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.     

Spatial versus tree representations of proximity data

In this paper we investigated two of the most common representations of proximities, two-dimensional euclidean planes and additive trees. Our purpose was to develop guidelines for comparing these representations, and to discover properties that could help diagnose which representation is more appropriate for a given set of data. In a simulation study, artificial data generated either by a plane or by a tree were scaled using procedures for fitting either a plane (KYST) or a tree (ADDTREE). As expected, the appropriate model fit the data better than the inappropriate model for all noise levels. Furthermore, the two models were roughly comparable: for all noise levels, KYST accounted for plane data about as well as ADDTREE accounted for tree data. Two properties of the data proved useful in distinguishing between the models: the skewness of the distribution of distances, and the proportion of elongated triangles, which measures departures from the ultrametric inequality, Applications of KYST and ADDTREE to some twenty sets of real data, collected by other investigators, showed that most of these data could be classified clearly as favoring either a tree or a two-dimensional representation.A portable PASCAL program implementing the Sattath and Tversky [1977] ADDTREE algorithm is available from J. Corter, Department of Psychology, Stanford University, Stanford, California 94305.     

Extended similarity trees

Proximity data can be represented by an extended tree, which generalizes traditional trees by including marked segments that correspond to overlapping clusters. An extended tree is a graphical representation of the distinctive features model. A computer program (EXTREE) that constructs extended trees is described and applied to several sets of conceptual and perceptual proximity data.This research was supported in part by a National Science Foundation Pre-doctoral Fellowship to the first author.A magnetic tape containing both the EXTREE program described in the article and ADDTREE/P program for fitting additive trees can also be obtained from the above address. Requests for the program should be accompanied by a check for $25 made out to Teachers College, to cover the costs of the tape and postage.     

An item response tree model with not-all-distinct end nodes for non-response modelling

The non-response model in Knott et al. (1991, Statistician, 40, 217) can be represented as a tree model with one branch for response/non-response and another branch for correct/incorrect response, and each branch probability is characterized by an item response theory model. In the model, it is assumed that there is only one source of non-responses. However, in questionnaires or educational tests, non-responses might come from different sources, such as test speededness, inability to answer, lack of motivation, and sensitive questions. To better accommodate such more realistic underlying mechanisms, we propose a a tree model with four end nodes, not all distinct, for non-response modelling. The Laplace-approximated maximum likelihood estimation for the proposed model is suggested. The validation of the proposed estimation procedure and the advantage of the proposed model over traditional methods are demonstrated in simulations. For illustration, the methodologies are applied to data from the 2012 Programme for International Student Assessment (PISA). The analysis shows that the proposed tree model has a better fit to PISA data than other existing models, providing a useful tool to distinguish the sources of non-responses.     

Judging similarity among strings described by hierarchical trees

The paper compares the tree-theoretical model of similarity judgement (in which the similarity between two objects is a function of the distance between them in a conceptual tree) with an averaging model of similarity judgement that is drawn jointly from information integration theory and from current research indicating the prevalence of anchoring and adjustment mechanisms in judgement. Results of an experiment are presented that suggest that even when subjects organize conceptual material as a hierarchical tree, judgments of similarity among the objects are better accounted for by an averaging mechanism than by distances in the tree. These data are discussed in terms of the differences between the representation in which knowledge is encoded and the processes that operate on the represented information.     

文本阅读中空间距离的心理表征

采用学习探测模式和回指解决相结合的研究范式,探讨情境模型中空间距离的心理表征问题。实验1分离几何距离和类别距离,探讨类别距离对回指解决的影响。结果表明,在控制几何距离的条件下,读者采用由房间数目体现的类别距离信息建构情境模型;实验2进一步探讨几何距离的作用,结果发现,类别距离信息相同的条件下,读者在情境模型中表征几何距离信息。研究表明,类别距离和几何距离分别对空间情境模型的回指解决产生独立影响     

Global and Local Feature Distinctiveness Effects in Language Acquisition

Various aspects of semantic features drive early vocabulary development, but less is known about how the global and local structure of the overall semantic feature space influences language acquisition. A feature network of English words was constructed from a large database of adult feature production norms such that edges in the network represented feature distances between words (i.e., Manhattan distances of probability distributions of features elicited for each pair of words). A word's global feature distinctiveness is measured with respect to all other words in the network and a word's local feature distinctiveness is measured relative to words in sub-networks derived from clustering analyses. This paper investigates how feature distinctiveness of individual words at local and global scales of the network influences language acquisition. Regression analyses indicate that global feature distinctiveness was associated with earlier age of acquisition ratings, and was a stronger predictor of age of acquisition than local feature distinctiveness. These results suggest that the global structure of the semantic feature network could play an important role in language acquisition, whereby globally distinctive concepts help to structure vocabulary development over the lifespan.     

