A Two-Stage Model of Category Construction

The current consensus is that most natural categories are not organized around strict definitions (a list of singly necessary and jointly sufficient features) but rather according to a family resemblance (FR) principle: Objects belong to the same category because they are similar to each other and dissimilar to objects in contrast categories. A number of computational models of category construction have been developed to provide an account of how and why people create FR categories (Anderson, 1990; Fisher, 1987). Surprisingly, however, only a few experiments on category construction or free sorting have been run and they suggest that people do not sort examples by the FR principle. We report several new experiments and a two-stage model for category construction. This model is contrasted with a variety of other models with respect to their ability to account for when FR sorting will and will not occur. The experiments serve to identify one basis for FR sorting and to support the two-stage model. The distinctive property of the two-stage model is that it assumes that people impose more structure than the examples support in the first stage and that the second stage adjusts for this difference between preferred and perceived structure. We speculate that people do not simply assimilate probabilistic structures but rather organize them in terms of discrete structures plus noise.     

A Unified Nonparametric IRT Model for <Emphasis Type="Italic">d</Emphasis>-Dimensional Psychological Test Data (<Emphasis Type="Italic">d</Emphasis>-ISOP)

The (univariate) isotonic psychometric (ISOP) model (Scheiblechner, 1995) is a nonparametric IRT model for dichotomous and polytomous (rating scale) psychological test data. A weak subject independence axiom W1 postulates that the subjects are ordered in the same way except for ties (i.e., similarly or isotonically) by all items of a psychological test. A weak item independence axiom W2 postulates that the order of the items is similar for all subjects. Local independence (LI or W3) is assumed in all models. With these axioms, sample-free unidimensional ordinal measurements of items and subjects become feasible. A cancellation axiom (Co) gives, as a result, the additive isotonic psychometric (ADISOP) model and interval scales for subjects and items, and an independence axiom (W4) gives the completely additive isotonic psychometric (CADISOP) model with an interval scale for the response variable (Scheiblechner, 1999). The d-ISOP, d-ADISOP, and d-CADISOP models are generalizations to d-dimensional dependent variables (e.g., speed and accuracy of response). The author would like to thank an Associate Editor and two anonymous referees and also Professor H.H. Schulze for their very valuable suggestions and corrections.     

On the multivariate asymptotic distribution of sequential Chi-square statistics

The multivariate asymptotic distribution of sequential Chi-square test statistics is investigated. It is shown that: (a) when sequential Chi-square statistics are calculated for nested models on the same data, the statistics have an asymptotic intercorrelation which may be expressed in closed form, and which is, in many cases, quite high; and (b) sequential Chi-squaredifference tests are asymptotically independent. Some Monte Carlo evidence on the applicability of the theory is provided.This research was carried out while the first author was Visiting Professor in the Department of Statistics in the University of South Africa, and was supported in part by a research grant (NSERC #67-4640) from the National Sciences and Engineering Council of Canada to the first author. The support of both of these organizations is acknowledged with gratitude.     

An identifiable model of two-stage learning

An eleven-parameter model for two-stage learning is developed. The model's principal advantage over extant two-stage models is that its parameter space is completely identifiable, thereby eliminating the tedious procedure of locating acceptable identifying restrictions. Identifiability is achieved by defining the model over a slightly modified outcome space. Following the identifiability proof, the necessary statistical machinery for parameter estimation, goodness-of-fit analyses, and hypothesis testing is presented. These latter developments are illustrated with data from an adult cued recall experiment and a free recall experiment with elementary school children.     

Cognitive Load and the Equality Heuristic: A Two-Stage Model of Resource Overconsumption in Small Groups

Two studies were conducted to test a two-stage model of the psychological mechanisms underlying the overconsumption of scarce resources in small groups. The model proposes that members of groups sharing resources first anchor their consumption choices on an “equal-division” heuristic and then, given sufficient cognitive capacity, adjust their choices in a self-serving direction. The results from both studies support the model. The first study found that when faced with a common resource pool almost all group members expressed thoughts regarding equality; however, individuals with sufficient cognitive capacity requested more from the pool and expressed more task-relevant thoughts than individuals lacking the necessary cognitive resources. The second study provided additional support for the two-stage model by demonstrating that group members' cognitions occur in the order predicted by the model and by demonstrating that an individual difference, social value orientation, affects thought processes only when individuals are not experiencing high cognitive loads. Implications are discussed.     

