A multinomial modeling analysis of the recognition-failure paradigm

The recognition-failure paradigm has received much theoretical consideration, especially the Tulving-Wiseman function and its exceptions. We show that the Tulving-Wiseman function does a poor job of accounting for the data, both when its fit is measured with a model-based, goodness-of-fit statistic and when a logically equivalent reformulation of the function is compared with data. We then present a simple multinomial model based on retrieval-independence theory that is capable of measuring storage and retrieval processes in recognition failure. The model is used to conduct a meta-analysis of the recognition-failure paradigm, and shows that violations of the Tulving-Wiseman function occur under conditions in which weak storage is coupled with strong retrieval. In addition, if storage and retrieval are assumed to be positively correlated across conditions, the model produces a theoretically motivated, alternative equation to the Tulving-Wiseman function that provides a virtually identical fit to the data.     

A mathematical analysis of a natural class of partitions of a graph

Any finite graph (nondirected, no loops) can be coupled with its complementary graph producing what we term a completed graph. This paper studies completed graphs in the context of a structural concept called stratification that is motivated by theoretical work in social psychology and sociology. A completed graph is stratified in case its node (vertex) set can be divided into two nonempty subsets with exactly one of the two types of ties holding between every pair of nodes from distinct sets. A completed graph is totally stratified in case every one of its nontrivial completed subgraphs is stratified. The first part of the paper relates the concept of stratification to the familiar graph property of connectedness. In particular, a completed graph is totally stratified if and only if it does not have a four point completed subgraph that is connected in both the original graph relation and its complementary relation. Using the concept of stratification, completed graphs can be decomposed uniquely into taxonomic structures, that is, nested sets of partitions. An algorithm for the decomposition based on the work with the concept of stratification is developed. The relationship between the notion of stratification and the ideas in balance theory is examined, and stratification is viewed as a generalization of Davis' notion of clustering. It turns out that the concepts of clique, status, and structural equivalence used throughout the social networks literature can be defined in an interesting way for completed graphs. Cliques are sets of nodes with similar internal links and statuses are sets of nodes with similar external links. Structurally equivalent sets are both cliques and statuses. The concepts of status and structural equivalence are closely related to the decomposition algorithm. In particular, for any totally stratified completed graph, the set of all statuses and the set of all maximal structurally equivalent sets can be generated by mathematical operations performed on the taxonomic decomposition of the completed graph. Finally some of our resuls are informally related to the blockmodeling approach to analyzing social network data discussed in several previous Journal of Mathematical Psychology articles.     

The statistical analysis of a thurstonian model for rating chess players

This paper formalizes and provides static and dynamic estimators for a scaling model for rating chess players. The model was suggested by the work of Arpad Elo, the inventor of the chess rating system in current use by both the United States and international chess federations. The model can be viewed as a Thurstone Case V model that permits draws (ties). A related model based on a linear approximation is also analyzed. In the chess application, possibly changing ability parameters are estimated sequentially from sparse data structures that often involve many fewer than $\text{M(M ? 1)}\text{2}$ observations on the M players to the rated. In contrast, psychological applications of paired-comparison scaling generally use models with no draw provision to estimate static parameters from a systematically obtained data structure such as a replicated “round robin” involving all M entities to be scaled. In the paper, both static and sequential estimators are provided and evaluated for a number of different data structures. Sampling theory for the estimators is developed. The application of rating systems to track temporally changing ability parameters may prove useful in many areas of psychology.     

Structural analysis of subjective categorical data

A general approach to the analysis of subjective categorical data is considered, in which agreement matrices of two or more raters are directly expressed in terms of error and agreement parameters. The method provides focused analyses of ratings from several raters for whom ratings have measurement error distributions that may induce bias in the evaluation of substantive questions of interest. Each rater's judgment process is modeled as a mixture of two components: an error variable that is unique for the rater in question as well as an agreement variable that operationalizes the true values of the units of observation. The statistical problems of identification, estimation, and testing of such measurement models are discussed.The general model is applied in several special cases. The most simple situation is that underlying Cohen's Kappa, where two raters place units into unordered categories. The model provides a generalization and systematization of the Kappa-idea to correct for agreement by chance. In applications with typical research designs, including a between-subjects design and a mixed within-subjects, between-subjects design, the model is shown to disentangle structural and measurement components of the observations, thereby controlling for possible confounding effects of systematic rater bias. Situations considered include the case of more than two raters as well as the case of ordered categories. The different analyses are illustrated by means of real data sets.The authors wish to thank Lawrence Hubert and Ivo Molenaar for helpful and detailed comments on a previous draft of this paper. Thanks are also due to Jens Möller und Bernd Strauß for the data from the 1992 Olympic Games. We thank the editor and three anonymous reviewers for valuable comments on an earlier draft.     

Individual differences and the all-or-none vs incremental learning controversy

This paper provides an analysis of the ability of the all-or-none and incremental learning frameworks augmented with individual difference assumptions to account for several standard all-or-none learning demonstrations. The paper allows the one element model (OEM) and the linear operator model (LOM) to have a completely arbitrary individual difference distribution. Among the results are: 1. the LOM can not account for either the Rock replacement studies or Bower's constancy of the error given error curve. 2. The OEM can account for Rock's and Bower's results only if there are no individual differences. 3. No independent responding scheme can jointly predict Rock's and Bower's results. 4. A beta distribution on the learning rate allows the LOM to achieve a close fit to at most one of Rock's and Bower's results. 5. An RT⁽ⁿ⁾ experiment can not rule out an independent responding scheme for any n, n ≥ 1.     

Early exposure to violence,domestic violence,attachment representations,and marital adjustment

The present study investigates the effects of violent experiences in childhood on current domestic violence and marital adjustment, using adult attachment theory as a conceptual framework. A nonclinical sample of 644 Canadian adults in long‐term romantic relationships completed measures of adult romantic attachment, conflict tactics scales, and dyadic adjustment. Structural equation modeling revealed that early experiences of violence affect adults' intimate violence directly and indirectly through anxiety over abandonment and avoidance of intimacy. The actor–partner interdependence model illustrated the importance of early exposure to violence in predicting both partners' attachment representations, intimate violence, and couple adjustment. Findings are discussed with reference to the clinical issues surrounding minor violence against the intimate partner.     

A context-free language for binary multinomial processing tree models

This paper provides a new formalization for the class of binary multinomial processing tree (BMPT) models, and theorems for the class are developed using the formalism. MPT models are a popular class of information processing models for categorical data in specific cognitive paradigms. They have a recursive structure that is productively described with the tools of formal language and computation theory. We provide an axiomatization that characterizes BMPT models as strings in a context-free language, and then we add model-theoretic axioms and definitions to interpret the strings as parameterized probabilistic models for categorical data. The language for BMPT models is related to the Full Binary Tree language, a well-studied context-free language. Once BMPT models are viewed from the perspective of the Full Binary Tree language, a number of theoretical and computational results can be developed. In particular, we have a number of results concerning the enumerations of BMPT models as well as the identifiability of subclasses of these models.