Clustering and spatial representation methods are often used in combination, to analyse preference ratings when a large number of individuals and/or object is involved. When analysed under an unfolding model, row-conditional linear transformations are usually most appropriate when the goal is to determine clusters of individuals with similar preferences. However, a significant problem with transformations that include both slope and intercept is the occurrence of degenerate solutions. In this paper, we propose a least squares unfolding method that performs clustering of individuals while simultaneously estimating the location of cluster centres and object locations in low-dimensional space. The method is based on minimising the mean squared centred residuals of the preference ratings with respect to the distances between cluster centres and object locations. At the same time, the distances are row-conditionally transformed with optimally estimated slope parameters. It is computationally efficient for large datasets, and does not suffer from the appearance of degenerate solutions. The performance of the method is analysed in an extensive Monte Carlo experiment. It is illustrated for a real data set and the results are compared with those obtained using a two-step clustering and unfolding procedure.

Although one of the flagships of psychometrics, factor analysis, could not have been invented without Francis Galton’s (1822–1911) groundbreaking concept of correlation, some other psychometric concepts had been explored already before his time. Christian Thomasius (1655−1728) pioneered personality assessment using numerical rating scales and introduced a first notion of psychometric reliability. It was Christian Wolff (1679−1754) who coined the term “psychometria” and who identified the basic difficulty of finding a suitable unit for measurement of psychological variables. Halfway the nineteenth century, Gustav Fechner (1801–1887) not only founded psychophysics but also introduced before Galton the statistical approach to the analysis of psychological data—which is so typical for psychometrics in general. He also developed some pathbreaking experimental designs for data collection, as well as the notions of a psychological scale and the psychometric function.

Two approaches to psychological scaling evolved in the nineteenth century. The subject-centred approach quantifies individual differences in ability by standardised person scores. It started with Francis Galton’s invention of the statistical scale, the basis of classic mental and educational testing. The stimulus-centred approach provides psychological scale values of stimuli by using just noticeable differences on a physical scale. It was the basis of psychophysics, brainchild of Gustav Fechner, who developed classic analysis methods for experimental psychology. The main part of the paper concerns a third approach, developed in the period 1941–1964. It combines person scores and stimulus scale values in a joint scale; main initiators were Louis Guttman and Clyde Coombs. Both wanted to work with minimal assumptions about measurement level and score distributions. Guttman’s least squares quantification method is compared with his scalogram method, which was more popular in the social and behavioural sciences. We critically discuss how Coombs developed his unfolding technique for scales with ordered metric measurement level. Finally, we bridge the gap between these two pioneers of one-dimensional non-metric scaling by demonstrating that Coombs scales for paired comparisons or rank orders may be obtained by least squares Guttman scaling supplemented with fitting an additive model.

In this paper a simple but effective procedure to avoid degeneracies in ordinal Unfolding for preference rank data based on the Kemeny distance is proposed. Considering Unfolding as a particular MDS procedure with missing within-set proximities, unknown proximities are first estimated using correlations related to the Kemeny distance, and then the complete proximity matrix is analyzed in a standard MDS framework. A simulation study shows that our proposal is able to both recover the order of the preferences and reproduce the position of both rankings and objects in a geometrical space. Several applications on real data sets show that our procedure returns non-degenerate Unfolding solutions.

Background: This study aimed to investigate whether people with borderline personality disorder (BPD) can benefit from reliving positive autobiographical memories in terms of mood and state self-esteem and elucidate the neural processes supporting optimal memory reliving. Particularly the role of vividness and brain areas involved in autonoetic consciousness were studied, as key factors involved in improving mood and state self-esteem by positive memory reliving. Methods: Women with BPD (N = 25), Healthy Controls (HC, N = 33) and controls with Low Self-Esteem (LSE, N = 22) relived four neutral and four positive autobiographical memories in an MRI scanner. After reliving each memory mood and vividness was rated. State self-esteem was assessed before and after the Reliving Autobio-graphical Memories (RAM) task. Results: Overall, mood and state self-esteem were lower in participants with BPD compared to HC and LSE, but both the BPD and LSE group improved significantly after positive memory reliving. Moreover, participants with BPD indicated that they relived their memories with less vividness than HC but not LSE, regardless of valence. When reliving (vs reading) memories, participants with BPD showed increased precuneus and lingual gyrus activation compared to HC but not LSE, which was inversely related to vividness. Discussion: Women with BPD seem to experience more challenges in reliving neutral and positive autobio-graphical memories with lower vividness and less deactivated precuneus potentially indicating altered autono-etic consciousness. Nevertheless, participants with BPD do benefit in mood and self-esteem from reliving positive memories. These findings underline the potential of positive autobiographical memory reliving and suggest that interventions may be further shaped to improve mood and strengthen self-views in people with BPD.

