Effects of conditionality on INDSCAL and ALSCAL weights

The role of conditionality in the INDSCAL and ALSCAL procedures is explained. The effects of conditionality on subject weights produced by these procedures is illustrated via a single set of simulated data. Results emphasize the need for caution in interpreting subject weights provided by these techniques.     

Goal attainment scaling: An idiosyncratic method to assess treatment effectiveness in agoraphobia

Goal attainment scaling (GAS) is an individually tailored way to measure treatment gains, using a highly standardized procedure. An advantage of the method is that it takes into account individual characteristics of the patients, and at the same time the data are suitable for quantitative analysis and comparable across patients. Despite the wide acceptance and use of the method in the evaluation of psychotherapy, data on its psychometric properties are rather scarce. In the current study, GAS was used as one of several outcome measures in a research project on the effectiveness of various treatments for panic disorder with agoraphobia. Guidelines for GAS are presented as well as data on the reliability and validity of the procedure. Results indicate that the procedure is reliable, valid, and sensitive to the improvement of patients during treatment. Comparison of GAS with standardized measures revealed considerable concordance, although the clinical end status of patients diverged somewhat dependent on the measure considered.     

A generalized majorization method for least souares multidimensional scaling of pseudodistances that may be negative

The usual convergence proof of the SMACOF algorithm model for least squares multidimensional scaling critically depends on the assumption of nonnegativity of the quantities to be fitted, called the pseudodistances. When this assumption is violated, erratic convergence behavior is known to occur. Three types of circumstances in which some of the pseudodistances may become negative are outlined: nonmetric multidimensional scaling with normalization on the variance, metric multidimensional scaling including an additive constant, and multidimensional scaling under the city-block distance model. A generalization of the SMACOF method is proposed to resolve the difficulty that is based on the same rationale frequently involved in robust fitting with least absolute residuals.I am grateful to Patrick Groenen and Rian van Blokland-Vogelesang for their help with some of the computations, and to the anonymous referees for their very useful comments.     

Effects of search cost on foraging and feeding: a three-component chain analysis

An experiment determined whether pigeons minimize number of key pecks per food delivery and maintain their baseline intake of food while key pecking on a three-component chain schedule. Pigeons at either 80% or 100% body weight obtained all their food during baseline and contingency sessions. During baseline sessions, pecks on the left and center keys had no consequences; each peck on the right key activated the feeder. During contingency sessions, pigeons key pecked on a three-component chain schedule simulating components of a foraging chain. In the search component either 3, 9 or 15 key pecks (varied parametrically across blocks of sessions) on the left key produced a stimulus on the middle key, indicating an encounter with either the low-cost prey (3 key pecks) or an equally probable high-cost prey (21 key pecks). In the procurement component the pigeon pecked either: (a) the left key once, thus returning to the search component, or (b) the middle key either 3 or 21 times, which activated the right response key. In the handling component one peck on the right key operated the feeder. The pigeons always procured the low-cost prey and minimized the number of key pecks per hopper by procuring the high-cost prey when the search-cost ratio was high (15 key pecks) but not when it was low (3 key pecks). All pigeons maintained their baselines of eating during contingency sessions by key pecking more frequently and eating more efficiently. The 80% body-weight birds produced higher overall rates of key pecking and eating. These results have implications for ecological theories of optimal foraging and for psychological theories of learned performance.     

Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis

An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution. Supported by The Netherlands Organization for Scientific Research (NWO) by grant nr. 030-56403 for the “PIONEER” project “Subject Oriented Multivariate Analysis” to the third author. We would like to thank the anonymous referees for their valuable remarks that have improved the quality of this paper.     

