Estimation Procedure for Reduced Rank Regression, PLSSVD

  • Willín Álvarez Universidad de Carabobo
  • Victor John Griffin Universidad de Carabobo
Keywords: Reduced Rank Multivariate Regression PLSSVD, Partial Least Squares, Singular Value Decomposition, Multicollinearity, reduced rank


This paper presents a procedure for coefficient estimation in a multivariate regression model of reduced rank in the presence of multicollinearity.  The procedure permits the prediction of the dependent variables taking advantage of both Partial Least Squares (PLS) and Singular Value Decomposition (SVD) methods, which is denoted by PLSSVD. Global variability indices and prediction error sums are used to compare the results obtained by classical regression with reduced rank (OLSSVD) and the PLSSVD procedure when applied to examples with different grades of multicollinearity (severe, moderate and low).  In addition, simulations to compare the methods were performed with different sample sizes under four scenarios. The new PLSSVD method is shown to be more effective when the multicollinearity is severe and especially for small sample sizes.

Author Biographies

Willín Álvarez, Universidad de Carabobo
Associate ProfesorMath DepartmentFaculty of Science and Technology
Victor John Griffin, Universidad de Carabobo
Agregate ProfesorMathematics DepartmentFaculty of Science and Technology


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How to Cite
Álvarez, W., & Griffin, V. J. (2016). Estimation Procedure for Reduced Rank Regression, PLSSVD. Statistics, Optimization & Information Computing, 4(2), 107-117.
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