The δ -machine is a statistical learning tool for classification based on dissimilarities or distances between profiles of the observations to profiles of a representation set, which was proposed by Yuan et al. (J Claasif 36(3): 442–470, 2019). So far, the δ -machine was restricted to continuous predictor variables only. In this article, we extend the δ -machine to handle continuous, ordinal, nominal, and binary predictor variables. We utilized a tailored dissimilarity function for mixed type variables which was defined by Gower. This measure has properties of a Manhattan distance. We develop, in a similar vein, a Euclidean dissimilarity function for mixed type variables. In simulation studies we compare the performance of the two dissimilarity functions and we compare the predictive performance of the δ -machine to logistic regression models. We generated data according to two population distributions where the type of predictor variables, the distribution of categorical variables, and the number of predictor variables was varied. The performance of the δ -machine using the two dissimilarity functions and different types of representation set was investigated. The simulation studies showed that the adjusted Euclidean dissimilarity function performed better than the adjusted Gower dissimilarity function; that the δ -machine outperformed logistic regression; and that for constructing the representation set, K -medoids clustering achieved fewer active exemplars than the one using K -means clustering while maintaining the accuracy. We also applied the δ -machine to an empirical example, discussed its interpretation in detail, and compared the classification performance with five other classification methods. The results showed that the δ -machine has a good balance between accuracy and interpretability.

Network methodology typically has two separate stages: (1) constructing a graph from relational data, and (2) drawing the graph on a map to comprehend its structure. Multidimensional scaling (MDS) is discussed as a distance-driven graph drawing method. It is shown that popular drawing methods in computer science that minimize the potential energy of a spring model are equivalent to a simple form of MDS without optimal transformation of the graphical distance. They share a weighted least squares loss function (Kruskal’s stress). The best way to minimize Stress (Guttman’s algorithm) is shown to be a particular force-directed updating scheme in terms of a spring model. With several analyses of two examples (a simple graph and an additive tree), it is shown that using shortest path distances in the graph as input to MDS gives better drawing results than just using its adjacency matrix. Inclusion of data weights in Stress to emphasize good fit of small distances turns out not to be essential. It may even be detrimental to correct representation of line length in a weighted graph.

We introduce the δ-machine, a statistical learning tool for classification based on (dis)similarities between profiles of the observations to profiles of a representation set consisting of prototypes. In this article, we discuss the properties of the δ-machine, propose an automatic decision rule for deciding on the number of clusters for the K-means method on the predictive perspective, and derive variable importance measures and partial dependence plots for the machine. We performed five simulation studies to investigate the properties of the δ-machine. The first three simulation studies were conducted to investigate selection of prototypes, different (dis)similarity functions, and the definition of representation set. Results indicate that we best use the Lasso to select prototypes, that the Euclidean distance is a good dissimilarity function, and that finding a small representation set of prototypes gives sparse but competitive results. The remaining two simulation studies investigated the performance of the δ-machine with imbalanced classes and with unequal covariance matrices for the two classes. The results obtained show that the δ-machine is robust to class imbalances, and that the four (dis)similarity functions had the same performance regardless of the covariance matrices. We also showed the classification performance of the δ-machine compared with three other classification methods on ten real datasets from UCI database, and discuss two empirical examples in detail.

