Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models

Patrick Groenen (), P. Giaquinto and H.A.L. Kiers
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H.A.L. Kiers: Erasmus Econometric Institute

No EI 2003-09 Revision_Date: 2009-07-29, Econometric Institute Report from Erasmus University Rotterdam, Econometric Institute

Abstract: For many least-squares decomposition models efficient algorithms are well known. A more difficult problem arises in decomposition models where each residual is weighted by a nonnegative value. A special case is principal components analysis with missing data. Kiers (1997) discusses an algorithm for minimizing weighted decomposition models by iterative majorization. In this paper, we for computing a solution. We will show that the algorithm by Kiers is a special case of our algorithm. Here, we will apply weighted majorization to weighted principal components analysis, robust Procrustes analysis, and logistic bi-additive models of which the two parameter logistic model in item response theory is a special case. Simulation studies show that weighted majorization is generally faster than the method by Kiers by a factor one to four and obtains the same or better quality solutions. For logistic bi-additive models, we propose a new iterative majorization algorithm called logistic majorization.

Keywords: weighted principal component analysis; iterative majorization; robust Procrustes analysis; logistic bi-additive model; IRT; two parameter logistic model (search for similar items in EconPapers)
Date: 2003-03-26

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http://hdl.handle.net/1765/1700 (application/pdf)

Related works:
Working Paper: Weighted majorization algorithms for weighted least squares decomposition models (2003)
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Persistent link: http://EconPapers.repec.org/RePEc:dgr:eureir:1765001700

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