A connectionist model of a continuous developmental transition in the balance scale task

A connectionist model of the balance scale task is presented which exhibits developmental transitions between ‘Rule I’ and ‘Rule II’ behavior [Siegler, R. S. (1976). Three aspects of cognitive development. Cognitive Psychology,8, 481–520.] as well as the ‘catastrophe flags’ seen in data from Jansen and van der Maas [Jansen, B. R. J., & van der Maas, H. L. J. (2001). Evidence for the phase transition from Rule I to Rule II on the balance scale task. Developmental Review, 21, 450–494]. The model extends a connectionist model of this task [McClelland, J. L. (1989). Parallel distributed processing: Implications for cognition and development. In R. G. M. Morris (Ed.), Parallel distributed processing: Implications for psychology and neurobiology (pp. 8–45). Oxford: Clarendon Press] by introducing intrinsic variability into processing and by allowing the network to adapt during testing in response to its own outputs. The simulations direct attention to several aspects of the experimental data indicating that children generally show gradual change in sensitivity to the distance dimension on the balance scale. While a few children show larger changes than are characteristic of the model, its ability to account for nearly all of the data using continuous processes is consistent with the view that the transition from Rule I to Rule II behavior is typically continuous rather than discrete in nature.     

On the language specificity of basic number processing: transcoding in a language with inversion and its relation to working memory capacity

Transcoding Arabic numbers from and into verbal number words is one of the most basic number processing tasks commonly used to index the verbal representation of numbers. The inversion property, which is an important feature of some number word systems (e.g., German einundzwanzig [one and twenty]), might represent a major difficulty in transcoding and a challenge to current transcoding models. The mastery of inversion, and of transcoding in general, might be related to nonnumerical factors such as working memory resources given that different elements and their sequence need to be memorized and manipulated. In this study, transcoding skills and different working memory components in Austrian (German-speaking) 7-year-olds were assessed. We observed that inversion poses a major problem in transcoding for German-speaking children. In addition, different components of working memory skills were differentially correlated with particular transcoding error types. We discuss how current transcoding models could account for these results and how they might need to be adapted to accommodate inversion properties and their relation to different working memory components.     

Changing explicit and implicit attitudes: The case of self-esteem

Three experiments investigated predictions concerning asymmetrical patterns of implicit and explicit self-esteem change. Specifically, we investigated the influence of knowledge about the own self that is momentarily salient as well as the influence of affective valence associated with the self in memory on implicit and explicit self-esteem. The latter was induced by evaluative conditioning, the former by directed thinking about oneself. We found that while evaluative conditioning changed implicit but not explicit self-esteem (Experiment 1), thinking about the own self altered explicit but not implicit self-esteem (Experiment 2). Moreover, in a third experiment, it could be shown that the effect of evaluative conditioning can spill over to the explicit level when participants are asked to focus on their feelings prior to making their self-report judgements (Experiment 3). Implications of our results are discussed in terms of recent controversies regarding dual-process models of attitudes and associative versus propositional modes of information processing.     

When head is tempered by heart: Heart rate variability modulates perception of other-blame reducing anger

This study examined the relationship between heart rate variability (HRV), as an index of individual differences in emotion regulation, and perception of other-blame, as a mechanism of anger induction. The physiological responses were recorded while subjects read a story from a computer screen. The story narrated a negative event in self-referred way -dismissal from a job as the result of a colleague’s action- under conditions of intentionality versus non-intentionality. Cognitive and emotional variables were assessed by questionnaire immediately after the physiological test. The resulting structural model supports the conclusion that HRV exerts its regulatory influence directly on perception of other-blame rather than on emotion. In situations of intentionality, individuals with higher HRV make less extreme evaluation of the offender’s blame, versus those with lower HRV, thus leading to a reduction in anger reaction. These results suggest that HRV is a direct index of cognitive rather than emotional regulation.     

The Mental Model Theory of Conditionals: A Reply to Guy Politzer

This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.     

Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

This article presents a developmental dual-process theory of the understanding of conditionals that integrates Evans’ heuristic–analytic theory within the revised mental model theory of conditional proposed by Barrouillet, Gauffroy, and Lecas (2008). According to this theory, the interpretation of a conditional sentence is driven by unconscious and implicit heuristic processes that provide individuals with an initial representation that captures its meaning by representing the cases that make it true. This initial model can be enriched with additional models (a process named fleshing out within the mental model theory) through the intervention of conscious and demanding analytic processes. Being optional, these processes construct representations of cases that are only compatible with the conditional, leaving its truth-value indeterminate when they occur. Because heuristic processes are relatively immune to developmental changes, while analytic processes strongly develop with age, the initial model remains stable through development whereas the number of additional models that can be constructed increases steadily. Thus, the dual-process mental model theory predicts in which cases conditionals will be deemed true, indeterminate, or false and how these cases evolve with age. These predictions were verified in children, adolescents and adults who were asked to evaluate the truth value and the probability of several types of conditionals. The results reveal a variety of developmental trajectories in the way different conditionals are interpreted, which can all be accounted for by our revised mental model theory.     

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.     

A Bayesian Semiparametric Latent Variable Model for Mixed Responses

In this paper we introduce a latent variable model (LVM) for mixed ordinal and continuous responses, where covariate effects on the continuous latent variables are modelled through a flexible semiparametric Gaussian regression model. We extend existing LVMs with the usual linear covariate effects by including nonparametric components for nonlinear effects of continuous covariates and interactions with other covariates as well as spatial effects. Full Bayesian modelling is based on penalized spline and Markov random field priors and is performed by computationally efficient Markov chain Monte Carlo (MCMC) methods. We apply our approach to a German social science survey which motivated our methodological development. We thank the editor and the referees for their constructive and helpful comments, leading to substantial improvements of a first version, and Sven Steinert for computational assistance. Partial financial support from the SFB 386 “Statistical Analysis of Discrete Structures” is also acknowledged.     

Rule transition on the balance scale task: a case study in belief change

For various domains in proportional reasoning cognitive development is characterized as a progression through a series of increasingly complex rules. A multiplicative relationship between two task features, such as weight and distance information of blocks placed at both sides of the fulcrum of a balance scale, appears difficult to discover. During development, children change their beliefs about the balance scale several times: from a focus on the weight dimension (Rule I) to occasionally considering the distance dimension (Rule II), guessing (Rule III), and applying multiplication (Rule IV; Siegler, 1981). Because of the detailed empirical findings the balance scale task has become a benchmark task for computational models of proportional reasoning. In this article, we present a large empirical study (N = 420) of which the findings provide a challenge for computational models. The effect of feedback and the effect of individually adapted training items on rule transition were tested for children using Rule I or Rule II. Presenting adapted training items initiates belief revision for Rule I but not for Rule II. The experience of making mistakes (by providing feedback) induces a change for both Rule I and Rule II. However, a delayed posttest shows that these changes are preserved after 2 weeks only for children using Rule I. We conclude that the transition from Rule I to Rule II differs from the transition from Rule II to a more complex rule. Concerning these empirical findings, we will review performance of computational models and the implications for a future belief revision model.

It is one Thing, to show a Man that he is in an Error, and another, to put him in possession of Truth. John Locke

     

Community types and mental health: a multilevel study of local environmental stress and coping

Research has found that neighborhood structural characteristics can influence residents' mental health. Few studies, however, have explored the proximal reasons behind such influences. This study investigates how different types of communities, in terms of environmental stressors (social and physical disorder and fear of crime) and social resources (informal ties and formal organizational participation), affect well-being, depression, and anxiety in adult residents. Data are from a survey of 412 residents nested in 50 street blocks. Block stressors and resources were cluster analyzed to identify six block types. After controlling for several individual- and block-level characteristics, results from multilevel models suggest that in communities facing relatively few stressors, higher levels of formal participation are associated with better mental health. Because high levels of formal participation were not found in communities with higher levels of stressors, the impact of participation in such contexts could not be examined. However, results suggest that in communities where stressors are more common, isolation from neighbors may have a protective effect on mental health.