Multidimensional Scaling Model Research Articles

The Role of Person-Culture Fit in Chinese Students' Cultural Adjustment in the United States: A Galileo Mental Model Approach

This article used a Galileo multidimensional scaling model to explain how intercultural communication affected sojourners' wellbeing in their host culture through the convergence of the mental models between sojourners and host nationals with whom the sojourners communicated. Participants were 126 sojourning Chinese in the United States and 30 associated domestic Americans. Data were collected shortly after the Chinese sojourners arrived in the United States and again 3 months later. A measure of person-culture fit was generated by comparing each Chinese sojourner's mental model with the aggregate mental model of the associated domestic Americans. Results showed that the amount of intercultural communication had a significant effect on person-culture fit, in turn affecting sojourners' adaptation outcomes. Theoretical and practical implications of the results are discussed.

Experience-dependent plasticity in the neural weighting of pitch dimensions: A machine learning approach

We conducted a cross-linguistic study to evaluate the impact of language experience on midbrain encoding of acoustic dimensions. Midbrain electrophysiological responses were recorded to the four Mandarin tones in native Chinese (N = 10) and English (N = 10) listeners, through a counter-balanced block design. English participants were trained over multiple days to achieve tone categorization accuracy and reaction time equal to that of the Chinese participants. We assessed the extent to which the four Mandarin tones could be discerned from the electrophysiological responses, using a data-driven machine learning approach. The machine learning output was used to generate dissimilarity matrices that were subjected to a multidimensional scaling (MDS) model. A two dimensional MDS solution emerged that corresponded to “pitch height” and “pitch direction” of the Mandarin tones. Findings derived from the individual differences scaling (INDSCAL) method revealed that, initially, pitch direction was weighted more by t...

Matrix Factorizations based on induced norms

We decompose a matrix Y into a sum of bilinear terms in a stepwise manner, by considering Y as a mapping between two finite dimensional Banach spaces. We provide transition formulas, and represent them in a duality diagram, thus generalizing the well known duality diagram in the french school of data analysis. As an application, we introduce a family of Euclidean multidimensional scaling models.

Stability analysis in nonstationary spatial covariance estimation

Space deformation modelling and estimation techniques based on Multidimensional Scaling (MDS) methods play an important role in nonparametric approaches to the covariance structure analysis of the spatiotemporal processes underlying environmental studies. Since any related procedure depends on the planar MDS representation, the stability of the estimated dispersion, together with the determination of the most influential stations in the estimation of the dispersion space, are important issues that must be analysed before performing the final mapping. In this paper, stability analysis, both in terms of the MDS model and of the variogram function, as well as concerning the derivation of kriging interpolation estimates, is addressed using a special analytical jackknife procedure. Furthermore, the influence of each station in the solution given is assessed, thus providing relevant information regarding not only the MDS procedure but also the interpolation process and the variogram estimation of the spatial dispersion.

A Bayesian approach to modeling group and individual differences in multidimensional scaling

Multidimensional scaling (MDS) models of mental representation assume stimuli are represented by points in a low-dimensional space, such that more similar stimuli are represented by points closer to each other. We consider possible individual differences in MDS representations, using the recently proposed K-INDSCAL model, which allows for both sub-groups of people with different representations, and individual differences in the attention people give to different stimulus dimensions. We develop a novel Bayesian implementation of the K-INDSCAL model, and demonstrate in a simulation study it is capable of inferring meaningful individual differences for the sorts of data sets typically available in psychology. We then apply the model to three existing data sets, involving the taste of colas, images of cats, and colors of different hues. Collectively, the results demonstrate the flexibility of the K-INDSCAL model in finding both group- and individual-level differences, and highlight the need for Bayesian methods to make these inferences.

Cross-Cultural Adaptation and Psychometric Properties of the Portuguese Version of the Aspiration Index (AI)

The aim of this study was to develop a cross-cultural adaptation version and to make a psychometric evaluation of the Aspiration Index (AI) for the Brazilian context. This instrument assesses the importance that individuals put in their life goals. Participants consisted of 971 Brazilian youth aged from 18 to 30 years old (M age = 22.8; SD=3.4). The cultural adaptation showed that it was appropriated both at a cultural and linguistic level. The confi rmatory factor analysis (CFA) demonstrated the adequacy of the original 11-factor model for the Brazilian context, and the multi-group CFA showed that this structure was invariant across different socio-economic groups. Furthermore, the multidimensional scaling modeling (MDS) replicated the results earlier studies, positing a two-dimension structure as representation of the data. With one dimension underlying the intrinsic (e.g., self-acceptance, affi liation) versus extrinsic goals (e.g., fi nancial success, image); and the second dimension defi ned by the self-transcendent (e.g., spirituality) and the physical goals (e.g. health). These results suggest that the AI is a reliable measure to assess different types of life goals and can be used with the Brazilian population from different regions and socioeconomic levels.

