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.     

Is there a natural order for expressing semantic relations?

All languages rely to some extent on word order to signal relational information. Why? We address this question by exploring communicative and cognitive factors that could lead to a reliance on word order. In Study 1, adults were asked to describe scenes to another using their hands and not their mouths. The question was whether this home-made "language" would contain gesture sentences with consistent order. In addition, we asked whether reliance on order would be influenced by three communicative factors (whether the communication partner is permitted to give feedback; whether the information to be communicated is present in the context that recipient and gesturer share; whether the gesturer assumes the role of gesture receiver as well as gesture producer). We found that, not only was consistent ordering of semantic elements robust across the range of communication situations, but the same non-English order appeared in all contexts. Study 2 explored whether this non-English order is found only when a person attempts to share information with another. Adults were asked to reconstruct scenes in a non-communicative context using pictures drawn on transparencies. The adults picked up the pictures for their reconstructions in a consistent order, and that order was the same non-English order found in Study 1. Finding consistent ordering patterns in a non-communicative context suggests that word order is not driven solely by the demands of communicating information to another, but may reflect a more general property of human thought.     

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.     

Reliability and validity of the Padua Inventory in an Iranian population

In order to study the reliability and validity of the Padua Inventory (PI), its items were translated into Persian and then back-translated into English as suggested by Brislin, Lonner, Thorndike, Cross-cultural research methods, Wiley, New York, 1973. Using the translated version of the PI, two studies were carried out. The first study included 219 healthy participants selected from Shiraz city in Iran to examine the reliability and factorial structure of the PI via test-retest, internal consistency and principal component analysis methods. The results of this study showed good reliability for the PI and confirmed its factorial structure reported by previous studies. The second study included four groups of participants as follows: patients with obsessive-compulsive disorder (OCD), patients with anxiety disorders, patients with depressive disorder and normal individuals. The PI scores were able to differentiate between OCD patients and normal individuals, but failed to differentiate between neurotic and OCD patients. Two subscales of PI-R version of the PI (precision and washing) differentiated depressive and OCD patients.     

Gesture is at the cutting edge of early language development

Children who produce one word at a time often use gesture to supplement their speech, turning a single word into an utterance that conveys a sentence-like meaning ('eat'+point at cookie). Interestingly, the age at which children first produce supplementary gesture-speech combinations of this sort reliably predicts the age at which they first produce two-word utterances. Gesture thus serves as a signal that a child will soon be ready to begin producing multi-word sentences. The question is what happens next. Gesture could continue to expand a child's communicative repertoire over development, combining with words to convey increasingly complex ideas. Alternatively, after serving as an opening wedge into language, gesture could cease its role as a forerunner of linguistic change. We addressed this question in a sample of 40 typically developing children, each observed at 14, 18, and 22 months. The number of supplementary gesture-speech combinations the children produced increased significantly from 14 to 22 months. More importantly, the types of supplementary combinations the children produced changed over time and presaged changes in their speech. Children produced three distinct constructions across the two modalities several months before these same constructions appeared entirely within speech. Gesture thus continues to be at the cutting edge of early language development, providing stepping-stones to increasingly complex linguistic constructions.     

Psychometric Modeling of response speed and accuracy with mixed and conditional regression

Human performance in cognitive testing and experimental psychology is expressed in terms of response speed and accuracy. Data analysis is often limited to either speed or accuracy, and/or to crude summary measures like mean response time (RT) or the percentage correct responses. This paper proposes the use of mixed regression for the psychometric modeling of response speed and accuracy in testing and experiments. Mixed logistic regression of response accuracy extends logistic item response theory modeling to multidimensional models with covariates and interactions. Mixed linear regression of response time extends mixed ANOVA to unbalanced designs with covariates and heterogeneity of variance. Related to mixed regression is conditional regression, which requires no normality assumption, but is limited to unidimensional models. Mixed and conditional methods are both applied to an experimental study of mental rotation. Univariate and bivariate analyzes show how within-subject correlation between response and RT can be distinguished from between-subject correlation, and how latent traits can be detected, given careful item design or content analysis. It is concluded that both response and RT must be recorded in cognitive testing, and that mixed regression is a versatile method for analyzing test data.I am grateful to Rogier Donders for putting his data at my disposal.     

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.