“Minimax length links” of a dissimilarity matrix and minimum spanning trees

A theorem is proved stating that the set of all minimax links, defined as links minimizing, over paths, the maximum length of links in any path connecting a pair of objects comprising nodes in an undirected weighted graph, comprise the union of all minimum spanning trees of that graph. This theorem is related to methods of fitting network models to dissimilarity data, particularly a method called Pathfinder due to Schvaneveldt and his colleagues, as well as to single linkage clustering, and results concerning the relationship between minimum spanning trees and single linkage hierarchical trees.Acknowledgments: The author thanks Phipps Arabie, Lawrence J. Hubert, and K. Christoph Klauer for a number of helpful suggestions and comments on various aspects of this paper.     

Models for measurement,precision, and the nondichotomization of graded responses

It is common in educational, psychological, and social measurement in general, to collect data in the form of graded responses and then to combine adjacent categories. It has been argued that because the division of the continuum into categories is arbitrary, any model used for analyzing graded responses should accommodate such action. Specifically, Jansen and Roskam (1986) enunciate ajoining assumption which specifies that if two categoriesj andk are combined to form categoryh, then the probability of a response inh should equal the sum of the probabilities of responses inj andk. As a result, they question the use of the Rasch model for graded responses which explicitly prohibits the combining of categories after the data are collected except in more or less degenerate cases. However, the Rasch model is derived from requirements of invariance of comparisons of entities with respect to different instruments, which might include different partitions of the continuum, and is consistent with fundamental measurement. Therefore, there is a strong case that the mathematical implication of the Rasch model should be studied further in order to understand how and why it conflicts with the joining assumption. This paper pursues the mathematics of the Rasch model and establishes, through a special case when the sizes of the categories are equal and when the model is expressed in the multiplicative metric, that its probability distribution reflects the precision with which the data are collected, and that if a pair of categories is collapsed after the data are collected, it no longer reflects the original precision. As a consequence, and not because of a qualitative change in the variable, the joining assumption is destroyed when categories are combined. Implications of the choice between a model which satisfies the joining assumption or one which reflects on the precision of the data collection considered are discussed.     

Perceptual unit formation in simple motion patterns

The present study investigated the proximal constraints that determine perceptual unit formation under minimal stimulus conditions. Projections of three moving dots, which could form two possible two-dot configurations, were presented to naive observers. In a forced-choice situation, their task was to report which two-dot configuration was perceived as a distinct perceptual unit. The results showed that common motions (arbitrary translations and rigid rotations in the frontoparallel plane) have stronger grouping power as compared to different relative motions (expansions/contractions, or simultaneous expansions/contractions and deformations in the frontoparallel plane). It was found that proximal changes of distances between elements in two-dot structures reduce grouping power. Changes of proximal directions, however, did not affect unit formation in two-dot structures at all. The effect of vector algebraic combinations on grouping power in three-dot strutures was also investigated. Evidently, visual vector analysis splits up motion combinations into their constituents, and in come cases this contributes to additive effects.     

An empirical couple typology based on differentiation

Both spouses of 100 married, heterosexual couples completed the Personal Authority in the Family System Questionnaire (PAFS-Q). A cluster analysis of the couples' scores on the four intimacy and fusion scales of the PAFS-Q produced four clusters that were meaningfully distinct in the patterns of differentiation of the wives and husbands. Couples comprising these clusters are described in terms of intergenerational theories of family interaction.This paper is based on the master's thesis of the first author submitted to the Graduate School of Texas Woman's University. A presentation based on this work was given at the 1988 annual convention of the Southwestern Psychological Association, Tulsa, Oklahoma. The authors thank Glenda Peters and Joe Natale for their contributions to the preparation of this paper. A more extensive report of the methodology and results of this study can be obtained from the second author.     

Teaching problem solving skills to teachers-in-training: An analogue experimental analysis of three methods

This analogue study sought to determine the relative effectiveness of different instructional methods for teaching problem solving skills to teachers-in-training. Three instructional conditions (didactic, didactic + modeling, and didactic + modeling with rehearsal/feedback) and a control condition were compared on measures of problem identification and problem analysis. Results indicated that the didactic + modeling and didactic + modeling with rehearsal/feedback conditions were superior to didactic training in teaching problem-solving skills. Discussed are possible explanations for differences between the instructional conditions, the implications of these findings, limitations of this study, and directions for further teacher-training research in problem solving.     