Evaluating the desirability of meals: an illustrative multiattribute decision analysis procedure to assess portfolios with interdependent items

This paper presents an exploratory study designed to address complex scaling problems in applying value/utility theory to measuring preferences over alternative combinations (or portfolios) of multiattributed items. This application considers meals served to nursing home residents as portfolios of food items and seeks to maximize meal appeal. We consider food interrelation and link single food measurements to overall meal measurements in the process of constructing meal desirability scales. We test the resulting scales to capture one expert's professional judgments and discuss issues raised in this specific application in the context of general portfolio evaluation problems. © 1998 John Wiley & Sons, Ltd.     

Risk-sensitive choice in humans as a function of an earnings budget

Risky choice in 3 adult humans was investigated across procedural manipulations designed to model energy-budget manipulations conducted with nonhumans. Subjects were presented with repeated choices between a fixed and a variable number of points. An energy budget was simulated by use of an earnings budget, defined as the number of points needed within a block of trials for points to be exchanged for money. During positive earnings-budget conditions, exclusive preference for the fixed option met the earnings requirement. During negative earnings-budget conditions, exclusive preference for the certain option did not meet the earnings requirement, but choice for the variable option met the requirement probabilistically. Choice was generally risk averse (the fixed option was preferred) when the earnings budget was positive and risk prone (the variable option was preferred) when the earnings budget was negative. Furthermore, choice was most risk prone during negative earnings-budget conditions in which the earnings requirement was most stringent. Local choice patterns were also frequently consistent with the predictions of a dynamic optimization model, indicating that choice was simultaneously sensitive to short-term choice contingencies, current point earnings, and the earnings requirement. Overall, these results show that the patterns of risky choice generated by energy-budget variables can also be produced by choice contingencies that do not involve immediate survival, and that risky choice in humans may be similar to that shown in nonhumans when choice is studied under analogous experimental conditions.     

Random effects diagonal metric multidimensional scaling models

By assuming a distribution for the subject weights in a diagonal metric (INDSCAL) multidimensional scaling model, the subject weights become random effects. Including random effects in multidimensional scaling models offers several advantages over traditional diagonal metric models such as those fitted by the INDSCAL, ALSCAL, and other multidimensional scaling programs. Unlike traditional models, the number of parameters does not increase with the number of subjects, and, because the distribution of the subject weights is modeled, the construction of linear models of the subject weights and the testing of those models is immediate. Here we define a random effects diagonal metric multidimensional scaling model, give computational algorithms, describe our experiences with these algorithms, and provide an example illustrating the use of the model and algorithms.We would like to thank J. Douglas Carroll for early consultation of this research, and Robert I. Jennrich for commenting on an earlier draft of this paper and for help on the computational algorithms. James O. Ramsay and Forrest W. Young were instrumental in providing the example data. This work was supported in part by National Institute of Mental Health grant 1 R43 MH57559-01. We would also like to thank the anonymous referees for comments that helped to clarify our work.     

Perceived organizational structure for teacher liking: the role of peers’ perceptions of teacher liking in teacher–student relationship quality,motivation, and achievement

Previous research has identified the role of perceived peer hierarchies, or organizational structures, in affecting students’ adjustment to school (Lease et al. 2003, Journal of Early Adolescence, 23, 194–217). The purpose of this study was to examine whether middle school classrooms can be described in terms of the perceived status individual students hold for who will and will not be ‘liked’ by the teacher. Specifically we examined: (1) Do students share a mutually agreed on representation, a perceived organizational structure, for describing relative status with their teacher? (2) Are teachers perceived as systematically favoring girls or boys? (3) Are peers’ perceptions of teacher liking associated with individual students’ social and academic motivation and relationship quality with teachers? (4) Are students identified by peers as ‘not liked’ at risk for long-term teacher rejection and underachievement? And, (5) What are the underlying criteria students use to judge teacher likeability? Data for this study were drawn from peer ratings from 516 (262 boys, 254 girls) middle school students in 20 classrooms. Findings indicate multidimensional scaling techniques can be used to map the ‘teacher-liking space,’ accounting for  > 90% of the variability in peers’ ratings of teacher likeability. Additionally, findings indicate perceived status in the teacher-liking space has consequences for students’ achievement and teacher relationship quality.