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Simulation Study: Incorporation of Mixed Variables into Principal Component Analysis
Abstract
Publications that are concerned to principal component analysis (PCA) and wealth
index is a very popular topic in economics for last several years. This paper also
aims to explore these two things. So far many authors established that the use of traditional PCA approach is not suitable for wealth index construction with all types of data. It is a more serious problem when the data set contains mixed variables. Researchers are trying to solve this issue for many years. This paper is dedicated to explore the two ways of using mixed data into PCA. Here we define mixed data as data set that contains both numeric and categorical variables jointly. Two methods that are discussed and compared are namely nonlinear PCA using homogeneity analysis and PCAmix. Properties of these two methods have also been discussed here with proper references. An extensive simulation study is performed to find the best approach for dealing with mixed data. We have found that PCAmix explains more variation, greater correlation with true scores and gives less misclassification than nonlinear PCA. Overall, PCAmix showed better result than nonlinear PCA in terms of proportion of explained variance, misclassification rate and rank correlation. Statistical analysis and simulation were done by using programming language R.
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