Maternal attitudes during pregnancy predict mother-infant physical proximity six months after birth

The purpose of this study was to develop an instrument for assessing maternal attitudes. Three photographs representing infants or mother-infant dyads were presented to 26 mothers in the second half of pregnancy and six months after birth. Nine mothers were clinical cases, seventeen mothers were nonpathological controls. Thirty-three semantic categories were used to code the mothers' responses to the pictures. Mothers' responses were coded independently by two researchers. The factor analysis of the codes yielded an ‘attraction to, vs rejection of, children’ factor. Compared with the control group, the mean factor score of the clinical group was significantly lower, i. e. reflected less attraction (p < 0.01). To study the relation between the attraction factor and the physical proximity of mothers and infants, 21 of these mother-infant dyads were videotaped in a semi-structured play interaction six months after birth. Recordings were coded independently by two researchers for various indices of proximity (spatial proximity, kisses, embraces, touches). The factor analysis of the codes yielded a factor contrasting distant vs close and tender interaction. A significant correlation was found between the attraction scores of pregnant women and the proximity scores of mother-infant interaction (r = 0.46; p < 0.05). These results suggest that this instrument is useful in assessing maternal attitudes of psychiatrically disturbed pregnant women and that maternal attitudes of pregnant women are significant predictors of physical proximity in motherinfant interaction at the end of the first semester.     

中学高年级学生作文能力结构特征的研究

对４９０名高三学生的１８个作文变量的测验资料,运用高阶因素分析法概括出中学高年级学生作文能力结构的三个群因素。第一个是作文能力的因素,它是作文认知活动的各种能力相互作用的一种协调发展程度。第二个是由词汇量、造句等能力组合成的词语能力,它是作文能力结构中的一个活跃因素。第三个是词汇量因素,它独立存在于一阶、二阶因素中,表明它是不同阶段认知活动的一个不可缺的因素。     

NONCONTINGENT DELIVERY OF ARBITRARY REINFORCERS AS TREATMENT FOR SELF-INJURIOUS BEHAVIOR

Results of recent research have shown that noncontingent reinforcement (NCR) can be effective in reducing the frequency of behavior problems. In typical NCR applications, the reinforcer that is responsible for behavioral maintenance (as demonstrated through a functional analysis) no longer follows occurrences of the target behavior but instead is delivered according to a time-based schedule. Thus, it is unclear if NCR would be effective if the target behavior continued to be reinforced or if arbitrary reinforcers (i.e., those irrelevant to behavioral maintenance) were substituted for the maintaining reinforcers in the NCR procedure. In this study, 2 individuals whose self-injurious behavior (SIB) was maintained by positive reinforcement were exposed to conditions in which arbitrary and maintaining reinforcers were withheld and were delivered either contingently or noncontingently. Results indicated that noncontingent delivery of arbitrary reinforcers was effective in reducing SIB even though occurrences of SIB produced access to the maintaining reinforcer. These results suggest that (a) arbitrary reinforcers may sometimes be substituted for maintaining reinforcers, (b) an important component of NCR procedures is alteration of a behavior's establishing operation, and (c) NCR with arbitrary reinforcers might therefore be effective when maintaining reinforcers cannot be identified or withheld during the course of treatment.     

THE USE OF POSITIVE AND NEGATIVE REINFORCEMENT IN THE TREATMENT OF ESCAPE-MAINTAINED DESTRUCTIVE BEHAVIOR

We identified 3 clients whose destructive behavior was sensitive to negative reinforcement (break from tasks) and positive reinforcement (access to tangible items, attention, or both). In an instructional context, we then evaluated the effects of reinforcing compliance with one, two, or all of these consequences (a break, tangible items, attention) when destructive behavior produced a break and when it did not (escape extinction). For 2 clients, destructive behavior decreased and compliance increased when compliance produced access to tangible items, even though destructive behavior resulted in a break. For 1 client, extinction was necessary to reduce destructive behavior and to increase compliance. Subsequently, when the schedule of reinforcement for compliance was faded for all clients, destructive behavior was lower and fading proceeded more rapidly when compliance produced multiple functional reinforcers (i.e., a break plus tangible items or attention) and destructive behavior was on extinction. The results are discussed in terms of the effects of relative reinforcement value and extinction on concurrent operants.     

TOWARD THE DEVELOPMENT OF STRUCTURED CRITERIA FOR INTERPRETATION OF FUNCTIONAL ANALYSIS DATA

Using functional analysis results to prescribe treatments is the preferred method for developing behavioral interventions. Little is known, however, about the reliability and validity of visual inspection for the interpretation of functional analysis data. The purpose of this investigation was to develop a set of structured criteria for visual inspection of multielement functional analyses that, when applied correctly, would increase interrater agreement and agreement with interpretations reached by expert consensus. In Study 1, 3 predoctoral interns interpreted functional analysis graphs, and interrater agreement was low (M = .46). In Study 2, 64 functional analysis graphs were interpreted by a panel of experts, and then a set of structured criteria were developed that yielded interpretive results similar to those of the panel (exact agreement = .94). In Study 3, the 3 predoctoral interns from Study 1 were trained to use the structured criteria, and the mean interrater agreement coefficient increased to .81. The results suggest that (a) the interpretation of functional analysis data may be less reliable than is generally assumed, (b) decision-making rules used by experts in the interpretation of functional analysis data can be operationalized, and (c) individuals can be trained to apply these rules accurately to increase interrater agreement. Potential uses of the criteria are discussed.