A general Bayesian multilevel multidimensional IRT model for locally dependent data

Many item response theory (IRT) models take a multidimensional perspective to deal with sources that induce local item dependence (LID), with these models often making an orthogonal assumption about the dimensional structure of the data. One reason for this assumption is because of the indeterminacy issue in estimating the correlations among the dimensions in structures often specified to deal with sources of LID (e.g., bifactor and two-tier structures), and the assumption usually goes untested. Unfortunately, the mere fact that assessing these correlations is a challenge for some estimation methods does not mean that data seen in practice support such orthogonal structure. In this paper, a Bayesian multilevel multidimensional IRT model for locally dependent data is presented. This model can test whether item response data violate the orthogonal assumption that many IRT models make about the dimensional structure of the data when addressing sources of LID, and this test is carried out at the dimensional level while accounting for sampling clusters. Simulations show that the model presented is effective at carrying out this task. The utility of the model is also illustrated on an empirical data set.     

On the Role of Mathematics in Explaining the Material World: Mental Models for Proportional Reasoning

Contemporary psychological research that studies how people apply mathematics has largely viewed mathematics as a computational tool for deriving an answer. The tacit assumption has been that people first understand a situation, and then choose which computations to apply. We examine an alternative assumption that mathematics can also serve as a tool that helps one to construct an understanding of a situation in the first place. Three studies were conducted with 6th-grade children in the context of proportional situations because early proportional reasoning is a premier example of where mathematics may provide new understanding of the world. The children predicted whether two differently-sized glasses of orange juice would taste the same when they were filled from a single carton of juice made from concentrate and water. To examine the relative contributions and interactions of situational and mathematical knowledge, we manipulated the formal features of the problem display (e.g., diagram vs. photograph) and the numerical complexity (e.g., divisibility) of the containers and the ingredient ratios. When the problem was presented as a diagram with complex numbers, or “realistically” with easy numbers, the children predicted the glasses would taste different because one glass had more juice than the other. But, when the problem was presented realistically with complex numbers, the children predicted the glasses would taste the same on the basis of empirical knowledge (e.g., “Juice can't change by itself”). And finally, when the problem was presented as a diagram with easy numbers, the children predicted the glasses would taste the same on the basis of proportional relations. These complex interactions illuminate how mathematical and empirical knowledge can jointly constrain the construction of a new understanding of the world. We propose that mathematics helped in the case of successful proportional reasoning because it made a complex empirical situation cognitively tractable, and thereby helped the children construct mental models of that situation. We sketch one aspect of the mental models that are constructed in the domain of quantity—a preference for specificity—that helps explain the current findings.     

Self-inhibiting effects of reinforcement

The reinforcers produced by one response reduce the rate of other, concurrently reinforced responses. An analysis of the logical and empirical implications of the relation indicates that one reinforcer must have this effect on responses maintained by other reinforcers even when all reinforcers are produced by the same class of responses. A quantitative expression of the relation leads to a formulation, mathematically equivalent to Herrnstein's (1970), in which the rate of a reinforced response is a joint function of (1) an excitatory effect of the reinforcers produced by that class of responses, and (2) an inhibitory effect of the total reinforcers produced both by that class and by other classes of responses.     

Developmental reversal in classification accuracy due to an increase with age in orientation-free judgments.

A complete developmental reversal in accuracy was obtained in Experiment I in which third graders, sixth graders, and adults judged the class membership of patterns presented in a same-different task. An examination of the task requirements and pattern classes employed led to the hypothesis that the reversal in accuracy resulted from an increase with age in orientation-free judgments. The results of Experiment II, in which adults were told to not rotate the patterns, and Experiment III, which was a replication of Experiment I using symmetric rather than areally skewed pattern classes, provided confirmation for that hypothesis.     

