Mixture Models of Categorization

Many currently popular models of categorization are either strictly parametric (e.g., prototype models, decision bound models) or strictly nonparametric (e.g., exemplar models) (F. G. Ashby & L. A. Alfonso-Reese, 1995, Journal of Mathematical Psychology, 39, 216-233). In this article, a family of semiparametric classifiers is investigated where categories are represented by a finite mixture distribution. The advantage of these mixture models of categorization is that they contain several parametric models and nonparametric models as a special case. Specifically, it is shown that both decision bound models (F. G. Ashby & W. T. Maddox, 1992, Journal of Experimental Psychology: Human Perception and Performance, 16, 598-612; 1993, Journal of Mathematical Psychology, 37, 372-400) and the generalized context model (R. M. Nosofsky, 1986, Journal of Experimental Psychology: General, 115, 39-57) can be interpreted as two extreme cases of a common mixture model. Furthermore, many other (semiparametric) models of categorization can be derived from the same generic mixture framework. In this article, several examples are discussed and a parameter estimation procedure for fitting these models is outlined. To illustrate the approach, several specific models are fitted to a data set collected by S. C. McKinley and R. M. Nosofsky (1995, Journal of Experimental Psychology: Human Perception and Performance, 21, 128-148). The results suggest that semi-parametric models are a promising alternative for future model development.     

The how and why of disagreement among perceivers: An exploration of person models

Impression formation has been conceptualized as a process whereby perceivers form person models of others, describing what the person is like and why (Park, DeKay, & Kraus, 1994). If they exist, person models could help explain why there appears to be little consensus in personality judgments; perceivers forming different models of a person would also view them differently on trait and affect ratings. Two experiments were conducted to test assumptions of the person-model paradigm using naturalistic targets. The structure of person models was examined, along with their content. Results demonstrated that three distinct person models emerge for each target and that the majority of perceivers can easily identify with one of the three models. We found that person models were valid across different groups of perceivers, and that the models differed in terms of masculinity-femininity and affect. Implications for the person model formulation process are discussed.     

The Influence of Communication Processes on Group Outcomes: Antithesis and Thesis

The influence of communication processes on group outcomes is discussed from two perspectives, one in which influence does not exist and one in which influence is central. Formal models for both perspectives are presented as a means of bracketing discussion of the role of communication processes in group outcomes. The implications of these models for future theorizing are discussed. The first of these two models is an extension of Hewes’s socioegocentric model (1986, 1996) . The second class of formal model, dual‐level connectionist models, integrates mental and communication processes to explain moment‐by‐moment communication behavior. This class of models is contrasted with important models of group influence that use atemporal aggregations of messages to predict group outcomes. Implications of dual‐level connections models for the role of “emergence” in group theorizing, the limitations of Markovian models of group communication research, and the decomposability of psychological and communication processes are elaborated.     

Theoretical and empirical review of multinomial process tree modeling

We review a current and popular class of cognitive models calledmultinomial processing tree (MPT) models. MPT models are simple, substantively motivated statistical models that can be applied to categorical data. They are useful as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. We formally describe the cognitive structure and parametric properties of the class of MPT models and provide an inferential statistical analysis for the entire class. Following this, we provide a comprehensive review of over 80 applications of MPT models to a variety of substantive areas in cognitive psychology, including various types of human memory, visual and auditory perception, and logical reasoning. We then address a number of theoretical issues relevant to the creation and evaluation of MPT models, including model development, model validity, discrete-state assumptions, statistical issues, and the relation between MPT models and other mathematical models. In the conclusion, we consider the current role of MPT models in psychological research and possible future directions.     

The Quality of Response Time Data Inference: A Blinded,Collaborative Assessment of the Validity of Cognitive Models

Psychonomic Bulletin & Review - Most data analyses rely on models. To complement statistical models, psychologists have developed cognitive models, which translate observed variables into...     

Intended and Unintended Reverberation of Traditional and Pro‐age Commercials as a Function of Viewer Age

Pro‐age advertising campaigns feature mature models, at least in part to reduce the depiction of unrealistic body ideals associated with the use of young models. The introduction of mature models into advertising campaigns may have hitherto unexamined effects on viewers' self‐esteem. We therefore compared the impact of mature and young models on women's levels of self‐esteem. Young adult and middle‐aged women were subtly exposed to young or pro‐age female models before completing an affective priming task designed to measure self‐esteem. As predicted, exposure influenced only appearance‐based self‐esteem, but not global self‐esteem. Furthermore, age congruency led to decreased self‐esteem, whereas age incongruency led to increased self‐esteem. Specifically, exposure to young models decreased young women's self‐esteem, just as exposure to mature models decreased middle‐aged women's self‐esteem. By contrast, exposure to mature models increased young women's self‐esteem, and exposure to young models increased middle‐aged women's self‐esteem. The implications for marketing campaigns are discussed. Copyright © 2013 John Wiley & Sons, Ltd.     

