PREG: Elements of a Model of Question Asking

PREG is a conceptual model of human question asking. The model contains a set of production rules that specify the conditions under which children and adults ask questions when they read expository texts. The essence of PREG's question-asking mechanism is the existence of discrepancies between the representation of text information and the reader's world knowledge, with a mediating role of pragmatics and metacognition. Both the explicit text and the world knowledge are represented in the form of a conceptual graph structure. Comparisons between text representations and readers' knowledge are carried out by examining the 3 components of conceptual graph structures: words, statements, and links between statements. Some of the predictions of PREG were tested on a corpus of questions generated by 8th-grade and 12th-grade students who read short scientific texts. These predictions were empirically supported when assessed on 2 criteria. First, the model was sufficient because it was able to account for nearly all of the questions produced by the students. Second, the model was discriminating; when signal detection analyses were applied to the data, PREG could identify the conditions in which particular classes of questions are or are not generated.     

Sequential processing in comprehension of hierarchical graphs

Hierarchical graphs represent the relationships between non-numerical entities or concepts (like computer file systems, family trees, etc). Graph nodes represent the concepts and interconnecting lines represent the relationships. We recorded participants' eye movements while viewing such graphs to test two possible models of graph comprehension. Graph readers had to answer interpretive questions, which required comparisons between two graph nodes. One model postulates a search and a combined search-reasoning stage of graph comprehension (two-stage model), whereas the second model predicts three stages, two stages devoted to the search of the relevant graph nodes and a separate reasoning stage. A detailed analysis of the eye movement data provided clear support for the three-stage model. This is in line with recent studies, which suggest that participants serialize problem solving tasks in order to minimize the overall processing load. Copyright © 2004 John Wiley & Sons, Ltd.     

Correspondence analysis and association models constrained by a conditional independence graph

The manner in which the conditional independence graph of a multiway contingency table effects the fitting and interpretation of the Goodman association model (RC) and of correspondence analysis (CA) is considered.Estimation of the row and column scores is presented in this context by developing a unified framework that includes both models. Incorporation of the conditional independence constraints inherent in the graph may lead to equal or additive scores for the corresponding marginal tables, depending on the topology of the graph. An example of doubly additive scores in the analysis of a Burt subtable is given.Thanks are due to anonymous referees who substantially improved the original draft of this paper.     

Graph‐Framing Effects in Decision Making

This study manipulated the graphical representation of options by framing the physical characters in figures and found that preferences could be affected even when the words and numbers of the problem were constant. Based on attribute substitution theory and an equate‐to‐differentiate approach, we proposed a two‐process model of graph‐framing effects. In the first mental process, the graph‐editing process, the physical features (e.g., distance, size) represented in the graph are visually edited, and the perceived numerical difference between the options is judged based on its physical features. The second mental process, the preferential choice process, occurs by an equate‐to‐differentiate approach in which people seek to equate the difference between options on the dimension on which the difference is smaller, thus leaving the greater other‐dimensional difference to be the determinant of the final choice. Four experiments were tested for graph‐framing effects. Experiment 1 found a graph‐framing effect in coordinate graphs resting on the (de)compression of the scales employed in the figures. Experiment 2 revealed additional graph‐framing effects in other question scenarios and showed that preference changes were mediated by perceived numerical distances. Experiment 3 further confirmed the presence of graph‐framing effects in sector graphs similar to those found in coordinate ones. Experiment 4 suggested that such graph‐framing effects could be eliminated when logical processing (e.g., introducing a mathematical operation before a choice task) was encouraged. This paper discusses related research and a possible substrate basis for graph‐framing effects. Copyright © 2011 John Wiley & Sons, Ltd.     

Latent Class Models for Diary Method Data: Parameter Estimation by Local Computations

The increasing use of diary methods calls for the development of appropriate statistical methods. For the resulting panel data, latent Markov models can be used to model both individual differences and temporal dynamics. The computational burden associated with these models can be overcome by exploiting the conditional independence relations implied by the model. This is done by associating a probabilistic model with a directed acyclic graph, and applying transformations to the graph. The structure of the transformed graph provides a factorization of the joint probability function of the manifest and latent variables, which is the basis of a modified and more efficient E-step of the EM algorithm. The usefulness of the approach is illustrated by estimating a latent Markov model involving a large number of measurement occasions and, subsequently, a hierarchical extension of the latent Markov model that allows for transitions at different levels. Furthermore, logistic regression techniques are used to incorporate restrictions on the conditional probabilities and to account for the effect of covariates. Throughout, models are illustrated with an experience sampling methodology study on the course of emotions among anorectic patients. Frank Rijmen was partly supported by the Fund for Scientific Research Flanders (FWO).     