General estimators for the reliability of qualitative data

We study a proportional reduction in loss (PRL) measure for the reliability of categorical data and consider the general case in which each ofN judges assigns a subject to one ofK categories. This measure has been shown to be equivalent to a measure proposed by Perreault and Leigh for a special case when there are two equally competent judges, and the correct category has a uniform prior distribution. We consider a general framework where the correct category is assumed to have an arbitrary prior distribution, and where classification probabilities vary by correct category, judge, and category of classification. In this setting, we consider PRL reliability measures based on two estimators of the correct category—the empirical Bayes estimator and an estimator based on the judges' consensus choice. We also discuss four important special cases of the general model and study several types of lower bounds for PRL reliability.Bruce Cooil is Associate Professor of Statistics, and Roland T. Rust is Professor and area head for Marketing, Owen Graduate School of Management, Vanderbilt University. The authors thank three anonymous reviewers and an Associate Editor for their helpful comments and suggestions. This work was supported in part by the Dean's Fund for Faculty Research of the Owen Graduate School of Management, Vanderbilt University.     

A Longitudinal Study of Shop Stewards’ Union Commitment and Perceptions of Union Instrumentality and Support

Although previous studies have hypothesised that union perceptions (e.g. perceived union instrumentality, perceived union support) predict members’ commitment to the union, these relationships have only been tested cross‐sectionally. Drawing on attitude–behavior consistency theory, this study hypothesised that union commitment may be an antecedent of union perceptions. Cross‐lagged structural equation models with one year separating waves of data collection (N = 676) provided the most support for a model suggesting that commitment precedes perceptions of the union. These results point to the need to consider new models of union commitment for shop stewards and, potentially, union members.     

When are item response models consistent with observed data?

The problem of deciding whether a set of mental test data is consistent with any one of a large class of item response models is considered. The classical assumption of locla independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model to fit a set of data. This leads to a condition that a set of data must satisfy if it is to be representable by any item response model that assumes both local independence and monotone item characteristic curves. An example is given to show that LND is strictly weaker than local independence. Thus rejection of LND models implies rejection of all item response models that assume local independence for a given set of data.This research was supported in part by Grant NIE-G-78-0157 to ETS from the NIE, by the Program Statistics Research Project, and by TOEFL Program Research. I would like to thank Dr. Douglas Jones of ETS for stimulating discussions during the early stages of this research, Dr. Frederick Lord of ETS for his encouragement of this work and comments on earlier drafts of this paper and Professor Robert Berk of Rutgers University for pointing out that conditions (a), (b) and (c) of Theorem 2 were also sufficient for LND and Monotonicity. Dr. Donald Alderman of ETS provided financial support for the development of a computer program to apply these results to data from the TOEFL program.     

The Present Status of the Frontal Lobe

This study contrasted two models of prospective remembering: i.e., remembering in the future to perform an action that has been planned. High anxiety or discomfort is predicted by the first model to be associated with forgetting, and by the second model to be associated with remembering but not performing. Questionnaire data from 73 male and female college students support the second model (p < .01). For planned actions that were forgotten, there was an inverse relationship between importance and comfortableness (p < .01). Prospective remembering may be facilitated by reducing potential conflict between the importance and comfortableness of a planned action, involving other persons, and utilizing external retrieval cues.     

Cross-Cultural Generalizability of CBCL Syndromes Across Three Continents: From the USA and Holland to Australia

The study asked how well Achenbach's 8-factor cross-informant model for the Child Behavior Checklist (Achenbach, 1991a, 1991b, 1991c) fits clinic data in the USA, Holland, and Australia. DeGroot et al.'s Dutch 8-factor model (DeGroot, Koot, & Verhulst 1994) was also tested for its cross-cultural generalizability. Achenbach's matched clinical sample data (N = 2110) were analyzed and contrasted with the previously reported Dutch findings (N = 2335), as well as a new data set collected on clinic referred children and adolescents in Australia (N = 2237). Confirmatory factor analyses supported the Dutch as much as the American model in the USA, Holland, and Australia. Although about 90% of items showed convergent validity across models and countries, the attention and especially the social problems factor found least support. Most double loadings in the current models were not upheld. Instead, additional analyses discovered a number of unmodelled loadings including many cross-loadings. This led to the redefinition of the social problems factor as a mean aggression factor (with associated social problems) whereas the original aggression factor focuses on emotional acting out and the delinquent factor describes an evasive, covert type of antisocial behavior. Overall most support was obtained for the withdrawn, somatic, anxious/depressed, thought problems, and aggressive factors.     