Academic and nonacademic community psychologists: An analysis of divergence in settings,roles, and values

Differences between academic and nonacademic psychologists may be viewed as immutable, worthy of encouragement, or as a situation which the latter group must remedy by becoming “more scientific.” We contend that for community psychology, which perceives theory, application, and action as valid aspects of its broad paradigm, it would be most adaptive toexplicitly address the challenge of managing a balance between diversity and cohesion. There are signs that the present leadership of Division 27 recognizes aspects of this problem and is reconsidering the role and purpose of the Division as an organizing framework for the discipline (Trickett, Note 3). It is our view that engendering a commitment from various subgroups within the membership to addressing the disparities revealed by our respondents is required for resolving what we see as major obstacles to future development of the discipline. The conceptual and empirical approach presented in this study can be an important tool in forging constructive solutions to the challenges we have presented.     

Simultaneous Decision on the Number of Latent Clusters and Classes for Multilevel Latent Class Models

The Multilevel Latent Class Model (MLCM) proposed by Vermunt (2003) has been shown to be an excellent framework for analyzing nested data with assumed discrete latent constructs. The nonparametric version of MLCM assumes 2 levels of discrete latent components to describe the dependency observed in data. Model selection is an important step in any statistical modeling. The task of model selection for MLCM amounts to the decision on the number of discrete latent components at both higher and lower levels and is more challenging than standard Latent Class Models. In this article, simulation studies were conducted to systematically examine the effects of sample sizes, clusters/classes distinctness, and the number of latent clusters and classes on the performance of various information criteria in recovering the true latent structure. Results of the simulation studies are summarized and presented. The final section presents the remarks and recommendations about the simultaneous decision regarding the number of latent classes and clusters when applying MLCMs to analyze empirical data.     

The role of contingency in classical conditioning

The assumption that classical conditioning depends on a contingent relation between the conditioned stimulus (CS) and the unconditioned stimulus (US), which was proposed some decades ago as an alternative to the traditional contiguity assumption, still is widely accepted as an empirical generalization, if no longer as a theoretical postulate. The first support for the contingency assumption was provided by experiments in which occasional CS-US pairings produced no response to the CS in random training--i.e., training in which the probability of the US was the same in the presence and absence of the CS. Those early experiments, the results of which too often are taken at face value, are reconsidered along with various later experiments that show conditioning, both of the CS and its context, in random training. The evidence suggests that CS-US contingency is neither necessary nor sufficient for conditioning and that the concept has long outlived any usefulness it may once have had in the analysis of conditioning.     

A method for obtaining an ordered metric scale

A method is presented for collecting data which will yield a scale on which the entities are ranked in preference (ordinality), the distances between the entities on the scale are ranked (ordered metric), and all combinations of the distances are ranked (higher-ordered metric). The sources drawn upon are von Neumann and Morgenstern (9), and lattice theory. An empirical example is given in which a higher-ordered metric scale is derived.I am grateful to Professor William L. Lepley (Department of Psychology) and Professor Jack R. Tessman (Department of Physics) for their critical reading of this paper. Paul Hurst and Robert Radlow participated in many discussions on the form of measurement discussed in this paper, and assisted in collecting data. I am also grateful to Professor T. C. Benton (Department of Mathematics) for certain source materials.     

Fundamentalist religion and its effect on mental health

The national self-help group, Fundamentalists Anonymous (F.A.), has focused attention upon mental problems that may be caused or exacerbated by authoritarian religion. In this article we outline assertions about the mental problems caused by membership in fundamentalist religion, illustrate these with two case histories, briefly discuss intervention strategies, and describe conceptual and empirical issues. While former members have presented problems severe enough to warrant professional treatment, a causal link between their symptoms and their religious membership has not yet been established, because there is little empirical work on the subject.An earlier version of this paper was presented at the annual meeting of the American Psychological Association in New York in August 1987.The authors express gratitude to Stephen Strack, Ph.D.; Robert Meagher, Ph.D.; Herman Feifel, Ph.D.; and Ted Schoenberger, M.D., for their helpful comments on previous drafts of this paper.     