Multidimensional Scaling by Majorization: A Review

A major breakthrough in the visualization of dissimilarities between pairs of objects was the formulation of the least-squares multidimensional scaling (MDS) model as defined by the Stress function. This function is quite flexible in that it allows possibly nonlinear transformations of the dissimilarities to be represented by distances between points in a low dimensional space. To obtain the visualization, the Stress function should be minimized over the coordinates of the points and the over the transformation. In a series of papers, Jan de Leeuw has made a significant contribution to majorization methods for the minimization of Stress in least-squares MDS. In this paper, we present a review of the majorization algorithm for MDS as implemented in the smacof package and related approaches. We present several illustrative examples and special cases.

Unveiling Bacterial Interactions through Multidimensional Scaling and Dynamics Modeling.

We propose a new strategy to identify and visualize bacterial consortia by conducting replicated culturing of environmental samples coupled with high-throughput sequencing and multidimensional scaling analysis, followed by identification of bacteria-bacteria correlations and interactions. We conducted a proof of concept assay with pine-tree resin-based media in ten replicates, which allowed detecting and visualizing dynamical bacterial associations in the form of statistically significant and yet biologically relevant bacterial consortia.

Student assignment involving perceptual mapping via multidimensional scaling and multi-attribute models

Research shows that college students are deficient in statistical skills. There is a need today for the development of learning tools that can help students overcome their anxiety of statistical applications. This study seeks to respond to that need by describing a student assignment involving multivariate statistics. The assignment integrates aspects of perceptual mapping via multidimensional scaling and multi-attribute models. A feedback questionnaire revealed that the assignment was well-received by students and successful in increasing their knowledge of statistics. Students felt the assignment did increase their knowledge of perceptual maps, multi-attribute models, and multidimensional scaling. Students showed an interest in learning more about statistics and marketing research. Since the assignment increased the student's interest in statistics and willingness to learn and use statistics, findings suggest that the students anxiety regarding statistics was reduced.

Sustainable Water Supply Model in Ambon Island

Land-use changes from forest to other use will affect watershed hydrological system that lead to water availability in Leitimur Peninsula watershed, Ambon Island. It aims to analyze sustainability index and sensitive attribute of watershed management and to design watershed management model in supporting sustainability of water resources in Leitimur Peninsula. The analysis applies the Multidimensional Scaling (MDS) model and the dynamic model (Stella). The findings signifies that multidimensional sustainability status is 50.97% indicating quite sustainable, while the best management model is by performing land and forest rehabilitation (LFR) and agricultural extensification through agro-forestry system.

A generalization of the MDS method by mixed integer linear and nonlinear mathematical models

The Multi-Dimensional Scaling (MDS) method is used in statistics to detect hidden interrelations among multidimensional data and it has a wide range of applications. The method’s input is a matrix that describes the similarity/dissimilarity among objects of unknown dimension. The objects are generally reconstructed as points of a lower dimensional space to reveal the geometric configuration of the objects. The original MDS method uses Euclidean distance, for measuring both the distance of the reconstructed points and the bias of the reconstructed distances from the original similarity values. In this paper, these distances are distinguished, and distances other than Euclidean are also used, generalizing the MDS method. Two different distances may be used for the two different purposes. Therefore the instances of the generalized MDS model are denoted as model, where the first distance is the type of distance of the reconstructed points and the second one measures the bias of the reconstructed distances and the similarity values. In the case of and distances mixed-integer programming models are provided. The computational experiences show that the generalized model can catch the key properties of the original configuration, if any exist.

Further Understanding of the International Index of Erectile Function at 15+ Years: Confirmatory Factor Analysis and Multidimensional Scaling.

