A monte carlo study of kruskal's variance based measure on stress

Researchers in the past ten years have studied various parameters involved in nonmetric multidimensional scaling by utilizing Monte Carlo procedures. This paper develops stress distributions using Kruskal's second stress formula based upon a null hypothesis of equal likelihood in the ranking of a set of proximities. These distributions can serve to determine whether a set of data has other than random structure.This research was supported in part by a grant from the Baruch College Scholar Assistance program.     

Improving the efficiency and effectiveness of interactively selected MDS data designs

Two revisions of interactive MDS data selection procedures are presented. One revision improves the estimates of the MDS parameters by adding an analysis of the volume of the spatial coordinates of stimuli. Frames of stimuli augmented by an analysis of volume should more nearly surround the swarm of stimulus points. The second revision, based on randomly ordering the list of stimuli, permits more efficient data designs to be selected by reducing the number of judgments collected but never analyzed.This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017), research grants (DA01070 and MH24149) from the U.S. Public Health Service, and a research and instruction award (IUC 2-47622-1990) from the University of California.     

Additive similarity trees

Similarity data can be represented by additive trees. In this model, objects are represented by the external nodes of a tree, and the dissimilarity between objects is the length of the path joining them. The additive tree is less restrictive than the ultrametric tree, commonly known as the hierarchical clustering scheme. The two representations are characterized and compared. A computer program, ADDTREE, for the construction of additive trees is described and applied to several sets of data. A comparison of these results to the results of multidimensional scaling illustrates some empirical and theoretical advantages of tree representations over spatial representations of proximity data.We thank Nancy Henley and Vered Kraus for providing us with data, and Jan deLeeuw for calling our attention to relevant literature. The work of the first author was supported in part by the Psychology Unit of the Israel Defense Forces.     

Effects of conditionality on INDSCAL and ALSCAL weights

The role of conditionality in the INDSCAL and ALSCAL procedures is explained. The effects of conditionality on subject weights produced by these procedures is illustrated via a single set of simulated data. Results emphasize the need for caution in interpreting subject weights provided by these techniques.     

A latent class unfolding model for analyzing single stimulus preference ratings

A multidimensional unfolding model is developed that assumes that the subjects can be clustered into a small number of homogeneous groups or classes. The subjects that belong to the same group are represented by a single ideal point. Since it is not known in advance to which group of class a subject belongs, a mixture distribution model is formulated that can be considered as a latent class model for continuous single stimulus preference ratings. A GEM algorithm is described for estimating the parameters in the model. The M-step of the algorithm is based on a majorization procedure for updating the estimates of the spatial model parameters. A strategy for selecting the appropriate number of classes and the appropriate number of dimensions is proposed and fully illustrated on some artificial data. The latent class unfolding model is applied to political science data concerning party preferences from members of the Dutch Parliament. Finally, some possible extensions of the model are discussed.The first author is supported as Bevoegdverklaard Navorser of the Belgian Nationaal Fonds voor Wetenschappelijk Onderzoek. Part of this paper was presented at the Distancia meeting held in Rennes, France, June 1992.     

Mixture-modelling-based Bayesian MH-RM algorithm for the multidimensional 4PLM

Several recent works have tackled the estimation issue for the unidimensional four-parameter logistic model (4PLM). Despite these efforts, the issue remains a challenge for the multidimensional 4PLM (M4PLM). Fu et al. (2021) proposed a Gibbs sampler for the M4PLM, but it is time-consuming. In this paper, a mixture-modelling-based Bayesian MH-RM (MM-MH-RM) algorithm is proposed for the M4PLM to obtain the maximum a posteriori (MAP) estimates. In a comparison of the MM-MH-RM algorithm to the original MH-RM algorithm, two simulation studies and an empirical example demonstrated that the MM-MH-RM algorithm possessed the benefits of the mixture-modelling approach and could produce more robust estimates with guaranteed convergence rates and fast computation. The MATLAB codes for the MM-MH-RM algorithm are available in the online appendix.     

Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution. Supported by The Netherlands Organization for Scientific Research (NWO) by grant nr. 030-56403 for the “PIONEER” project “Subject Oriented Multivariate Analysis” to the third author. We would like to thank the anonymous referees for their valuable remarks that have improved the quality of this paper.     

An improved stochastic EM algorithm for large-scale full-information item factor analysis

In this paper, we explore the use of the stochastic EM algorithm (Celeux & Diebolt (1985) Computational Statistics Quarterly, 2, 73) for large-scale full-information item factor analysis. Innovations have been made on its implementation, including an adaptive-rejection-based Gibbs sampler for the stochastic E step, a proximal gradient descent algorithm for the optimization in the M step, and diagnostic procedures for determining the burn-in size and the stopping of the algorithm. These developments are based on the theoretical results of Nielsen (2000, Bernoulli, 6, 457), as well as advanced sampling and optimization techniques. The proposed algorithm is computationally efficient and virtually tuning-free, making it scalable to large-scale data with many latent traits (e.g. more than five latent traits) and easy to use for practitioners. Standard errors of parameter estimation are also obtained based on the missing-information identity (Louis, 1982, Journal of the Royal Statistical Society, Series B, 44, 226). The performance of the algorithm is evaluated through simulation studies and an application to the analysis of the IPIP-NEO personality inventory. Extensions of the proposed algorithm to other latent variable models are discussed.     

Maternal postpartum depression is a risk factor for infant emotional variability at 4 months

Maternal postpartum depression (PPD) is a risk for disruption of mother–infant interaction. Infants of depressed mothers have been found to display less positive, more negative, and neutral affect. Other studies have found that infants of mothers with PPD inhibit both positive and negative affect. In a sample of 28 infants of mothers with PPD and 52 infants of nonclinical mothers, we examined the role of PPD diagnosis and symptoms for infants’ emotional variability, measured as facial expressions, vocal protest, and gaze using microanalysis, during a mother–infant face-to-face interaction. PPD symptoms and diagnosis were associated with (a) infants displaying fewer high negative, but more neutral/interest facial affect events, and (b) fewer gaze off events.  PPD diagnosis, but not symptoms, was associated with less infant vocal protest. Total duration of seconds of infant facial affective displays and gaze off was not related to PPD diagnosis or symptoms, suggesting that when infants of depressed mothers display high negative facial affect or gaze off, these expressions are more sustained, indicating lower infant ability to calm down and re-engage, interpreted as a disturbance in self-regulation. The findings highlight the importance of not only examining durations, but also frequencies, as the latter may inform infant emotional variability.     

多维对数正态作答时间模型：对潜在加工速度多维性的探究

在心理与教育测量中, 潜在加工速度反映学生运用潜在能力解决问题的效率。为在多维测验中探究潜在加工速度的多维性并实现参数估计, 本研究提出多维对数正态作答时间模型。实证数据分析及模拟研究结果表明：(1)潜在加工速度具有与潜在能力相匹配的多维结构; (2)新模型可精确估计个体水平的多维潜在加工速度及与作答时间有关的题目参数; (3)冗余指定潜在加工速度具有多维性带来的负面影响低于忽略其多维性所带来的。