A taxonomy of item response models

A number of models for categorical item response data have been proposed in recent years. The models appear to be quite different. However, they may usefully be organized as members of only three distinct classes, within which the models are distinguished only by assumptions and constraints on their parameters. “Difference models” are appropriate for ordered responses, “divide-by-total” models may be used for either ordered or nominal responses, and “left-side added” models are used for multiple-choice responses with guessing. The details of the taxonomy and the models are described in this paper. The present study was supported in part by two postdoctoral fellowships awarded to Lynne Steinberg: an Educational Testing Service Postdoctoral Fellowship at ETS, Princeton, NJ and an NIMH Individual National Research Service Award at Stanford University, Stanford, CA. Helpful comments by the editor and three anonymous reviewers are gratefully acknowledged.     

An analysis of some conditions for representingN state Markov processes as general all or none models

Recently Markov learning models with two unidentifiable presolution success states, an error state, and an absorbing learned state, have been suggested to handle certain aspects of data better than the three state Markov models of the General All or None model type. In attempting to interpret psychologically, and evaluate statistically the adequacy of various classes of Markov models, a knowledge of the relationship between the classes of models would be helpful. This paper considers some aspects of the relationship between the class of General All or None models and the class of Stationary Absorbing Markov models withN error states, andM presolution success states.     

Computer simulations of global memory models

Computer simulation models of memory—including the so-called global memory models—have had and continue to have a profound impact on current memory research and theory. Unfortunately, no memory textbooks published before 1998 present these models to students. The arguments for and against these types of models are summarized along with reasons why the models should be taught at both the undergraduate and graduate levels. A set of freely available computer programs that can facilitate classroom presentation is then briefly described.     

Evidence for a Higher-Order ESEM Structure of ADHD in a Sample of Chinese Children

Exploratory structural equation modeling (ESEM) solutions have been proposed to represent the factor structures of attention-deficit/hyperactivity disorder (ADHD) in recent literature, yet no studies have assessed those structures in Chinese children. The primary aim of this study was to comprehensively examine the factor structures of the Chinese version of the ADHD Rating Scale-IV (ADHD RS-IV): Home Version. Data on 458 Chinese children aged 3–8 years (boys: 246; 54%) were used to test and compare eleven factor models: confirmatory factor analysis (CFA) models (one-factor, two-factor and three-factor), second-order CFA model, bifactor CFA models (two and three specific factors), ESEM models (two-factor and three-factor), second-order ESEM model, and bifactor ESEM models (two and three specific factors). The results showed that, overall, ESEM models displayed better fit than CFA models. Specifically, the second-order ESEM model with three first-order factors best represented of the ADHD factor structure in our sample. In addition, measurement invariance testing results showed that scalar invariance was established across gender, age and informant groups. Implications for future research are discussed.

     

Estimating Complex Measurement and Growth Models Using the R Package PLmixed

Measurement models, such as factor analysis and item response theory models, are commonly implemented within educational, psychological, and behavioral science research to mitigate the negative effects of measurement error. These models can be formulated as an extension of generalized linear mixed models within a unifying framework that encompasses various kinds of multilevel models and longitudinal models, such as partially nonlinear latent growth models. We introduce the R package PLmixed, which implements profile maximum likelihood estimation to estimate complex measurement and growth models that can be formulated within the general modeling framework using the existing R package lme4 and function optim. We demonstrate the use of PLmixed through two examples before concluding with a brief overview of other possible models.     

The Role of Negative Information in Distributional Semantic Learning

Distributional models of semantics learn word meanings from contextual co‐occurrence patterns across a large sample of natural language. Early models, such as LSA and HAL (Landauer & Dumais, 1997; Lund & Burgess, 1996), counted co‐occurrence events; later models, such as BEAGLE (Jones & Mewhort, 2007), replaced counting co‐occurrences with vector accumulation. All of these models learned from positive information only: Words that occur together within a context become related to each other. A recent class of distributional models, referred to as neural embedding models, are based on a prediction process embedded in the functioning of a neural network: Such models predict words that should surround a target word in a given context (e.g., word2vec; Mikolov, Sutskever, Chen, Corrado, & Dean, 2013). An error signal derived from the prediction is used to update each word's representation via backpropagation. However, another key difference in predictive models is their use of negative information in addition to positive information to develop a semantic representation. The models use negative examples to predict words that should not surround a word in a given context. As before, an error signal derived from the prediction prompts an update of the word's representation, a procedure referred to as negative sampling. Standard uses of word2vec recommend a greater or equal ratio of negative to positive sampling. The use of negative information in developing a representation of semantic information is often thought to be intimately associated with word2vec's prediction process. We assess the role of negative information in developing a semantic representation and show that its power does not reflect the use of a prediction mechanism. Finally, we show how negative information can be efficiently integrated into classic count‐based semantic models using parameter‐free analytical transformations.     

