Analyzing sequential categorical data: Individual variation in markov chains

Markov chains are probabilistic models for sequences of categorical events, with applications throughout scientific psychology. This paper provides a method for anlayzing data consisting of event sequences and covariate observations. It is assumed that each sequence is a Markov process characterized by a distinct transition probability matrix. The objective is to use the covariate data to explain differences between individuals in the transition probability matrices characterizing their sequential data. The elements of the transition probability matrices are written as functions of a vector of latent variables, with variation in the latent variables explained through a multivariate regression on the covariates. The regression is estimated using the EM algorithm, and requires the numerical calculation of a multivariate integral. An example using simulated cognitive developmental data is presented, which shows that the estimation of individual variation in the parameters of a probability model may have substantial theoretical importance, even when individual differences are not the focus of the investigator's concerns.Research contributing to this article was supported by B.R.S. Subgrant 5-35345 from the University of Virginia. I thank the DADA Group, Bill Fabricius, Don Hartmann, William Griffin, Jack McArdle, Ivo Molenaar, Ronald Schoenberg, Simon Tavaré, and several anonymous reviewers for their discussion of these points.     

Modeling item responses when different subjects employ different solution strategies

A model is presented for item responses when different subjects employ different strategies, but only responses, not choice of strategy, can be observed. Using substantive theory to differentiate the likelihoods of response vectors under a fixed set of strategies, we model response probabilities in terms of item parameters for each strategy, proportions of subjects employing each strategy, and distributions of subject proficiency within strategies. The probabilities that an individual subject employed the various strategies can then be obtained, along with a conditional estimate of proficiency under each. A conceptual example discusses response strategies for spatial rotation tasks, and a numerican example resolves a population of subjects into subpopulations of valid responders and random guessers.The first author's work was supported by Contract No. N00014-85-K-0683, project designation NR 150-539, from the Cognitive Science Program, Cognitive and Neural Sciences Division, Office of Naval Research. We are grateful to Murray Aitkin, Isaac Bejar, Neil Dorans, Frederiksen, and Marklyn Wingersky for their comments and suggestions, and to Alison Gooding, Maxine Kingston, Donna Lembeck, Joling Liang, and Kentaro Yamamoto for their assistance with Example 2.     

Toward a theory of verbal behavior

This paper is a reply to an accompanying set of six commentaries by Sidman; Hayes and Barnes; Schusterman, Kastak, and Reichmuth; Tonneau and Sokolowski; Lowenkron; and Moerk. Those commentaries were prompted by our article “On the Origins of Naming and Other Symbolic Behavior” (1996), which was, in turn, followed by 26 commentaries and a reply. In the course of the present reply, we further develop the naming account to embrace more complex verbal relations such as same, different, more, and less. We also examine what we see as the lack of conceptual coherence in equivalence theories, including relational frame theory, and the disparities between these accounts and the findings from empirical research.     

Intuitionistic Autoepistemic Logic

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.     

Theory in Child Psychosocial Treatment Research: Have It or Had It? A Pragmatic Alternative

In the area of child psychosocial intervention research, substantial progress in addressing challenging methodological issues has been made. In this article we suggest that continued movement forward requires maintaining a balance between methodological and theoretical issues, and that it would be advantageous to begin to think about matching advances in methodological sophistication by similar advances in theoretical sophistication. The need to advance our understanding of theoretical issues is especially important in light of the challenges raised by postmodernism, particularly as these challenges relate to knowledge development. We discuss these challenges and describe how a pragmatic orientation may be a useful way to respond to them. We also describe how a pragmatic orientation has been useful in our work in developing, implementing and evaluating psychosocial interventions for children with phobic and anxiety disorders.     

Multiple information sources in interceptive timing

This study was designed to explore the limitations of tau (τ) as an explanatory construct for the timing of interceptive action. This was achieved by examining the effects of environmental structure and binocular vision on the timing of the grasp in a simple one-handed catch. In two experiments, subjects were required to catch luminous balls of different diameters (4, 6, 8 and 10 cm) in a completely darkened room. In the first experiment the influence of the presence vs. absence of an environmental background structure (both under monocular viewing) was tested, and in the second experiment the influence of monocular vs. binocular vision was examined. It was found that irrespective of the presence of environmental structure, an effect of ball size occurred in the monocular viewing conditions. That is, in monocular viewing conditions the grasp was initiated and completed earlier for the larger balls as compared to the smaller ones, while in the binocular viewing condition subjects behaved in accordance with a constant time to contact strategy: no effects of ball size were found. It is concluded that under binocular viewing a binocular information source is used, while in the monocular viewing condition a lower order information source like image size or image velocity is probably involved.     

Reviews

Russell,Robert John, Murphy, Nancey and Peacocke, Arthur R. (eds) Chaos and Complexity: Scientific Perspectives on Divine Action
Tigue, John W. The Transformation of Consciousness in Myth: Integrating the Thought of Jung and Campbell     

Chaos and God's Abundance: An Ontology of Variety in the Divine Life

The primordial chaos of Genesis 1 may be understood as the Pandemonium Tremendum (or PT), the infinite field of variety or abundance within God. The concept of variety is taken from Claude Shannon's theory of communication. Especially significant is Shannon's notion that communication is the limitation of variety through decision processes. In one model of the divine life suggested by the theory, the PT is the boundless source of potential reaped by an agential God in the act of creation as a communication process. Other models for creation include the PT in a biased mode and creatures themselves as decision agents.