Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models
2003-03-26
Research Paper
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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.
- iterative majorization
- IRT
- logistic bi-additive model
- robust Procrustes analysis
- weighted principal component analysis
- two parameter logistic model
- algorithm
- function
- majorization
- model
- majorizing function
- method
- value
- majorizing
- analysis
- weight
- iteration
- majorization algorithm
- difference
- 1 x 2
- problem
- procrustes analysis
- effect
- iterative majorization algorithm
- number
- log likelihood