Decision processes in verifying category membership statements: Implications for models of semantic memory

Current models of semantic memory assume that natural categories are well-defined. Specific predictions of two such models, the Smith, Shoben, and Rips (1974a) two-stage feature comparison model and the Glass and Holyoak (1974/75) ordered search model, were tested and disconfirmed in Experiment I. We propose an alternative model postulating fuzzy categories represented as sets of characteristic properties. This model, combined with a Bayesian decision process, accounts for the results of three additional experiments, as well as for the major findings in the semantic memory literature. We argue that people verify category membership statements by assessing similarity relations between concepts rather than by using information which logically specifies the truth value of the sentence. Our data also imply that natural categories are fuzzy rather than well-defined.     

Probability matching in visual selective attention

Jonides (1980, p. 111) suggested a model to account for shifts of spatial attention in visual search tasks with less than 100% cue validity. This two-stage probability matching model was subsequently tested by Jonides (1983). Reaction time distribution characteristics indeed provided some support for the model. In the present paper the relevant data presented in Jonides (1980, 1981, 1983) are further analysed. The results of this analysis strongly support the probability matching hypothesis. Probability matching is apparently a very important strategic characteristic of visual spatial attention that deserves much more study.     

Direct quantitative judgments of sums and a two-stage model for psychophysical judgments

Judged magnitudes of differences between stimuli have previously been shown to support a two-stage interpretation of magnitude estimation, in which input transformations and output transformations are each describable as power functions. In an effort to provide support for the model independent of the difference estimation procedure. the present investigation employed two additional judgment tasks. We obtained magnitude judgments and category judgments of the combined magnitudes (sums) of paired weights from two groups of Ss. Values of the inferred input exponent k calculated from the two sets of data were very similar and were also remarkably similar to the exponent previously calculated from magnitude estimations of differences between weights. The output exponent calculated from magnitude judgments of sums described a concave upward function; however. the similar function describing category judgments was essentially linear. These results show that the inferred input exponent is not the result of the difference estimation task, and in addition provides support for the contention that the interval scale may be a less biased sensory measure than the magnitude scale. The introduction of an additive constant to the model improved its fit to the data but the rule by which it was introduced made very little difference.     

The relative sensitivities of same-different and identification judgment models to perceptual dependence

Probabilistic models of same-different and identification judgments are compared (within each paradigm) with regard to their sensitivity to perceptual dependence or the degree to which the underlying psychological dimensions are correlated. Three same-different judgment models are compared. One is a step function or decision bound model and the other two are probabilistic variants of a similarity model proposed by Shepard. Three types of identification models are compared: decision bound models, a probabilistic multidimensional scaling model, and probabilistic models based on the Shepard-Luce choice rule. The decision bound models were found to be most sensitive to perceptual dependence, especially when there is considerable distributional overlap. The same-different model based on the city-block metric and an exponential decay similarity function, and the corresponding identification model were found to be particularly insensitive to perceptual dependence. These results suggest that if a Shepard-type similarity function accurately describes behavior, then under typical experimental conditions it should be difficult to see the effects of perceptual dependence. This result provides strong support for a perceptualindependence assumption when using these models. These theoretical results may also play an important role in studying different decision rules employed at different stages of identification training.We thank Robert Melara, Jerome Busemeyer and three anonymous reviewers for comments on an earlier draft of this paper.     

Relating latent class membership to external variables: An overview

In this article we provide an overview of existing approaches for relating latent class membership to external variables of interest. We extend on the work of Nylund-Gibson et al. (Structural Equation Modeling: A Multidisciplinary Journal, 2019, 26, 967), who summarize models with distal outcomes by providing an overview of most recommended modeling options for models with covariates and larger models with multiple latent variables as well. We exemplify the modeling approaches using data from the General Social Survey for a model with a distal outcome where underlying model assumptions are violated, and a model with multiple latent variables. We discuss software availability and provide example syntax for the real data examples in Latent GOLD.     

