Factor Analysis Regression for Predictive Modeling with High-Dimensional Data

Randy Carter () and Netsanet Michael ()
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Randy Carter: State University of New York at Buffalo
Netsanet Michael: The Boeing Company

Journal of Quantitative Economics, 2022, vol. 20, issue 1, No 7, 115-132

Abstract: Abstract Factor analysis regression (FAR) of $$y _i$$ y i on $${{\varvec{x}}}_i=(x _{1i},x _{2i},\ldots ,x _{pi})$$ x i = ( x 1 i , x 2 i , … , x pi ) , i = 1,2,...,n, has been studied only in the low-dimensional case $$(p n )$$ ( p > n ) . In this paper, we develop a high-dimensional version of FAR based on a computationally efficient method of factor extraction. We compare the performance of our high-dimensional FAR with partial least squares regression (PLSR) and principal component regression (PCR) under three underlying correlation structures: arbitrary correlation, factor model correlation structure, and when y is independent of x. Under each structure, we generated Monte Carlo training samples of sizes $$n

Keywords: Bilinear factor model; Principal component analysis; Principal component regression; Partial least squares; Factor structure covariance matrix; Factor analysis regression; Mean square error of prediction; Monte Carlo studies; Cross-validation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s40953-022-00322-x

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