Template-Type: ReDIF-Paper 1.0
Author-Name: Groenen, P.J.F.
Author-Name-Last: Groenen
Author-Name-First: Patrick
Author-Person: pgr229
Author-Name: Giaquinto, P.
Author-Name-Last: Giaquinto
Author-Name: Kiers, H.A.L.
Author-Name-Last: Kiers
Author-Name-First: Henk
Title: Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models
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.
Creation-Date: 2003-03-26
File-URL: https://repub.eur.nl/pub/1700/feweco20030326124022.pdf
File-Format: application/pdf
Series: RePEc:ems:eureir
Number: EI 2003-09
Keywords: IRT, iterative majorization, logistic bi-additive model, robust Procrustes analysis, two parameter logistic model, weighted principal component analysis
Handle: RePEc:ems:eureir:1700