Idealisation,naturalism, and rationality: Some lessons from Minimal Rationality

In his bookMinimal Rationality (1986), Christopher Cherniak draws deep and widespread conclusions from our finitude, and not only for philosophy but also for a wide range of science as well. Cherniak's basic idea is that traditional philosophical theories of rationality represent idealisations that are inaccessible to finite rational agents. It is the purpose of this paper to apply a theory of idealisation in science to Cherniak's arguments. The heart of the theory is a distinction between idealisations that represent reversible, solely quantitative simplifications and those that represent irreversible, degenerate idealisations which collapse out essential theoretical structure. I argue that Cherniak's position is best understood as assigning the latter status to traditional rationality theories and that, so understood, his arguments may be illuminated, expanded, and certain common criticisms of them rebutted. The result, however, is a departure from traditional, formalist theories of rationality of a more radical kind than Cherniak contemplates, with widespread ramifications for philosophical theory, especially philosophy of science itself.I would like to thank Professor R. E. Butts and the Department of Philosophy at the University of Western Ontario, Canada, for generous support and stimulating discussion during the research leave at which time this paper was prepared, and the University of Newcastle and its vice-chancellor, Professor K. Morgan, for support. I am greatly indebted to extended discussion with Professor H. I. Brown, to thoughtful comments from two anonymousSynthese referees, and to discussion with Professor W. Harper; between them they have sharpened and corrected the presentation at several places, especially Sections 3 (referees), 4passim (Brown), 4.1 (referee), 4.3 (Harper). More specific acknowledgement is given as appropriate.     

Evaluation of self-administered rational emotive therapy programs for interpersonal anxiety

Self-administered rational emotive therapy (RET), withA New Guide to Rational Living (Ellis & Harper, 1975), as the treatment manual, was evaluated by comparing three groups which varied in terms of therapist contact (therapist administered, minimal contact, self-administered). University students who volunteered for the research program involving the treatment of interpersonal anxiety were randomly assigned to one of these treatments or to a wait-list control group. The results for 72 subjects who completed the 5-week program indicated the three treatment groups made significant gains over untreated controls on some of the self-report measures. No between-group differences appeared on ratings by significant others. A four- to five-month follow-up, which obtained data from 41 (58%) of the subjects, provided some support for the maintenance of treatment effects for the therapist administered and minimal contact groups. Correlations of assessed irrational beliefs with outcome measures provided some support for the RET model.Norris D. Vestre, Ph.D., is a Professor in the Department of Psychology, Arizona State University. Terrence J. Judge, M.C., R.N.C., is a nurse therapist at Camelback Vista Treatment Center, Scottsdale, Arizona.     

A comparison of two response time models applied to perceptual matching

Two models, a Poisson race model and a diffusion model, are fit to data from a perceptual matching task. In each model, information about the similarity or the difference between two stimuli accumulates toward thresholds for either response. Stimulus variables are assumed to influence the rate at which information accumulates, and response variables are assumed to influence the level of the response thresholds. Three experiments were conducted to assess the performance of each model. In Experiment 1, observers performed under different response deadlines; in Experiment 2, response bias was manipulated by changing the relative frequency ofsame anddifferent stimuli. In Experiment 3, stimulus pairs were presented at three eccentricities: foveal, parafoveal, and peripheral. We examined whether the race and diffusion models could fit the response time and accuracy data through changes only in response parameters (for Experiments 1 and 2) or stimulus parameters (for Experiment 3). Comparisons between the two models suggest that the race model, which has not been studied extensively, can account for perceptual matching data at least as well as the diffusion model. Furthermore, without the constraints on the parameters provided by the experimental conditions, the diffusion and the race models are indistinguishable. This finding emphasizes the importance of fitting models across several conditions and imposing logical psychological constraints on the parameters of models.     

Nonparametric polytomous IRT models for invariant item ordering, with results for parametric models

It is often considered desirable to have the same ordering of the items by difficulty across different levels of the trait or ability. Such an ordering is an invariant item ordering (IIO). An IIO facilitates the interpretation of test results. For dichotomously scored items, earlier research surveyed the theory and methods of an invariant ordering in a nonparametric IRT context. Here the focus is on polytomously scored items, and both nonparametric and parametric IRT models are considered.The absence of the IIO property in twononparametric polytomous IRT models is discussed, and two nonparametric models are discussed that imply an IIO. A method is proposed that can be used to investigate whether empirical data imply an IIO. Furthermore, only twoparametric polytomous IRT models are found to imply an IIO. These are the rating scale model (Andrich, 1978) and a restricted rating scale version of the graded response model (Muraki, 1990). Well-known models, such as the partial credit model (Masters, 1982) and the graded response model (Samejima, 1969), do no imply an IIO.     

Structural Modeling of Measurement Error in Generalized Linear Models with Rasch Measures as Covariates

This paper proposes a structural analysis for generalized linear models when some explanatory variables are measured with error and the measurement error variance is a function of the true variables. The focus is on latent variables investigated on the basis of questionnaires and estimated using item response theory models. Latent variable estimates are then treated as observed measures of the true variables. This leads to a two-stage estimation procedure which constitutes an alternative to a joint model for the outcome variable and the responses given to the questionnaire. Simulation studies explore the effect of ignoring the true error structure and the performance of the proposed method. Two illustrative examples concern achievement data of university students. Particular attention is given to the Rasch model.