Extending task analytic models of graph-based reasoning: A cognitive model of problem solving with Cartesian graphs in ACT-R/PM

Models of graph-based reasoning have typically accounted for the variation in problem solving performance with different graph types in terms of a task analysis of the problem relative to the particular visual properties of each graph type [e.g., Human Computer Interaction 8 (1993) 353; Proceedings of the Twenty-first Annual Conference of the Cognitive Science Society. Lawrence Erlbaum Associates, Mahwah, NJ (1999) 531]. This approach has been used to explain response time and accuracy differences in experimental situations where data are averaged over experimental conditions. An experiment is reported in which participants’ eye movements were recorded while they were solving various problems with different graph types. The eye movement data revealed fine grained fixation patterns that are not captured by current analyses based on optimal fixation sequences. It is argued that these patterns reveal the effects of working memory limitations during the time course of problem solving. An ACT-R/PM model of the experiment is described in which a similar pattern of eye fixations is produced as a natural consequence of the decay in activation of perceptual chunks over time.     

Graph theory of tower tasks

The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be projected onto the graph. The mathematical model is also at the base of a computerized test tool to administer various types of tower tasks.     

图表加工的理论模型

图表作为一种以图形和表格记录、展示和传递信息的表征方式已得到广泛应用。图表加工是指人们对图表所呈现信息的认知加工。文章首先说明并简要评述图表加工的规则模型、认知过程模型和计算模型,然后介绍2004年提出的层次框架模型,最后进行小结并指出未来的研究方向     

Multidimensional scaling and threshold graphs

A set of data has a Guttman scale if and only if a corresponding graph is a threshold graph. In this paper we relate the concepts of disjunctive and conjuctive Guttman scales, and biorder dimension to the threshold dimension of a graph. For those graphical properties that can be tested in polynomial time, the comparable Guttman scaling techniques can be performed in polynomial time. Fast algorithms are provided for computing a Guttman scale, and the conjunctive and disjunctive dimension of data with no 3-crowns. We define an extended Guttman scale to indicate strength of agreement, dominance, etc., and show that this, too, exists if and only if a particular graph is a threshold graph.     

The discrimination of graphical elements

A model is proposed to account for how people discriminate quantities shown in pie charts and divided bar graphs (i.e. which proportion is larger, A or B?). The incremental estimation model assumes that an observer sequentially samples from the available perceptual features in a graph. The relative effectiveness of sampled perceptual features is represented by the spread of probability distributions, in the manner of signal detection theory. The model's predictions were tested in two experiments. Participants took longer with pies than divided bars and longer with non‐aligned than aligned proportions in Experiment 1. In Experiment 2, participants took longer with divided bars than pies when graphs were of unequal size. Generally, graphical formats producing longer response times incurred a greater time penalty when the difference between proportions was reduced. These results were in accordance with the model's predictions. Implications for graphical display design are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Studies on the balancing,the minimal balancing,and the minimum balancing processes for social groups with planar and nonplanar graph structures

Balancing processes of social groups which transform an unbalanced group to a balanced one by changing the interpersonal relations in the group are characterized in terms of signed graphs. The graphs are given by categorizing the (interpersonal) relations within groups as positive or negative. A balanced state of a group is defined as one in which all the circuits of the graph have a positive sign, and the other cases are called unbalanced states. First, we show that a balancing process for a signed graph (changing the signs of its lines) is decomposed into that for each of the block components of the graph. Second, we classify signed graphs as planar and nonplanar. For the planar cases, we define the dual graph of a planar signed graph, and the balancing processes are characterized by specified sets of lines of the graph. According to the characterization, effective algorithms to derive the minimal and the minimum balancing processes are proposed. For the nonplanar cases, the balancing processes are characterized in terms of adjacency matrices of nonplanar signed graphs by introducing the notion of sign vectors. The characterization results in effective algorithms to derive the minimal and the minimum balancing processes. These discussions are also extended to the case where interpersonal relations have their own directions.     

Pattern redundancy and detection in very short-term memory

A tachistoscopically presented target letter is detected better in a background of redundant items than in nonredundant material. The present experiment extended this finding by showing that detection rate increased systematically across three levels of background letter redundancy. A conclusion based on the earlier findings was that a serial process of letters in memory could not account for the effects of background redundancy on detection accuracy. Contrary to this conclusion, the present analysis showed that detection for semiredundant displays was successfully predicted by two variants of a serial process model. One model assumed that the scan of a letter is faster when the letter is the same as any prior letter scanned in the matrix. The other model assumes that nonredundant letters are processed serially and that redundant letters are processed all at once, i.e., in parallel.     

Plot units and narrative summarization

In order to summarize a story, it is necessary to access a high level analysis of the story that highlights its central concepts. A technique of memory representation based on plot units appears to provide a rich foundation for such an analysis. Plot units are conceptual structures that overlap with each other when a narrative is cohesive. When overlapping intersections between plot units are interpreted as arcs in a graph of plot units, the resulting graph encodes the plot of the story. Structural features of the graph then reveal which concepts are central to the story, and which concepts are peripheral. Plot unit analysis is currently being investigated as a processing strategy for narrative summarization by both computer simulation and psychological experiments.     

