What do you think I think you think?: Strategic reasoning in matrix games

In reasoning about strategic interpersonal situations, such as in playing games, an individual's representation of the situation often includes not only information about the goals and rules of the game, but also a mental model of other minds. Often such mental models involve a hierarchy of reflexive reasoning commonly employed in social situations ("What do you think I think you think..."), and may be related to the developmental notion of 'theory of mind'. In two experiments, the authors formally investigate such interpersonal recursive reasoning in college-age adults within the context of matrix games. Participants are asked to predict the moves of another player (experimenter's confederate) in a two-choice, sequential-move game that may terminate at various stages with different payoffs for each player. Participants are also asked to decide optimally on their own moves based on the prediction made. Errors concerning the prediction, or translation of those predictions into decisions about one's action, were recorded. Results demonstrate the existence of a "default" mental model about the other player in the game context that is dynamically modified as new evidence is accumulated. Predictions about this other player's behavior are, in general, used consistently in decision-making, though the opponent tends to be modeled, by default, to behave in a myopic fashion not anticipating the participant's own action.     

Molecular analyses of the principal components of response strength

Killeen and Hall (2001) showed that a common factor called strength underlies the key dependent variables of response probability, latency, and rate, and that overall response rate is a good predictor of strength. In a search for the mechanisms that underlie those correlations, this article shows that (a) the probability of responding on a trial is a two-state Markov process; (b) latency and rate of responding can be described in terms of the probability and period of stochastic machines called clocked Bernoulli modules, and (c) one such machine, the refractory Poisson process, provides a functional relation between the probability of observing a response during any epoch and the rate of responding. This relation is one of proportionality at low rates and curvilinearity at higher rates.     

On normal theory based inference for multilevel models with distributional violations

Data in social and behavioral sciences are often hierarchically organized though seldom normal, yet normal theory based inference procedures are routinely used for analyzing multilevel models. Based on this observation, simple adjustments to normal theory based results are proposed to minimize the consequences of violating normality assumptions. For characterizing the distribution of parameter estimates, sandwich-type covariance matrices are derived. Standard errors based on these covariance matrices remain consistent under distributional violations. Implications of various covariance estimators are also discussed. For evaluating the quality of a multilevel model, a rescaled statistic is given for both the hierarchical linear model and the hierarchical structural equation model. The rescaled statistic, improving the likelihood ratio statistic by estimating one extra parameter, approaches the same mean as its reference distribution. A simulation study with a 2-level factor model implies that the rescaled statistic is preferable.This research was supported by grants DA01070 and DA00017 from the National Institute on Drug Abuse and a University of North Texas faculty research grant. We would like to thank the Associate Editor and two reviewers for suggestions that helped to improve the paper.     

Interval length and time-use by children with AD/HD: a comparison of four models

Predictions made by 4 competing models of time use by children with AD/HD were tested using a computerized version of the Matching Familiar Figures Test in 2 studies. In Study 1 teacher-identified AD/HD children (N = 10) and non-AD/HD controls (N = 10) completed the task under 3 different trial duration conditions (5, 10, and 15 s). In Study 2 the same task was completed by a group of children with a diagnosis of Hyperkinetic Disorder (N = 12) and controls (N = 12). In both studies AD/HD children performed poorly on trials of both 5- and 15-s duration but as well as controls on the 10-s trials. This quadratic function provided support for the State Regulation Deficit model of time use in AD/HD. The value of tailoring the temporal features of learning contexts to the conceptual style of AD/HD children is discussed.     

The "Natural" and the "Formal"

The paper presents an argument against a metaphysical conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. (More generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: the realm of the natural, constituted by the things of our empirical world, and the realm of the formal, constituted by the structures that we use as prisms to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic.     

Do Coping Styles Differ Across Sociocultural Groups? The Role of Measurement Equivalence in Making This Judgment

Cross-sociocultural group measurement equivalency is an important issue that generally has not been studied in the coping literature. Measurement equivalency of the COPE (Carver, Scheier, & Weintraub, 1989) was assessed across two sociocultural groups, a sample of 100 Anglo middle-class divorced mothers and a sample of 122 low-income Mexican American/Mexican immigrant mothers. A series of restrictive confirmatory factor analyses revealed that seven of the COPE's subscales may be measuring the same underlying construct across populations. However, scores derived from the subscales may not represent the same magnitude of the construct in these two groups. This study makes an important first step in furthering the understanding of coping strategies in low-income Mexican American/Mexican immigrant mothers. This study also illustrates the importance of testing for measurement equivalency before conducting comparative research in disparate populations.     

