New Modeling Approaches Based on Varimax Rotation of Functional Principal Components

Christian Acal, Ana M. Aguilera and Manuel Escabias
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Christian Acal: Department of Statistics and O.R. and IEMath-GR, University of Granada, 18071 Granada, Spain
Ana M. Aguilera: Department of Statistics and O.R. and IEMath-GR, University of Granada, 18071 Granada, Spain
Manuel Escabias: Department of Statistics and O.R. and IEMath-GR, University of Granada, 18071 Granada, Spain

Mathematics, 2020, vol. 8, issue 11, 1-15

Abstract: Functional Principal Component Analysis (FPCA) is an important dimension reduction technique to interpret the main modes of functional data variation in terms of a small set of uncorrelated variables. The principal components can not always be simply interpreted and rotation is one of the main solutions to improve the interpretation. In this paper, two new functional Varimax rotation approaches are introduced. They are based on the equivalence between FPCA of basis expansion of the sample curves and Principal Component Analysis (PCA) of a transformation of the matrix of basis coefficients. The first approach consists of a rotation of the eigenvectors that preserves the orthogonality between the eigenfunctions but the rotated principal component scores are not uncorrelated. The second approach is based on rotation of the loadings of the standardized principal component scores that provides uncorrelated rotated scores but non-orthogonal eigenfunctions. A simulation study and an application with data from the curves of infections by COVID-19 pandemic in Spain are developed to study the performance of these methods by comparing the results with other existing approaches.

Keywords: functional data analysis; functional principal components; varimax rotation; B-splines; COVID-19 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (7)

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