Adjusting variables in constructing composite indices by using principal component analysis: illustrated by Colombo district data

Abstract

Constructing composite indices, variables have to be reduced and principal component analysis (PCA) is widely used for this purpose. Although, PCA is conducted after standardizing variables to overcome unit and value dependency problems, variables lose their inherent variability. To address that issue, two options were tested. First option was transforming variables by dividing their means, resulting new means and variances becoming one and square of coefficient of variance (CV2) respectively. Second option was making meaningful adjustment to original variables to convert them as unitless. Grama Niladhari (GN) division level data on thirteen variables in Colombo district were used and second option was successful illustrating contribution of first two PCs to total variability by 96.34%. However, in the conventional method, 8 PCs were needed to reach that proportion. Expressing some variables on a per household basis and dividing GN density by total density were two adjustments made and that resulted in meaningful variable reduction in the index.

Keywords

• coefficient of variation, composite indices, principal component analysis