Maximization of sums of quotients of quadratic forms and some generalizations

Monotonically convergent algorithms are described for maximizing six (constrained) functions of vectors x, or matricesX with columns x₁, ..., x _r . These functions are h₁(x)= _k (xA _kx)(xC _kx)^–1, H₁(X)= _k tr (XA _k X)(XC _k X)^–1, h₁(X)= _{k l} (x _l A _kx _l ) (x _l C _kx _l )^–1 withX constrained to be columnwise orthonormal, h₂(x)= _k (xA _kx)²(xC _kx)^–1 subject to xx=1, H₂(X)= _k tr(XA _kX)(XA_kX)(XC_kX)^–1 subject toXX=I, and h₂(X)= _{k l} (x _l A _kx _l )² (x _l C _kX _l )^–1 subject toXX=I. In these functions the matricesC _k are assumed to be positive definite. The matricesA _k can be arbitrary square matrices. The general formulation of the functions and the algorithms allows for application of the algorithms in various problems that arise in multivariate analysis. Several applications of the general algorithms are given. Specifically, algorithms are given for reciprocal principal components analysis, binormamin rotation, generalized discriminant analysis, variants of generalized principal components analysis, simple structure rotation for one of the latter variants, and set component analysis. For most of these methods the algorithms appear to be new, for the others the existing algorithms turn out to be special cases of the newly derived general algorithms.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the author. The author is obliged to Jos ten Berge for stimulating this research and for helpful comments on an earlier version of this paper.     

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.     

ANTECEDENT INFLUENCES ON BEHAVIOR DISORDERS

The influence of antecedent events on behavior disorders has been relatively understudied by applied behavior analysts. This lack of research may be due to a focus on consequences as determinants of behavior and a historical disagreement on a conceptual framework for describing and interpreting antecedent variables. We suggest that antecedent influences can be described using terms derived from basic behavioral principles and that their functional properties can be adequately interpreted as discriminative and establishing operations. A set of studies on assessment and treatment of behavior disorders was selected for review based on their relevance to the topic of antecedent events. These studies were categorized as focusing on assessment of antecedent events, antecedent treatments for behavior disorders maintained by either positive or negative reinforcement, and special cases of antecedent events in behavior disorders. Some directions for future research on antecedent influences in the analysis and treatment of behavior disorders are discussed.