Likelihood inference on the underlying structure of IRT models

The assumptions underlying item response theory (IRT) models may be expressed as a set of equality and inequality constraints on the parameters of a latent class model. It is well known that the same assumptions imply that the parameters of the manifest distribution have to satisfy a more complicated set of inequality constraints which, however, are necessary but not sufficient. In this paper, we describe how the theory for likelihood-based inference under equality and inequality constraints may be used to test the underlying assumptions of IRT models. It turns out that the analysis based directly on the latent structure is simpler and more flexible. In particular, we indicate how several interesting extensions of the Rasch model may be obtained by partial relaxation of the basic constraints. An application to a data set provided by Educational Testing Service is used to illustrate the approach.We thank Dr. Gorman and Dr. Rogers of the Educational Testing Service for providing the data analyzed in Section 4. We also thank three reviewers for comments and suggestions.This revised article was published online in August 2005 with the PDF paginated correctly.     

What's measured is not necessarily managed: cognitive contingencies of organizational measurement

Organizational measurement is necessary for managing incremental improvements or change efforts. Some have argued that indicators of financial performance measure the past and should be joined by "lead" measures such as management development and customer relations, assumed to be drivers of performance. Approaches of "lead" measures have met criticism for not contributing to operational management. The present is an empirical case study where measures from a customer satisfaction survey and a management assessment instrument were analyzed and compared to actual measures of financial performance. The effects of measures obtained seem to depend on the interpretations and reflection taking place in the organization. The pursuit of "lead" indicators did not seem to drive results. Counter-intuitively, higher scores on these measures were related to poorer financial performance. The explication of and reflection on the underlying dynamic seemed to turn the development in a profitable direction.     

Translating Toulmin Diagrams: Theory Neutrality in Argument Representation

The Toulmin diagram layout is very familiar and widely used, particularly in the teaching of critical thinking skills. The conventional box-and-arrow diagram is equally familiar and widespread. Translation between the two throws up a number of interesting challenges. Some of these challenges (such as the relationship between Toulmin warrants and their counterparts in traditional diagrams) represent slightly different ways of looking at old and deep theoretical questions. Others (such as how to allow Toulmin diagrams to be recursive) are diagrammatic versions of questions that have already been addressed in artificial intelligence models of argument. But there are further questions (such as the relationships between refutations, rebuttals and undercutters, and the roles of multiple warrants) that are posed as a specific result of examining the diagram inter-translation problem. These three classes of problems are discussed. To the first class are addressed solutions based on engineering pragmatism; to the second class, are addressed solutions drawn from the appropriate literature; and to the third class, fuller exploration is offered justifying the approaches taken in developing solutions that offer both pragmatic utility and theoretical interest. Finally, these solutions are explored briefly in the context of the Araucaria system, showing the ways in which analysts can tackle arguments either using one diagrammatic style or another, or even a combination of the two.     

Racial Differences in Responses to the Caregiver Strain Questionnaire

The aim of this study was to examine differences in responses to the Caregiver Strain Questionnaire (CGSQ) between African American and White caregivers of children with emotional and behavioral challenges. Significant item- and scale-level differences were detected across groups with African Americans consistently reporting less strain. We examined whether these differences were more likely due to nonequivalent measurement than to real differences in the experience of caregiver strain. Confirmatory factor analysis showed that the model fit the data well for both racial groups, but there were some differences in structural components. Internal consistency was equivalent across the groups. In an examination of criterion validity, regression analyses showed that African American caregivers experienced a slower rate of increase in objective caregiver strain at a given increase in child internalizing problems. No other race differences were found in the regression analyses. In general, we conclude that the CGSQ can be useful for detecting caregiver strain and identifying family support needs for both White and African American caregivers. Differences across groups in reports of caregiver strain, however, call for more research on racial differences in the impact on the family of caring for a child with emotional and behavioral disorders.