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: FEW-Econometrie en besliskunde

No 314, 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 propose a more efficient algorithm called weighted majorization 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 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-cmp
Date: 2003
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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:2003314

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