What dot clusters and bar graphs reveal: subitizing is fast counting and subtraction

In two studies, we found that dot enumeration tasks resulted in shallow-sloped response time (RT) functions for displays of 1-4 dots and steep-sloped functions for displays of 5-8 dots, replicating results implicating subitizing and counting processes for low and high ranges of dots, respectively. Extracting number from a specific type of bar graph within the same numerical range produced a shallow-sloped but scallop-shaped RT function. Factor analysis confirmed two independent subranges for dots, but all bar graph values defined a unitary factor. Significantly, factor scores and asymmetries both showed correlations of bar graph recognition to dot subitizing but not to dot counting, strongly suggesting that subitizing was used in both enumeration of low numbers of dots and bar graph recognition. According to these results, subitizing appears to be a nonverbal process operating flexibly in either additive or subtractive fashion on analog quantities having spatial extent, a conclusion consistent with a fast-counting model of subitizing but not with other models of the subitizing process.     

Response latencies in the yes/no detection task: An assessment of two basic models

Two general forms of model for response latency in the yes no signal detection task are described and their predictions examined in the light of experimental data. One model supposes a latency function along the detection axis and the other supposes that a count is made of multiple observation, Experiment I looks at the auditory detection situation with short observation interval, but the results are generally equixocal, although the latency function model gives a simpler interpretation Other results are then discussed, particularly those of Gescheider et al (1969). and it is concluded that an attempt must be made to replicate the results of Carterette et al (1965) for the extended observation interval detection experiment. This is achieved in Experiment II. and the obtained order of mean latencies is then examined in terms of the models The counting model appears by far the more suitable for this situation.     

决策中的图形框架效应

决策框架效应作为一种违背不变性原则的非理性偏差, 已经得到研究的广泛证实。本研究突破了传统研究中主要由语言描述引发框架效应的限制, 从图形表征这一新的视角对图形框架效应做了深入探讨。本研究共包括6个实验, 通过操纵选项在不同图形表征版本中物理属性差异的突出性, 发现在表达信息不变的情况下, 人们判断和决策的偏好会受到图形表征的影响, 即出现了图形框架效应。研究结果表明, 图形框架效应普遍存在于各种决策情境以及各种图形表征方式中。基于属性替代理论和齐当别原则, 我们提出了一种解释图形框架效应内部作用机制的两阶段心理加工模型--图形编辑的齐当别模型(The Graph-edited Equate-to-differentiate Model, GEM)。     

Shedding light on the graph schema: Perceptual features versus invariant structure

Most theories of graph comprehension posit the existence of a graph schema to account for people’s prior knowledge of how to understand different graph types. The graph schema is, however, a purely theoretical construct: No empirical studies have explicitly examined the nature of the graph schema. We sought to determine whether graph schemas are based on perceptual features or on a common invariant structure shared between certain graph types. We isolated the process of activating the graph schema by presenting the graphs to participants in pure and mixed blocks. Any differences in reaction time between the blocks could be attributed to loading the appropriate schema. Results from a series of experiments using five types of graphs suggest that graph schemas are based on the graphical framework, a common invariant structure among certain types of graphs.     

Graph matching approach and generalized median graph for automatic labeling of cortical sulci with parallel and distributed algorithms

The human brain cortex is very complex structure containing folds (gyri) and fissures (sulci) that were the subject of our study in this paper. The sulcus is one of the most important features in order to know the different functions areas of the brain. The exact identification of sulci on human brain using MRI images is helpful in many studies and applications related to brain diseases and human behavior. Automatic labeling of cortical sulci with all this complexity and inter-subject variability, this is considered non-trivial task. In this paper, we have proposed a new graph based approach of automatic labeling of cortical sulci with parallel and distributed algorithms using graph matching and generalized median graph. The graph matching is very important in many studies and applications such as pattern recognition and classification. The generalized median graph of a set of graphs is a way to represent a set of graphs by a comprehensive graph that minimizes the sum of the distances to all graphs. We have used the characteristics of shape, orientation and location to describe the sulci. The results that we have obtained prove that our approach is accurate and acceptable in this field which uses the graph matching for automatic labeling of cortical sulci.     

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.     

When Are Graphs Worth Ten Thousand Words? An Expert-Expert Study

This study analyzes the interpretive activities of scientists related to familiar and unfamiliar graphs. The analyses show that when scientists were familiar with a graph, they read it transparently and thereby leapt beyond the material basis to the thing the graph is said to be about. In contrast, when scientists were less familiar with the particular graphs, their reading turned out to be a complex iterative process. In this process, scientists linked graphs to possible worlds by means of complex inferences. They checked whether an expression referred to the actual properties of the worldly things the graphs are speaking of. They also checked graphical expressions themselves on the basis of certain circumstances. In a few instances, the scientists abandoned all attempts in interpreting the graphs and classified them as meaningless. Grounded in the data, a 2-stage model is proposed. This model accounts for different levels of reading graphs observed in this study.