Latent change classes in dichotomous data

Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). The LLRA does not require observable criteria representing a single underlying latent trait, but it postulates the generalizability of the treatment effects over criteria and subjects. To test this latter crucial assumption, the mixture LLRA was proposed that allows directly unobservable types of subjects to have different treatment effects. As the earlier methods for estimating the parameters of the mixture LLRA have specific drawbacks, a further method based on the conditional maximum likelihood principle will be presented here. In contrast to the earlier conditional methods, it uses all of the dichotomous change data while having fewer parameters. Further, its goodness-of-fit tests become more sensitive to a falsely specified number of change-types even though the treatment effects are biased. For typically occurring small to moderate sample sizes, however, parametric bootstrapping of the distributions of the fit statistics is recommended for performing hypotheses tests. Finally, three applications of the new method to empirical data are described: first, about the effect of the so-called Trager psychophysical integration, second, about the effect of autogenic therapy on patients with psychosomatic symptoms, and, third, about the effect of religious education on the attitude towards sects. The mixture LLRA is implemented in the menu-driven program MIXLLRA which can be obtained from Ivo Ponocny via e-mail (ivo.ponocny@univie.ac.at).     

Testing a linear relation between true scores of two measures

We concern ourselves with the hypothesis that two variables have a perfect disattenuated correlation, hence measure the same trait except for errors of measurement. This hypothesis is equivalent to saying, within the adopted model, that true scores of two psychological tests satisfy a perfect linear relation. Statistical tests of this hypothesis are derived when the relation is specified with the exception of the additive constant. Two approaches are presented and various assumptions concerning the error parameters are used. Then the results are reinterpreted in terms of the possible existence of an unspecified perfect linear relation between true scores of two psychological tests. A numerical example is appended by way of illustration. Research reported in this paper has been supported by grant GB-18230 from National Science Foundation.     

The relation between hierarchical and euclidean models for psychological distances

In one well-known model for psychological distances, objects such as stimuli are placed in a hierarchy of clusters like a phylogenetic tree; in another common model, objects are represented as points in a multidimensional Euclidean space. These models are shown theoretically to be mutually exclusive and exhaustive in the following sense. The distances among a set ofn objects will be strictly monotonically related either to the distances in a hierarchical clustering system, or else to the distances in a Euclidean space of less thann — 1 dimensions, but not to both. Consequently, a lower bound on the number of Euclidean dimensions necessary to represent a set of objects is one less than the size of the largest subset of objects whose distances satisfy the ultrametric inequality, which characterizes the hierarchical model.This work was supported in part by Grant GB-13588X from the National Science Foundation. I would like to thank L. M. Kelly and A. A. J. Marley for their helpful comments and suggestions.     

On the Reality of Illusory Conjunctions

The reality of illusory conjunctions in perception has been sometimes questioned, arguing that they can be explained by other mechanisms. Most relevant experiments are based on migrations along the space dimension. But the low rate of illusory conjunctions along space can easily hide them among other types of errors. As migrations over time are a more frequent phenomenon, illusory conjunctions can be disentangled from other errors. We report an experiment in which series of colored letters were presented in several spatial locations, allowing for migrations over both space and time. The distribution of frequencies were fit by several multinomial tree models based on alternative hypothesis about illusory conjunctions and the potential sources of free-floating features. The best-fit model acknowledges that most illusory conjunctions are migrations in the time domain. Migrations in space are probably present, but the rate is very low. Other conjunction errors, as those produced by guessing or miscategorizations of the to-be-reported feature, are also present in the experiment. The main conclusion is that illusory conjunctions do exist.     

Internal multidimensional unfolding about a single-ideal—A probabilistic solution

A solution is presented for an internal multidimensional unfolding problem in which all the judgments of a rectangular proximity matrix are a function of a single-ideal object. The solution is obtained by showing that when real and ideal objects are represented by normal distributions in a multidimensional Euclidean space, a vector of distances among a single-ideal and multiple real objects follows a multivariate quadratic form in normal variables distribution. An approximation to the vector's probability density function (PDF) is developed which allows maximum likelihood (ML) solutions to be estimated. Under dependent sampling, the likelihood function contains information about the parametric distances among real object pairs, permitting the estimation of single-ideal solutions and leading to more robust multiple-ideal solutions. Tests for single- vs. multiple-ideal solutions and dependent vs. independent sampling are given. Properties of the proposed model and parameter recovery are explored. Empirical illustrations are also provided.     

Avoiding degeneracy in multidimensional unfolding by penalizing on the coefficient of variation

Multidimensional unfolding methods suffer from the degeneracy problem in almost all circumstances. Most degeneracies are easily recognized: the solutions are perfect but trivial, characterized by approximately equal distances between points from different sets. A definition of an absolutely degenerate solution is proposed, which makes clear that these solutions only occur when an intercept is present in the transformation function. Many solutions for the degeneracy problem have been proposed and tested, but with little success so far. In this paper, we offer a substantial modification of an approach initiated bythat introduced a normalization factor based on thevariance in the usual least squares loss function. Heiser unpublishedthesis, (1981) and showed that the normalization factor proposed by Kruskal and Carroll was not strong enough to avoid degeneracies. The factor proposed in the present paper, based on the coefficient of variation, discourages or penalizes nonmetric transformations of the proximities with small variation, so that the procedure steers away from solutions with small variation in the interpoint distances. An algorithm is described for minimizing the re-adjusted loss function, based on iterative majorization. The results of a simulation study are discussed, in which the optimal range of the penalty parameters is determined. Two empirical data sets are analyzed by our method, clearly showing the benefits of the proposed loss function.The authors would like to thank the editor, an associate editor, and three reviewers for their valuable comments and suggestions to improve the quality of this work.This revised article was published online in August 2005 with the PDF paginated correctly.     

