Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models
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||IRT, iterative majorization, logistic bi-additive model, robust Procrustes analysis, two parameter logistic model, weighted principal component analysis|
Groenen, P.J.F., Giaquinto, P., & Kiers, H.A.L.. (2003). Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models (No. EI 2003-09). Retrieved from http://hdl.handle.net/1765/1700