Acceleration model in the heterogeneous case of the general graded response model

A new model, called acceleration model, is proposed in the framework of the heterogenous case of the graded response model, based on processing functions defined for a finite or enumerable number of steps. The model is expected to be useful in cognitive assessment, as well as in more traditional areas of application of latent trait models. Criteria for evaluating models are proposed, and soundness and robustness of the acceleration model are discussed. Graded response models based on individual choice behavior are also discussed, and criticisms on model selection in terms of fitnesses of models to the data are also given.This research was supported by the Office of Naval Research (N00014-90-J-1456).     

A note on the equivalence of the graded response model and the sequential model

This paper concerns items that consist of several item steps to be responded to sequentially. The item scoreX is defined as the number of correct responses until the first failure. Samejima's graded response model states that each steph=1,...,m is characterized by a parameterb _h , and, for a subject with ability, Pr(Xh; )=F(–b _h ). Tutz's general sequential model associates with each step a parameterdh, and it states that Pr(Xh;)= _r ^=1h G(–d _r ). Tutz's (1991, 1997) conjectures that the models are equivalent if and only ifF(x)=G(x) is an extreme value distribution. This paper presents a proof for this conjecture.     

Testing between the TRACE model and the fuzzy logical model of speech perception

The TRACE model of speech perception (McClelland & Elman, 1986) is contrasted with a fuzzy logical model of perception (FLMP) (Oden & Massaro, 1978). The central question is how the models account for the influence of multiple sources of information on perceptual judgment. Although the two models can make somewhat similar predictions, the assumptions underlying the models are fundamentally different. The TRACE model is built around the concept of interactive activation, whereas the FLMP is structured in terms of the integration of independent sources of information. The models are tested against test results of an experiment involving the independent manipulation of bottom-up and top-down sources of information. Using a signal detection framework, sensitivity and bias measures of performance can be computed. The TRACE model predicts that top-down influences from the word level influence sensitivity at the phoneme level, whereas the FLMP does not. The empirical results of a study involving the influence of phonological context and segmental information on the perceptual recognition of a speech segment are best described without any assumed changes in sensitivity. To date, not only is a mechanism of interactive activation not necessary to describe speech perception, it is shown to be wrong when instantiated in the TRACE model.     

Equilibria of the Rescorla-Wagner model

The Rescorla-Wagner model has been a leading theory of animal causal induction for nearly 30 years, and human causal induction for the past 15 years. Recent theories (especially Psychol. Rev. 104 (1997) 367) have provided alternative explanations of how people draw causal conclusions from covariational data. However, theoretical attempts to compare the Rescorla-Wagner model with more recent models have been hampered by the fact that the Rescorla-Wagner model is an algorithmic theory, while the more recent theories are all computational. This paper provides a detailed derivation of the long-run behavior of the Rescorla-Wagner model under a wide range of parameters and experimental setups, so that the model can be compared with computational theories. It also shows that the model agrees with competing theories on a wider range of cases than had previously been thought. The paper concludes by showing how recently suggested modifications of the Rescorla-Wagner model impact the long-run behavior of the model.     

Fitting the factor analysis model

When the covariance matrix (p×P) does not satisfy the formal factor analysis model for m factors, there will be no factor matrix (p×m) such that =(-) is diagonal. The factor analysis model may then be replaced by a tautology where is regarded as the covariance matrix of a set of residual variates. These residual variates are linear combinations of discarded common factors and unique factors and are correlated. Maximum likelihood, alpha and iterated principal factor analysis are compared in terms of the manner in which is defined, a maximum determinant derivation for alpha factor analysis being given. Weighted least squares solutions using residual variances and common variances as weights are derived for comparison with the maximum likelihood and alpha solutions. It is shown that the covariance matrix defined by maximum likelihood factor analysis is Gramian, provided that all diagonal elements are nonnegative. Other methods can define a which is nonGramian even when all diagonal elements are nonnegative.A modified version of this paper forms part of a Ph.D. thesis submitted to the University of South Africa.Presently at the National Institute for Personnel Research, South Africa.     