The objective of this study was to describe confirmatory factor analysis (CFA) and multidimensional scaling (MDS) on the International Index of Erectile Function (IIEF) to confirm the structure and to enrich understanding of the IIEF, thereby heightening appreciation of the factors and responses underlying sexual functioning for men with erectile dysfunction. Baseline, end of double-blind, and end of open-label data sets were derived from all data from 2 previously published sildenafil trials. For the CFA model, an acceptable fit of the data was shown for each data set, as indicated by a Bentler comparative fit index >0.9, statistically significant path coefficients ( t values >1.96), and (except for IIEF item 6at baseline) statistically significant standardized path coefficients ≥0.4. For MDS modeling, the distance matrix created for each data set, based on polychoric correlations, interpreted relationships between the IIEF items in 2-dimensional space across the "sexual intercourse interference" dimension (horizontal axis) and the "sexual satisfaction" dimension (vertical axis). The 5-factor structure of the IIEF was confirmed by CFA and enriched with visual interpretation by MDS.

Scaling Politically Meaningful Dimensions Using Texts and Votes

Item response theory models for roll‐call voting data provide political scientists with parsimonious descriptions of political actors' relative preferences. However, models using only voting data tend to obscure variation in preferences across different issues due to identification and labeling problems that arise in multidimensional scaling models. We propose a new approach to using sources of metadata about votes to estimate the degree to which those votes are about common issues. We demonstrate our approach with votes and opinion texts from the U.S. Supreme Court, using latent Dirichlet allocation to discover the extent to which different issues were at stake in different cases and estimating justice preferences within each of those issues. This approach can be applied using a variety of unsupervised and supervised topic models for text, community detection models for networks, or any other tool capable of generating discrete or mixture categorization of subject matter from relevant vote‐specific metadata.

A Structural Equation Multidimensional Scaling Model for One-Mode Asymmetric Dissimilarity Data

A multidimensional scaling (MDS) model is proposed for 2-way 1-mode asymmetric dissimilarity data, to estimate the unknown symmetric subjacent dissimilarity matrix while the objects are represented in a low-dimensional space. In the context of least squares MDS allowing transformations, and considering both triangular parts of the asymmetric dissimilarity matrix as effects of the unobserved symmetric dissimilarities, an alternating estimation procedure is proposed in which the unknown symmetric dissimilarity matrix is estimated in a covariance structure framework. Real and artificial data are analyzed to illustrate the proposed procedure.

Modeling Viewpoint Shifts in Probabilistic Choice

A number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory. This article presents the development of a new stochastic choice model based on multidimensional scaling. This allows decision-makers to have multiple viewpoints, whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint. The implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint. This paper also presents the maximum likelihood estimation of the proposed model, and reanalyzes Tversky's gamble experiment data.

Perception of Musical Timbre by Cochlear Implant Listeners

Several studies have shown that the ability to identify the timbre of musical instruments is reduced in cochlear implant (CI) users compared with normal-hearing (NH) listeners. However, most of these studies have focused on tasks that require specific musical knowledge. In contrast, the present study investigates the perception of timbre by CI subjects using a multidimensional scaling (MDS) paradigm. The main objective was to investigate whether CI subjects use the same cues as NH listeners do to differentiate the timbre of musical instruments. Three groups of 10 NH subjects and one group of 10 CI subjects were asked to make dissimilarity judgments between pairs of instrumental sounds. The stimuli were 16 synthetic instrument tones spanning a wide range of instrument families. All sounds had the same fundamental frequency (261 Hz) and were balanced in loudness and in perceived duration before the experiment. One group of NH subjects listened to unprocessed stimuli. The other two groups of NH subjects listened to the same stimuli passed through a four-channel or an eight-channel noise vocoder, designed to simulate the signal processing performed by a real CI. Subjects were presented with all possible combinations of pairs of instruments and had to estimate, for each pair, the amount of dissimilarity between the two sounds. These estimates were used to construct dissimilarity matrices, which were further analyzed using an MDS model. The model output gave, for each subject group, an optimal graphical representation of the perceptual distances between stimuli (the so-called "timbre space"). For all groups, the first two dimensions of the timbre space were strikingly similar and correlated strongly with the logarithm of the attack time and with the center of gravity of the spectral envelope, respectively. The acoustic correlate of the third dimension differed across groups but only accounted for a small proportion of the variance explained by the MDS solution. Surprisingly, CI subjects and NH subjects listening to noise-vocoded simulations gave relatively more weight to the spectral envelope dimension and less weight to the attack-time dimension when making their judgments than NH subjects listening to unprocessed stimuli. One possible reason for the relatively higher salience of spectral envelope cues in real and simulated CIs may be that the degradation of local fine spectral details produced a more stable spectral envelope across the stimulus duration. The internal representation of musical timbre for isolated musical instrument sounds was found to be similar in NH and in CI listeners. This suggests that training procedures designed to improve timbre recognition in CIs will indeed train CI subjects to use the same cues as NH listeners. Furthermore, NH subjects listening to noise-vocoded sounds appear to be a good model of CI timbre perception as they show the same first two perceptual dimensions as CI subjects do and also exhibit a similar change in perceptual weights applied to these two dimensions. This last finding validates the use of simulations to evaluate and compare training procedures to improve timbre perception in CIs.