Early prediction of academic performance is important for student support. The authors explored, in a multivariate approach, whether pre-entry data (e.g., high school study results, preparative activities, expectations, capabilities, motivation, and attitude) could predict university students' first-year academic performance. Preregistered applicants for a bachelor's program filled out an intake questionnaire before study entry. Outcome data (first-year grade point average, course credits, and attrition) were obtained 1 year later. Prediction accuracy was assessed by cross-validation. Students who performed better in preparatory education, followed a conventional educational path before entering, and expected to spend more time on a program-related organization performed better during their first year at university. Concrete preuniversity behaviors were more predictive than psychological attributions such as self-efficacy. Students with a "love of learning" performed better than leisure-oriented students. The intake questionnaire may be used for identifying up front who may need additional support, but is not suitable for student selection.

BACKGROUND:Interpersonal difficulties in borderline personality disorder (BPD) could be related to the disturbed self-views of BPD patients. This study investigates affective and neural responses to positive and negative social feedback (SF) of BPD patients compared with healthy (HC) and low self-esteem (LSE) controls and how this relates to individual self-views.METHODS:BPD (N = 26), HC (N = 32), and LSE (N = 22) performed a SF task in a magnetic resonance imaging scanner. Participants received 15 negative, intermediate and positive evaluative feedback words putatively given by another participant and rated their mood and applicability of the words to the self.RESULTS:BPD had more negative self-views than HC and felt worse after negative feedback. Applicability of feedback was a less strong determinant of mood in BPD than HC. Increased precuneus activation was observed in HC to negative compared with positive feedback, whereas in BPD, this was similarly low for both valences. HC showed increased temporoparietal junction (TPJ) activation to positive v. negative feedback, while BPD showed more TPJ activation to negative feedback. The LSE group showed a different pattern of results suggesting that LSE cannot explain these findings in BPD.CONCLUSIONS:The negative self-views that BPD have, may obstruct critically examining negative feedback, resulting in lower mood. Moreover, where HC focus on the positive feedback (based on TPJ activation), BPD seem to focus more on negative feedback, potentially maintaining negative self-views. Better balanced self-views may make BPD better equipped to deal with potential negative feedback and more open to positive interactions.

In this paper, we present the academic genealogy of presidents of the Psychometric Society by constructing a genealogical tree, in which Ph.D. students are encoded as descendants of their advisors. Results show that most of the presidents belong to five distinct lineages that can be traced to Wilhelm Wundt, James Angell, William James, Albert Michotte or Carl Friedrich Gauss. Important psychometricians Lee Cronbach and Charles Spearman play only a marginal role. The genealogy systematizes important historical knowledge that can be used to inform studies on the history of psychometrics and exposes the rich and multidisciplinary background of the Psychometric Society.

Typically, ranking data consist of a set of individuals, or judges, who have ordered a set of items—or objects—according to their overall preference or some pre-specified criterion. When each judge has expressed his or her preferences according to his own best judgment, such data are characterized by systematic individual differences. In the literature, several approaches have been proposed to decompose heterogeneous populations of judges into a defined number of homogeneous groups. Often, these approaches work by assuming that the ranking process is governed by some distance-based probability models. We use the flexible class of methods proposed by Ben-Israel and Iyigun, which consists in a probabilistic distance clustering approach, and define the disparity between a ranking and the center of a cluster as the Kemeny distance. This class of methods allows for probabilistic allocation of cases to classes, thus being a form of soft or fuzzy, clustering. The allocation probability is unequivocally related to the chosen distance measure.

Autobiographical memory is vital for our well‐being and therefore used in therapeutic interventions. However, not much is known about the (neural) processes by which reliving memories can have beneficial effects. This study investigates what brain activation patterns and memory characteristics facilitate the effectiveness of reliving positive autobiographical memories for mood and sense of self. Particularly, the role of vividness and autonoetic consciousness is studied. Participants (N = 47) with a wide range of trait self‐esteem relived neutral and positive memories while their bold responses, experienced vividness of the memory, mood, and state self‐esteem were recorded. More vivid memories related to better mood and activation in amygdala, hippocampus and insula, indicative of increased awareness of oneself (i.e., prereflective aspect of autonoetic consciousness). Lower vividness was associated with increased activation in the occipital lobe, PCC, and precuneus, indicative of a more distant mode of reliving. While individuals with lower trait self‐esteem increased in state self‐esteem, they showed less deactivation of the lateral occipital cortex during positive memories. In sum, the vividness of the memory seemingly distinguished a more immersed and more distant manner of memory reliving. In particular, when reliving positive memories higher vividness facilitated increased prereflective autonoetic consciousness, which likely is instrumental in boosting mood.