Expanding the rasch model to a general model having more than one dimension

The well-known Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model has retained the property of the specific objectivity of the Rasch model. For a restricted variant of the model, maximum likelihood estimates of its parameters and a statistical test of the model are given. The results of an application to a mathematics test involving six components are described.     

A probabilistic threshold model: Analyzing semantic categorization data with the Rasch model

According to the Threshold Theory (Hampton, 1995, 2007) semantic categorization decisions come about through the placement of a threshold criterion along a dimension that represents items' similarity to the category representation. The adequacy of this theory is assessed by applying a formalization of the theory, known as the Rasch model (Rasch, 1960; Thissen & Steinberg, 1986), to categorization data for eight natural language categories and subjecting it to a formal test. In validating the model special care is given to its ability to account for inter- and intra-individual differences in categorization and their relationship with item typicality. Extensions of the Rasch model that can be used to uncover the nature of category representations and the sources of categorization differences are discussed.     

A relation between a between-item multidimensional IRT model and the mixture rasch model

Two generalizations of the Rasch model are compared: the between-item multidimensional model (Adams, Wilson, and Wang, 1997), and the mixture Rasch model (Mislevy & Verhelst, 1990; Rost, 1990). It is shown that the between-item multidimensional model is formally equivalent with a continuous mixture of Rasch models for which, within each class of the mixture, the item parameters are equal to the item parameters of the multidimensional model up to a shift parameter that is specific for the dimension an item belongs to in the multidimensional model. In a simulation study, the relation between both types of models also holds when the number of classes of the mixture is as small as two. The relation is illustrated with a study on verbal aggression. Frank Rijmen was supported by the Fund for Scientific Research Flanders (FWO). This research is also funded by the GOA/2000/02 granted from the KU Leuven. We would like to thank Kristof Vansteelandt for providing the data of the study on verbal aggression.     

Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model

In this paper, we reconsider the merits of unfolding solutions based on loss functions involving a normalization on the variance per subject. In the literature, solutions based on Stress-2 are often diagnosed to be degenerate in the majority of cases. Here, the focus lies on two frequently occurring types of degeneracies. The first type typically locates some subject points far away from a compact cluster of the other points. In the second type of solution, the object points lie on a circle. In this paper, we argue that these degenerate solutions are well fitting and informative. To reveal the information, we introduce mixtures of plots based on the ideal point model of unfolding, the vector model, and on the signed distance model. In addition to a different representation, we provide a new iterative majorization algorithm to optimize the average squared correlation between the distances in the configuration and the transformed data per individual. It is shown that this approach is equivalent to minimizing Kruskal’s Stress-2.This revised article was published online in August 2005 with the PDF paginated correctly.     

The adaptive change model: an advance on the transtheoretical model of change

The author proposed a hypothetical model of change, the adaptive change model (ACM), to advance the current conceptualization and operationalization of the transtheoretical model of change (TTM; D. Grimley, J. Prochaska, W. Velicer, M. Blais, & C. DiClemente, 1994; J. Prochaska, 1979; J. Prochaska & C. DiClemente, 1984). He used exploratory factor analysis to identify items contributing to 2 sets of factors defining the Adaptive Change Questionnaire (T. Bowles, 2001). The factors were consistent for both clinical (n = 222) and nonclinical (n = 194) respondents. The first set of factors defined the process of change and included Openness to Opportunity, Visualization, Planning, Action, and Closure. The second set of factors described the factors that support change and included Social Support, Inner Drive, and Negative Emotions. Through analysis of gender effects, the author found that men scored significantly and slightly higher than did women on Openness to Opportunity, Visualization, and Inner Drive. There were no interactions involving gender and clinical status. Discriminant function analysis predicting clinical status on the basis of the 8 factors placed 80% of respondents in the correct category. The author discusses the relevance of the ACM in comparison with the characteristics of the TTM.