Posttraumatic reactions to an earthquake: Multidimensional scaling profile analysis of adolescent survivors

The current study examined the prototypical profiles of posttraumatic stress reactions among a sample of 282 adolescent survivors of the 2008 Wenchuan earthquake in China. Based on a dimensional perspective, the results of profile analysis via multidimensional scaling (PAMS) model revealed a two-dimensional solution corresponding to four profiles: intrusion, avoidance/arousal, partial avoidance, and hyperarousal. These profiles of posttraumatic stress symptoms equally manifested across gender. In addition, the Intrusion Profile was found to be associated with more elevated psychological distress symptoms. Results are discussed with respect to the typical posttraumatic stress symptoms following the earthquake.

Women active citizenship and wellbeing: the Italian case

The paper analyses several indicators (political participation, trade union organizations, ecological associations, voluntary and cultural activities) of active citizenship in Italy, focusing on the profiles of the activists in relation to wellbeing and gender differences. A sample of around 49,000 individuals and 19,000 families from the survey “Aspect of daily life”, collected by the Italian National Institute of Statistics in 2010 was used for the analysis. We apply multivariate statistical methods (correspondence analysis, fuzzy clustering, multidimensional scaling and regression models) to describe the sample and detect the predictors of satisfaction and trust in people.

Scaling Meaningful Political Dimensions

Item response theory (IRT) models for roll-call voting data provide political scientists with parsimonious descriptions of political actors' relative preferences. However, models using only voting data tend to obscure variation in preferences across different issues due to identification and labeling problems that arise in multidimensional scaling models. Latent Dirichlet Allocation (LDA) models are an increasingly applied approach to using relative term frequencies to estimate the degree to which each text in a corpus discusses a set of issues. However, while models based on relative term frequencies are powerful for discovering which issues are being discussed in which texts, they have proven less useful for discovering variation in political positions within corpuses that cover a range of issues. We combine these two models into a new model for discovering preference variation within issues, using voting data augmented with texts describing each vote. We demonstrate our approach using data from the U.S. Supreme Court.

Korarchaeota Diversity, Biogeography, and Abundance in Yellowstone and Great Basin Hot Springs and Ecological Niche Modeling Based on Machine Learning

Over 100 hot spring sediment samples were collected from 28 sites in 12 areas/regions, while recording as many coincident geochemical properties as feasible (>60 analytes). PCR was used to screen samples for Korarchaeota 16S rRNA genes. Over 500 Korarchaeota 16S rRNA genes were screened by RFLP analysis and 90 were sequenced, resulting in identification of novel Korarchaeota phylotypes and exclusive geographical variants. Korarchaeota diversity was low, as in other terrestrial geothermal systems, suggesting a marine origin for Korarchaeota with subsequent niche-invasion into terrestrial systems. Korarchaeota endemism is consistent with endemism of other terrestrial thermophiles and supports the existence of dispersal barriers. Korarchaeota were found predominantly in >55°C springs at pH 4.7–8.5 at concentrations up to 6.6×106 16S rRNA gene copies g−1 wet sediment. In Yellowstone National Park (YNP), Korarchaeota were most abundant in springs with a pH range of 5.7 to 7.0. High sulfate concentrations suggest these fluids are influenced by contributions from hydrothermal vapors that may be neutralized to some extent by mixing with water from deep geothermal sources or meteoric water. In the Great Basin (GB), Korarchaeota were most abundant at spring sources of pH<7.2 with high particulate C content and high alkalinity, which are likely to be buffered by the carbonic acid system. It is therefore likely that at least two different geological mechanisms in YNP and GB springs create the neutral to mildly acidic pH that is optimal for Korarchaeota. A classification support vector machine (C-SVM) trained on single analytes, two analyte combinations, or vectors from non-metric multidimensional scaling models was able to predict springs as Korarchaeota-optimal or sub-optimal habitats with accuracies up to 95%. To our knowledge, this is the most extensive analysis of the geochemical habitat of any high-level microbial taxon and the first application of a C-SVM to microbial ecology.