Weighted least squares fitting using ordinary least squares algorithms

A general approach for fitting a model to a data matrix by weighted least squares (WLS) is studied. This approach consists of iteratively performing (steps of) existing algorithms for ordinary least squares (OLS) fitting of the same model. The approach is based on minimizing a function that majorizes the WLS loss function. The generality of the approach implies that, for every model for which an OLS fitting algorithm is available, the present approach yields a WLS fitting algorithm. In the special case where the WLS weight matrix is binary, the approach reduces to missing data imputation.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author.     

Probability matrix decomposition models

In this paper, we consider a class of models for two-way matrices with binary entries of 0 and 1. First, we considerBoolean matrix decomposition, conceptualize it as alatent response model (LRM) and, by making use of this conceptualization, generalize it to a larger class of matrix decomposition models. Second,probability matrix decomposition (PMD) models are introduced as a probabilistic version of this larger class of deterministic matrix decomposition models. Third, an algorithm for the computation of the maximum likelihood (ML) and the maximum a posteriori (MAP) estimates of the parameters of PMD models is presented. This algorithm is an EM-algorithm, and is a special case of a more general algorithm that can be used for the whole class of LRMs. And fourth, as an example, a PMD model is applied to data on decision making in psychiatric diagnosis. This paper is based on a chapter of the first author's doctoral dissertation, written at the University of Leuven and supervised by Paul De Boeck.     

Statistical evaluation of measures of fit in the Lingoes-Borg procrustean individual differences scaling

PINDIS, as recently presented by Lingoes and Borg [1978] not only marks the latest development within the scope of individual differences scaling, but, may be of benefit in some closely related topics, such as target analysis. Decisions on whether the various models available from PINDIS fit fallible data are relatively arbitrary, however, since a statistical theory of the fit measures is lacking. Using Monte Carlo simulation, expected fit measures as well as some related statistics were therefore obtained by scaling sets of 4(4)24 random configurations of 5(5)30 objects in 2, 3, and 4 dimensions (individual differences case) and by fitting one random configuration to a fixed random target for 5(5)30 objects in 2, 3, and 4 dimensions (target analysis case). Applications are presented.     

On the estimation of polychoric correlations and their asymptotic covariance matrix

A general theory for parametric inference in contingency tables is outlined. Estimation of polychoric correlations is seen as a special case of this theory. The asymptotic covariance matrix of the estimated polychoric correlations is derived for the case when the thresholds are estimated from the univariate marginals and the polychoric correlations are estimated from the bivariate marginals for given thresholds. Computational aspects are also discussed.The research was supported by the Swedish Council for Research in the Humanities and Social Sciences (HSFR) under the programMultivariate Statistical Analysis. The author thanks a reviewer for pointing out an error in the original version of the paper.     

基于RSM对Q矩阵相同的无锚题测验的等值

传统锚题-非等组设计下的测验等值,等值要求的满足具有主观性,并且由于锚题失效或难以获得等因素的影响,则该方法的使用受到了限制。因此,本研究基于规则空间模型的Q矩阵理论,生成两个Q矩阵相同但无锚题的测验的共同受测者,使用共同组设计,利用同时性估计的方法对测验进行等值,并考虑了作答失误率和测验结构对等值稳定性的影响。结果表明:共同组设计同时估计方法的等值稳定性取得了优于或等于锚题-非等组同时估计方法;失误率的增大也会导致等值稳定性的下降;并且不同的测验结构也对等值稳定性产生了影响,其中直线型和收敛型结构稳定性较好,发散型和无结构型较差。     

A Conceptual Toolkit for Intensive Early Behavioral Intervention Teachers

Intensive early behavioral intervention (IEBI) for children with autism requires effective team work involving professional therapists, parents, teachers and others. It is important for all team members to employ a common conceptual and procedural vocabulary so that communication among them is clear, unambiguous, and effective. This article outlines the rationale of a small and practical vocabulary or conceptual toolkit that we have found useful in working with teachers and families in designing, implementing, and analyzing the details of behavioral programs to help autistic children learn to speak and understand language. Special attention is given to a heuristic device called the language matrix. Illustrative data describing the course of generative language acquisition by a child with autism taught according to the language matrix approach are included.     

Newton Algorithms for Analytic Rotation: an Implicit Function Approach

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to m factors and p variables. The speed of the new algorithms is compared to that of existing algorithms and to that of Newton algorithms based on alternative parameterizations. Several rotation criteria were examined and the algorithms were evaluated over a range of values for m. Initial guesses for Newton algorithms were improved by subconvergence iterations of the gradient projection algorithm. Simulation results suggest that no one algorithm is fastest for minimizing all criteria for all values of m. Among competing algorithms, the gradient projection algorithm alone was faster than the implicit function algorithm for minimizing a quartic criterion over oblique rotation matrices when m is large. In all other conditions, however, the implicit function algorithms were competitive with or faster than the fastest existing algorithms. The new algorithms showed the greatest advantage over other algorithms when minimizing a nonquartic component loss criterion.     

A discriminated similarity matrix construction based on sparse subspace clustering algorithm for hyperspectral imagery

The clustering of hyperspectral images is a challenging task because of the high dimensionality of the data. Sparse subspace clustering (SSC) algorithm is one of the popularly used clustering algorithm for high dimensionality data. However, SSC has not fully used the spectral and spatial information during similarity matrix construction based on single sparse representation coefficient for hyperspectral Imagery (HSI) clustering. In this paper, two novel similarity matrix construction methods named as Cosine-Euclidean similarity matrix (abbreviated as CE) and Cosine-Euclidean dynamic weighting similarity matrix (abbreviated as CEDW) are proposed for HSI clustering. They can combine the high spectral information and rich spatial information. Firstly, CE utilizes the cosine similarity of spectral information based on overall sparse representation vectors and classical Euclidean distance of spatial information to construct a novel similarity matrix. Secondly, inheriting CE merits, dynamic weighting adjustment method is introduced to CEDW for some external influence factors to the HSI information. Several experiments on HSI demonstrated that the proposed algorithms are effective for HSI clustering.     

No Matrix Term-Equivalent to Wroński's 3-element Matrix is Finitely Based

Motivated by a question of W. Rautenberg, we prove that any matrix that is term-equivalent to the well-known nonfinitely based matrix of A. Wroski is itself also nonfinitely based.     

Pure Versus Co-occurring Externalizing and Internalizing Symptoms in Children: The Potential Role of Socio-Developmental Milestones

Co-occurring internalizing and externalizing disorders are moderately prevalent in children, adolescents, and adults (Anderson, Williams, McGee, & Silva, 1987; McConaughy & Skiba, 1994), but much remains to be understood regarding why some children show “pure” versus co-occurring internalizing and externalizing symptoms. One possible influence that has previously not been considered is the failure to attain socio-developmental milestones, which paradoxically may prevent the development of co-occurring symptoms for some children. The present study proposes a model in which failure to attain relevant socio-developmental milestones might explain why some children may not develop heterotypic co-occurring symptoms. Specifically, it is proposed that specific clusters of internalizing symptoms (i.e., high social anxiety, withdrawal, and inhibition) and externalizing symptoms (i.e., high impulsivity, hyperactivity, and emotional reactivity) may be associated with the failure to attain socio-developmental milestones (i.e., poor peer relations for anxious children, lack of self-reflection and evaluation for impulsive/reactive children) that, in turn, may prevent subgroups of children from developing co-occurring, heterotypic symptoms.