Typically, rank data consist of a set of individuals, or judges, who have ordered a set of items or objects according to their overall preference or some prespecified criterion. When each judge has expressed his or her preferences according to his own best judgment, such data are characterized by systematic individual differences. In the literature several approaches have been proposed in order to decompose heterogeneous populations into a defined number of homogeneous groups. Often, these approaches work by assuming that the ranking process is governed by some distance-based models. We use the flexible class of methods proposed by Ben-Israel and Iyigun, which consists in a probabilistic-distance clustering approach, and define the disparity between a ranking and the center of a cluster as the Kemeny distance. This class of methods allows for probabilistic allocation of cases to classes, being a form of fuzzy clustering, rather than hard clustering, where the probability is unequivocally related to the chosen distance measure. Abstract In genere, i ‘rank data’ consistono in una serie di individui, o giudici, che hanno espresso le loro preferenze su un set di oggetti, o item, ordinando questi ultimi sulla base delle loro preferenze dal piú preferito al meno preferito. In letteratura sono stati proposti diversi approcci volti a decomporre popolazioni di giudici nel complesso eterogenee in termini di preferenze espresse in un numero ristretto di sotto-popolazioni internamente omogenee. Molto spesso tali approcci seguono approcci basati su misture di modelli basati su distanze, che prevedono sia, in taluni casi, la scelta della distanza piú adeguata, sia la stima di massima verosimglianza di una serie di parametri. In questo lavoro si propone un approccio di ‘soft clustering’ che si basa sul concetto di probabilistic distance clustering, utilizzando la distanza di Kemeny come metrica di riferimento. Antonio D’Ambrosio University of Naples Federico II, Italy, e-mail: antdambr@unina.it Willem J. Heiser Leiden University, The Netherlands e-mail: heiser@fsw.leidenuniv.nl

The way we view ourselves may play an important role in our responses to interpersonal interactions. In this study, we investigate how feedback valence, consistency of feedback with self-knowledge and global self-esteem influence affective and neural responses to social feedback. Participants (N = 46) with a high range of self-esteem levels performed the social feedback task in an MRI scanner. Negative, intermediate and positive feedback was provided, supposedly by another person based on a personal interview. Participants rated their mood and applicability of feedback to the self. Analyses on trial basis on neural and affective responses are used to incorporate applicability of individual feedback words. Lower self-esteem related to low mood especially after receiving non-applicable negative feedback. Higher self-esteem related to increased posterior cingulate cortex and precuneus activation (i.e. self-referential processing) for applicable negative feedback. Lower self-esteem related to decreased medial prefrontal cortex, insula, anterior cingulate cortex and posterior cingulate cortex activation (i.e. self-referential processing) during positive feedback and decreased temporoparietal junction activation (i.e. other referential processing) for applicable positive feedback. Self-esteem and consistency of feedback with self-knowledge appear to guide our affective and neural responses to social feedback. This may be highly relevant for the interpersonal problems that individuals face with low self-esteem and negative self-views.

Background. Early prediction of academic performance is important for student selection and support. We explored, in a multivariate approach, whether pre-entry data (e.g., expectations, capabilities, motivation, attitude) could predict university students’ first year academic performance. Methods. Pre-registered applicants for a bachelor’s program filled out the Leiden Intake Questionnaire (LIQ) before study-entry (N=739). Outcome data (first-year GPA, course credits, attrition) were obtained one year later. Results. Students who performed better in preparatory education, and students who followed a conventional educational path before entering performed better during their first year at university. Non-Dutch students were less successful than Dutch students, and students who expected to spend more time on a study organization were more successful. Conclusions. The LIQ may be used for identifying upfront who may need additional support, but is not suitable for student selection. Future work on academic performance should include cross-validation to determine how well the findings may generalize.

