H.A.L. Kiers
http://repub.eur.nl/ppl/36/
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RePub, Erasmus University RepositoryOblique rotation in correspondence analysis: a step forward in the simplest interpretation
http://repub.eur.nl/pub/10381/
Mon, 25 Jun 2007 00:00:01 GMT<div>U. Lorenzo-Seva</div><div>M. van de Velden</div><div>H.A.L. Kiers</div>
Correspondence analysis (CA) is a popular method that can be used to analyze relationships between categorical variables. It is closely related to several popular multivariate analysis methods such as canonical correlation analysis and principal component analysis. Like principal component analysis, CA solutions can be rotated orthogonally as well as obliquely to simple structure, without affecting the total amount of explained inertia. However, some specific aspects of CA prevent standard rotation procedures from being applied in a straightforward fashion. In particular, the role played by weights assigned to points and dimensions, and the duality of CA solutions, are unique to CA. For orthogonal simple structure rotation, recently procedures have been proposed. In this paper, we construct oblique rotation methods for CA that takes into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models
http://repub.eur.nl/pub/1700/
Wed, 26 Mar 2003 00:00:01 GMT<div>P.J.F. Groenen</div><div>P. Giaquinto</div><div>H.A.L. Kiers</div>
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.