Application of the pi* goodness-of-fit index to latent structure models

Testing model fit for latent structure models (latent trait models and latent class models) is difficult because of the lack of goodness-of-fit statistics with a known distribution. This paper describes the application of the pi* goodness-of-fit statistic to latent structure models. The statistic pi* is based on the concept of latent classes and has a natural interpretation when applied to these models. This statistic assumes that the population is made up of several classes that follow a parametric model, and a residual class outside the model. The value of pi* is the population proportion in the residual class. This paper describes the estimation algorithms of pi* for latent trait and latent class models and an empirical example with a scale of study habits. There are two latent classes in these data: bad and regular students, which are related to the student s responsibility.     

Optimization-Based Model Fitting for Latent Class and Latent Profile Analyses

Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model. The second stage then uses mixture modeling treating the class membership as known. The proposed approach is theoretically justifiable, directly checks the conditional independence assumption, and converges much faster than the full likelihood approach when analyzing high-dimensional data. This paper also develops a new classification rule based on latent variable models. The proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease, which makes it perfect for analyzing high-throughput genomic data. Simulation studies and real data analysis demonstrate the advantages of the proposed method.     

Assessing Parameter Invariance in the BLIM: Bipartition Models

In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge structures. The BLIM assumes a probability distribution on the knowledge states and a lucky guess and a careless error probability for each problem. A key assumption of the BLIM is that the lucky guess and careless error probabilities do not depend on knowledge states (invariance assumption). This article proposes a method for testing the violations of this specific assumption. The proposed method was assessed in a simulation study and in an empirical application. The results show that (1) the invariance assumption might be violated by the empirical data even when the model’s fit is very good, and (2) the proposed method may prove to be a promising tool to detect invariance violations of the BLIM.     

Extending sequence-class membership with matching to sample

Three normal adults were first trained to point sequentially to each member of several pairs of visual stimuli. This baseline training established one class of stimuli to which subjects responded first, and another class of stimuli to which they responded second. Then, in a matching-to-sample procedure, baseline-sequence stimuli served as samples and new visual stimuli served as comparisons. Subjects were trained to choose one group of new comparisons when the sample was a "first" stimulus from the sequence baseline, and to choose the other new comparison stimuli when the sample was a "second" from the sequence baseline. When the new stimuli were then presented as pairs in the posttest, two subjects pointed to them in sequences predictable on the basis of the stimulus-class membership established during matching to sample. The failure of one subject to demonstrate sequential transfer was shown to be a consequence of the failure of the matching-to-sample procedure to establish stimulus classes. The production of sequences that were not directly trained suggested an empirical approach to the analysis of simple grammatical behavior.     

The ‘ability’ scale in item characteristic curve theory

For the six available sets of empirical data, the discrimination (slope) parameter of the logistic item characteristic curve was found to have a significant positive correlation over items with the difficulty (location) parameter. This unpleasant situation can be eliminated by a suitably chosen transformation of the ability scale. An example of the transformation is given and some empirical results of using the transformed scale are shown.     

Following freud in Vienna the psychological Wednesday society and the Viennese psychoanalytical society 1902–1938

Abstract

Mühlleitner E, Reichmayr J. Following freud in Vienna. The Psychological Wednesday Society and the Viennese Psychoanalytical Society 1902-1938. Int Forum Psychoanal 1997;6:73-102. Stockholm. ISSN 0803-706X.

