihood (ML)/ordinary least squares (OLS) methods of estimation. However, these methods of estimation of variance covariance matrix are based on the assumption that sample elements, on which the indicator variables are measured, are independent and identically distributed. In complex survey designs, the independence assumption of units does not hold that leads to erroneous estimation of variance covariance matrix under OLS methods. Therefore, in case of survey data there is a need to develop PC based index using survey weights and auxiliary information which excludes the effect of multicollinearity among the indicator variables as well as accounts for the effect of complex survey designs through which the sample data is collected. Therefore under this study different methods of indices development are proposed which are capable to incorporate the survey weights and auxiliary information available in the data.