A Latent Block Distance-Association Model for Profile by Profile Cross-Classified Categorical Data

Abstract

Distance association models constitute a useful tool for the analysis and graphical representation of cross-classified data in which distances between points inversely describe the association between two categorical variables. When the number of cells is large and the data counts result in sparse tables, the combination of clustering and representation reduces the number of parameters to be estimated and facilitates interpretation. In this article, a latent block distance-association model is proposed to apply block clustering to the outcomes of two categorical variables while the cluster centers are represented in a low dimensional space in terms of a distance-association model. This model is particularly useful for contingency tables in which both the rows and the columns are characterized as profiles of sets of response variables. The parameters are estimated under a Poisson sampling scheme using a generalized EM algorithm. The performance of the model is tested in a Monte Carlo experiment, and an empirical data set is analyzed to illustrate the model.     

Giving Up the Goods: Rethinking the Human Right to Subsistence,Institutional Justice,and Imperfect Duties

Either a person's claim to subsistence goods is held against institutions equipped to distribute social benefits and burdens fairly or it is made regardless of such a social scheme. If the former, then one's claim is not best understood as based on principles setting out a subsistence goods entitlement, but rather on principles of equitable social distribution — a fair share. If, however, the claim is not against a given social scheme, no plausible principle exists defining what counts as a reasonable burden for any of the available agents to secure subsistence. No justifiable principle exists implying generalised perfect duties any agent could clearly follow or clearly breach that secure subsistence conditions for others. At best we can justify rescue duties under very specific conditions, or general but imperfect duties to improve arrangements. Neither of these obviously correlates with human rights standards. Attempts in the literature to overcome the dilemma by claiming basic rights can correlate with imperfect duties or can generate duties to work towards institutions that ‘perfect’ our imperfect duties, are faulty. I then show how the dilemma can be avoided by accounts of human rights focusing on minimum respectful treatment rather than goods or interests.     

Relativistic effects in visual perception of real and apparent motion

Timing in the visual field is regarded as an additive conjoint measurement structure, psychophysical extension of stimulus path as an extensive measurement structure. These two sets of postulates lead to the derivation of an essential maximum for velocity perception. Apparent phi motion perception under strictly stationary stimulus conditions is described as relative motion of the first stimulus' psychophysical mapping with respect to a moving perceptual subsystem. The essential maximum of velocity modifies the relative motion postulate: relativistic dilatation of seen length of path is predicted. Testable properties of the model, comparison with experimental data from "real" motion and apparent phi motion perception are discussed.     

Visual body-size adaptation and estimation of tactile distance

Estimating the size of bodies is crucial for interactions with physical and social environments. Body-size perception is malleable and can be altered using visual adaptation paradigms. However, it is unclear whether such visual adaptation effects also transfer to other modalities and influence, for example, the perception of tactile distances. In this study, we employed a visual adaptation paradigm. Participants were exposed to images of expanded or contracted versions of self- or other-identity bodies. Before and after this adaptation, they were asked to manipulate the width of body stimuli to appear as ‘normal’ as possible. We replicated an effect of visual adaptation such that the body-size selected as most ‘normal’ was larger after exposure to expanded and thinner after exposure to contracted adaptation stimuli. In contrast, we did not find evidence that this adaptation effect transfers to distance estimates for paired tactile stimuli delivered to the abdomen. A Bayesian analysis showed that our data provide moderate evidence that there is no effect of visual body-size adaptation on the estimation of spatial parameters in a tactile task. This suggests that visual body-size adaptation effects do not transfer to somatosensory body-size representations.     

The effects of feature necessity and extrinsicity on gradedness of category membership and class inclusion relations*

Two theories of differences among natural language categories in graded membership and strength of class inclusion are contrasted. The two sets of hypotheses tested were: (1) that categories represented by features which many people believe to be necessary would have less graded memberships, and stronger class inclusion, than those represented by features which few people believe to be necessary, and (2) that categories which people believe are represented primarily by intrinsic features (i.e. features that are true of an entity in isolation; see Barr & Caplan, 1987) would have less graded structures, and stronger class inclusion, than those which people believe are represented primarily by extrinsic features (i.e. features representing relations between an entity and other entities). The findings suggest that feature necessity and feature extrinsicity have independent effects on gradedness of category membership and on class inclusion.