The Use of Discrete Data in the PCA: Theory, Simulations, and Applications to the Socioeconomic Indices

• Activity Number: 233
• Type: Contributed
• Date/Time: Tuesday, August 10, 2004 : 12:00 PM to 1:50 PM
• Sponsor: Business and Economics Statistics Section
• Author(s): Stanislav Kolenikov*+ and Gustavo Angeles
• Companies: University of North Carolina, Chapel Hill and University of North Carolina, Chapel Hill
• Keywords: welfare index ; principal components ; polychoric correlation ; discrete data ; Monte Carlo simulation

Abstract

We analyze construction of a welfare index when a more desirable income or expenditure data are not available. The principal component analysis is used to find the weights of variables aggregated into a socioeconomic index. As long as the inputs are often discrete (such as binary indicators of possession of a durable good such as a refrigerator or a car, or ordinal indicators such as the material used in household's dwelling -- e.g., straw, wooden, or tin roof), there is a number of ways this discreteness can be taken into account. We advocate the use of polychoric and polyserial correlations as measures of the statistical association between the ordinal indicators (including binary ones), and show that the index based on the polychoric correlations performs better in ranking households as compared to other alternatives (such as using the ordinal variables per se in PCA, or constructing dummy variable indicators for each of the categories). We show the results of a Monte Carlo simulation, as well as applications to the real datasets, of the examples where the differences between methods may be very notable.