This study of the composition and structure of the Psychological Wednesday Society and the Viennese Psychoanalytical Society during its existence (1902 to 1938) is a contribution to the history of the psychoanalytic movement and an enlargement of the historiographical and empirical basis of psychoanalysis. Traditional opinions about the Wednesday Psychological Society and the Viennese Psychoanalytical Society which tend to be based on generalized observations about groups within the societies can be compared and corrected. The first chapter contains an overview of the development of the membership size: which persons were accepted in which year, the fluctuations of the membership size during this period. The following data on all 150 members is listed in the addendum to the text: first and last name, date and place of birth and death, duration of membership, and year and country of exile. This study, with the aid of tables and figures, presents the size and movement of the group and its structural tendency after World War 1 to become more homogeneous with regard to sex, age, religion and profession. Furthermore, it defines more closely the continuation and discontinuation of the movement. The fluctuations of the membership size are presented in the context of the history of the societies and in relation to the events in the history of this period. Information is given on the average age of members at admission to the group, duration of membership, on the relation of native and foreign members, and the hierarchy within the society. In a total overview of the period, a trend from the initial heterogeneous-harmonic group dynamic to a homogeneous structure is recognizable. The observations in connection with training psychoanalyses, later professional practice and scientific productivity show interesting sex-specific differences. Along with the special role which women played in theViennese Psychoanalytical Society, it is characteristic of this group, that for almost all members, psychoanalytical publications can be traced. The second chapter is concerned with the geographic origin, the familiar milieu and religious background. This field of study is also well known to the scientific Freud-biographic and can be expanded to all the members.Fifty psychoanalysts were, like Sigmund Freud, the daughters and sons of Jewish immigrants from countries of the Hapsburg monarchy. They moved to Vienna either with their parents or alone for school or university education or for professional training. The figures arrived at by the analysis of data regarding 150 members over the 36 year period show that one forth of the total number of members were non-Jewish. After the First World War, the percentage of Jewish members of the Viennese Psychoanalytical Society increased. The group of analysts became more homogeneous with regard to religion and the professional spectnim. Also included in the text are data on emigration, exile and the meaning of women's participation in the Viennese Psychoanalytical Society     

Probability as a Theory Dependent Concept

It is argued that probability should be defined implicitly by the distributions of possible measurement values characteristic of a theory. These distributions are tested by, but not defined in terms of, relative frequencies of occurrences of events of a specified kind. The adoption of an a priori probability in an empirical investigation constitutes part of the formulation of a theory. In particular, an assumption of equiprobability in a given situation is merely one hypothesis inter alia, which can be tested, like any other assumption. Probability in relation to some theories – for example quantum mechanics – need not satisfy the Kolmogorov axioms. To illustrate how two theories about the same system can generate quite different probability concepts, and not just different probabilistic predictions, a team game for three players is described. If only classical methods are allowed, a 75% success rate at best can be achieved. Nevertheless, a quantum strategy exists that gives a 100% probability of winning. This revised version was published online in June 2006 with corrections to the Cover Date.     

Preference for decision structures in a social dilemma situation

Additional results from Rutte and Wilke's (1984) study are presented. In the context of a social dilemma situation two variables were manipulated: use and variance. Preference for various decision structures is the issue of the present paper. It appeared that a large majority structure and an unanimity structure were mast preferred. A small majority structure and a structure in which each decides for him/herself were intermediately preferred. Whereas a structure in which one person, a leader, decides for all was least preferred. Further analysis of these data suggested that only the latter two decision structures were influenced by the use and variance manipulations.     

A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data

Item response theory (IRT) is one of the most widely utilized tools for item response analysis; however, local item and person independence, which is a critical assumption for IRT, is often violated in real testing situations. In this article, we propose a new type of analytical approach for item response data that does not require standard local independence assumptions. By adapting a latent space joint modeling approach, our proposed model can estimate pairwise distances to represent the item and person dependence structures, from which item and person clusters in latent spaces can be identified. We provide an empirical data analysis to illustrate an application of the proposed method. A simulation study is provided to evaluate the performance of the proposed method in comparison with existing methods.

     

Typicality, graded membership, and vagueness

This paper addresses theoretical problems arising from the vagueness of language terms, and intuitions of the vagueness of the concepts to which they refer. It is argued that the central intuitions of prototype theory are sufficient to account for both typicality phenomena and psychological intuitions about degrees of membership in vaguely defined classes. The first section explains the importance of the relation between degrees of membership and typicality (or goodness of example) in conceptual categorization. The second and third section address arguments advanced by Osherson and Smith (1997), and Kamp and Partee (1995), that the two notions of degree of membership and typicality must relate to fundamentally different aspects of conceptual representations. A version of prototype theory-the Threshold Model-is proposed to counter these arguments and three possible solutions to the problems of logical selfcontradiction and tautology for vague categorizations are outlined. In the final section graded membership is related to the social construction of conceptual boundaries maintained through language use.