A test of torque-control and equilibrium-point models of motor control

Based upon predictions of equilibrium-point (EP) models of motor control, a recent article by Jaric et al. (1999) [Human Movement Sciences, 18, 49–66] reported that the peak velocity (PV) of an inertially loaded single degree-of-freedom elbow movement was not altered to a statistically distinguishable degree by the accuracy of the subject's expectation about the size of the load. They concluded that their results confirmed their EP models and were incompatible with what they described as torque-control models. A review of the literature and analysis of a more extensive set of data does not support that conclusion. To the contrary, if the actual load is heavier (or lighter) than expected, it is moved more slowly (or faster) than it would have been, had expectation matched reality. Torque-control models predict those consequences, EP models do not.     

The Relation Between Chosen Role Models and the Self-Esteem of Men and Women

This study was designed to investigate choice of role models and levels of self-esteem within a sample of college students (N = 120). Participants rated themselves and their chosen role models on 29 character traits, which allowed determination of the self-perceived likeness of the participant to their role models (difference score). The difference score was then correlated with four subtypes of self-esteem. As predicted, participants chose more same-sex than other-sex role models; women were more likely than men to choose other-sex role models. The results indicated that choice of same-sex, as opposed to other-sex role models, is not indicative of higher levels of self-esteem in general. However, self-perceived likeness of role model to participant is significantly related to self-esteem, particularly for women.     

Psychophysical study of numbers

Summary This paper develops three theoretical models to predict the numbers generated by Ss in an experiment described by Baird and Noma, 1975, Exp. II. The models (digit, base, and quarter) are each grounded on different assumptions about the process underlying number generation without the constraints of physical stimuli usually present in psychophysical tasks. Each of the models proved applicable to a restricted subrange of the physical continuum from 1–1000. A combination of models seems necessary to adequately predict number generation.This article is the second in a five-part series. Reprint requests should be sent to John C. Baird.     

Log-Multiplicative Association Models as Item Response Models

Log-multiplicative association (LMA) models, which are special cases of log-linear models, have interpretations in terms of latent continuous variables. Two theoretical derivations of LMA models based on item response theory (IRT) arguments are presented. First, we show that Anderson and colleagues (Anderson &; Vermunt, 2000; Anderson &; Böckenholt, 2000; Anderson, 2002), who derived LMA models from statistical graphical models, made the equivalent assumptions as Holland (1990) when deriving models for the manifest probabilities of response patterns based on an IRT approach. We also present a second derivation of LMA models where item response functions are specified as functions of rest-scores. These various connections provide insights into the behavior of LMA models as item response models and point out philosophical issues with the use of LMA models as item response models. We show that even for short tests, LMA and standard IRT models yield very similar to nearly identical results when data arise from standard IRT models. Log-multiplicative association models can be used as item response models and do not require numerical integration for estimation.     

Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.1978 Psychometric Society Presidential Address.This research has been supported by the Bank of Sweden Tercentenary Foundation under the project entitledStructural Equation Models in the Social Sciences, Karl G. Jöreskog, project director.     

Detection of Malingering of Psychiatric Disorder With the Personality Assessment Inventory: An Investigation of Criminal Defendants

582 Ss in 8 experiments viewed 1 of 9 films portraying models involved in achievement (Ach), affiliation (Aff), or neutral (Neu) activity. Ss who viewed Ach models after an interval of adaptation to the setting produced more TAT n Ach immediately after the film than other adapted Ss. Under other conditions, Ss who viewed Ach models produced significantly less n Ach than Ss who viewed non-Ach models. Results were ordered to a “subself” conception of personality organization and three theoretical propositions: (a) Models elicit fantasy thematically similar to their activity unless S is incompatibly preoccupied, (b) in which case models cause suppression of similar fantasy; but (c) in fantasy both elicitation and suppression are short-lived.     

The Effect of Team Mental Models Divergence on Creative Performance During Situational Changes

This study developed a model of team mental models’ influence on team adaptive performance at different stages. It proposed that mental models have different relationships with adaptive performance as a function of the performance stage when teams experience changes: early on (i.e., during situation assessment) more divergent mental models are needed for performance; later on (i.e., during plan execution) more convergent mental models are needed. The model was tested in an experiment with 33 teams (N= 99) faced with unforeseen change at task midway. Partially supporting the predictions of a divergence-convergence model, at situation assessment, teams that developed more dissimilar mental models attained a higher performance originality, but not higher efficiency or usefulness. However, at plan execution, team mental models’ convergence did not lead to higher performance. Implications for research on team mental models are discussed.