Preference rankings usually depend on the characteristics of both the individuals judging a set of objects and the objects being judged. This topic has been handled in the literature with log-linear representations of the generalized Bradley-Terry model and, recently, with distance-based tree models for rankings. A limitation of these approaches is that they only work with full rankings or with a pre-specified pattern governing the presence of ties, and/or they are based on quite strict distributional assumptions. To overcome these limitations, we propose a new prediction tree method for ranking data that is totally distribution-free. It combines Kemeny’s axiomatic approach to define a unique distance between rankings with the CART approach to find a stable prediction tree. Furthermore, our method is not limited by any particular design of the pattern of ties. The method is evaluated in an extensive full-factorial Monte Carlo study with a new simulation design.

The ten most frequently cited articles appearing in Psychometrika since its establishment in 1936 are highlighted in a series of ten commentaries.They are grouped in three themes, with chronological ordering within these groups.The first group regards some characteristic problems in factor analysis, the second group is about the analysis of proximities, and the third group addresses psychometric concerns in multivariate analysis. 11.Solutions for Problems in the Factor Analysis Model KAISER, H. F. (1958).The varimax criterion for analytic rotation in factor analysis.Psychometrika, 23,[187][188][189][190][191][192][193][194][195][196][197][198][199][200] (5237 citations according to Google Scholar as of April, 2016)Applications of Principal Components Analysis or Exploratory Factor Analysis in the behavioral sciences are usually followed by rotation aiming at simple structure.And the rotation method used is very often Kaiser's normal varimax.What makes varimax so popular?Varimax rotation is certainly not the only simple structure rotation method, nor was it the first:The first analytic criterion for determining psychologically interpretable factors was presented in 1953 by Carroll.[Kaiser thereby ignored earlier proposals to partially use analytic rotation criteria along with graphical methods (e.g., Tucker, 1944), probably because he strongly disliked graphical methods] […] before the advent of computers, rotations were always carried out on a subjective graphical basis.Scientifically, of course, this was nonsense, and perhaps led, more than anything else, to a bad name for factor analysis among professional mathematicians and statisticians (Kaiser, 1960, pp.146-147).Kaiser considered Carroll's proposal a breakthrough: the first method to optimize a single criterion operationalizing Thurstone's (1947) rules for simple structure.On the other hand, he made it clear that there was room for improvement, to say the least:In the light of later developments, Carroll's criterion should probably be relegated to the limbo of 'near misses'; however, this does not detract from the fact that it was the first attempt to break away from an inflexible devotion to Thurstone's ambiguous, arbitrary, and mathematically unmanageable qualitative rules for his intuitively compelling notion of simple structure (p.188).

Dynamic testing may be useful in assessing cognitive potential in disadvantaged populations such as ethnic minorities. Majority and minority culture children's performance on a dynamic test of figural matrices was examined using a pretest–training–posttest design. Dynamically tested children were compared to practice- and attention-control groups at three inner-city schools (N=111). School performance and teacher ratings of learning-ability were lower for ethnic minority children. Ethnicity was related to pretest performance, but not change from pretest to posttest for the dynamic testing condition. Instructional-needs were similar for both culture groups, and related to pretest performance, performance change and teacher ratings. AnimaLogica appears to provide similar indices of cognitive potential for both indigenous and ethnic minority children and these indices do not appear attributable to individual differences in working memory. Generally the focus in multicultural assessment lies in limiting cultural bias within the test and norms; however, dynamic administration of cognitive assessments may be an additional, practical method to help educators ascertain children's cognitive potential in culturally diverse schools.

Multiple-choice (MC) analogy items are often used in cognitive assessment. However, in dynamic testing, where the aim is to provide insight into potential for learning and the learning process, constructed-response (CR) items may be of benefit. This study investigated whether training with CR or MC items leads to differences in the strategy progression and understanding of analogical reasoning in 5- to 6-year-olds (N = 111). A pretest-training-posttest control group design with randomized blocking was utilized, where two experimental groups were trained according to the graduated prompts method. Results show that both training conditions improved more during dynamic testing compared with untrained controls. As expected, children in the CR condition required more prompting during training and showed different strategy-use patterns compared with the MC group. However, the quality of solution explanations was significantly better for children in the CR condition. It appears that possible performance advantages of training with CR items are most apparent when active processing is required. In the future, we advise including items such as CR or analogy construction in dynamic testing that allow for fine-grained analysis of strategy-use to further discern differences in children's analogical reasoning understanding.