A maximin model for IRT-based test design with practical constraints

A maximin model for IRT-based test design is proposed. In the model only the relative shape of the target test information function is specified. It serves as a constraint subject to which a linear programming algorithm maximizes the information in the test. In the practice of test construction, several demands as linear constraints in the model. A worked example of a text construction problem with practical constraints is presented. The paper concludes with a discussion of some alternative models of test construction.The authors are indebted to Jos J. Adea for suggesting Equation 17 as a Simplification of an earlier version of this constraint. This research was suuorted in part by a grant from the Dutch Organization for Research (NWO) through the Foundation for Psychological and Psychonomic Research in the Netherlands (Psychon).     

On perceiving morality and potency: Social values and the effects of person perception in a give-some dilemma

The present study examines a two-person give-some dilemma characterized by the conflict between the pursuit of own benefits (not giving) and collective benefits (giving). The major purpose was two-fold: (a) to examine the effects of person perceptions manipulated along the dimensions of morality (goodness) and potency (strength) on co-operation, and (b) to examine whether pre-existing differences between individuals in their preference for specific self-other outcome distributions (social values) would modify the effects of person perception. First, we predicted and found that across social values the degree of co-operative behaviour increased as a linear function of the extent to which the other was seen as moral. Concerning the perceptions in terms of potency, we found a significant quadratic trend; another seen as moderate on potency elicited more co-operative behaviour than another seen as either high or low on potency. These effects of person perception were not moderated by social value. More interesting was the finding that even though persons classified as pro-social (co-operators and altruists) and pro-self (individualists and competitors) held about the same expectation about the magnitude of another's co-operation, pro-socials behaved more co-operatively than pro-selfs. This suggests that under certain conditions behavioural differences between pro-socials and pro-selfs are not conditional upon expectational differences between those two social values.     

An efficient algorithm for PARAFAC of three-way data with large numbers of observation units

The CANDECOMP algorithm for the PARAFAC analysis ofn×m×p three-way arrays is adapted to handle arrays in whichn>mp more efficiently. For such arrays, the adapted algorithm needs less memory space to store the data during the iterations, and uses less computation time than the original CANDECOMP algorithm. The size of the arrays that can be handled by the new algorithm is in no way limited by the number of observation units (n) in the data.The authors are obliged to Jos ten Berge for his comments on an earlier version of this paper. The research of Henk A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Using aptitude measurements for the optimal assignment of subjects to treatments with and without mastery scores

For assigning subjects to treatments the point of intersection of within-group regression lines is ordinarily used as the critical point. This decision rule is critized and, for several utility functions and any number of treatments, replaced by optimal monotone, nonrandomized (Bayes) rules. Both treatments with and without mastery scores are considered. Moreover, the effect of unreliable criterion scores on the optimal decision rule is examined, and it is illustrated how qualitative information can be combined with aptitude measurements to improve treatment assignment decisions. Although the models in this paper are presented with special reference to the aptitude-treatment interaction problem in education, it is indicated that they apply to a variety of situations in which subjects are assigned to treatments on the basis of some predictor score, as long as there are no allocation quota considerations.     

Similarity of attitudes and instrumentality as determinants of aggression by policemen

The influences of two determinants of aggression were investigated by means of a two by two factorial design. Aggression was operationally defined in terms of the amount and intensity of obnoxious sounds which the subject delivered to the confederate while the latter was trying to perform a task involving estimation of distances. In order to manipulate the first independent variable one half of the group of subjects were led to believe that the victim was someone who had many attitudes similar to their own. The other subjects thought they had to cope with a partner whose attitudes were dissimilar. The second independent variable was manipulated by suggesting to one half of the group of subjects that they would be able to earn increasing sums of money (up to a fixed maximum) depending on the loudness of sounds they were prepared to deliver to their partner. In the non-reward condition money was not mentioned. The subjects were young policemen. The data showed a strong effect of the similarity variable, with significantly more aggression being shown to a dissimilar partner. However, external reward did not lead to a clear increase of aggression. In the discussion attention is given to the relevance of these data to the problem of control of violence in our society.     

Compathy or Physical Empathy: Implications for the Caregiver Relationship

In this article a case is made for the importance of a previously overlooked phenomenon, physical empathy orcompathy,defined as the physical manifestation of caregiver distress that occurs in the presence of a patient in physical pain or distress. According to the similarity of a caregiver's response to the original symptoms, there can be four types of compathetic response: identical, initiated, transferred, and converted. Controlling for the compathetic response may involve narrowing one's focus and/or changing caregiver attitudes. Finally, we argue that while the compathetic response may be beneficial to the caregiving relationship, enabling the provision of appropriate and adequate humane treatment and care, the caregiver must at times shield against the compathetic response in order to provide care.     

Observed-score equating as a test assembly problem

A set of linear conditions on item response functions is derived that guarantees identical observed-score distributions on two test forms. The conditions can be added as constraints to a linear programming model for test assembly that assembles a new test form to have an observed-score distribution optimally equated to the distribution on an old form. For a well-designed item pool and items fitting the IRT model, use of the model results into observed-score pre-equating and prevents the necessity ofpost hoc equating by a conventional observed-score equating method. An empirical example illustrates the use of the model for an item pool from the Law School Admission Test.The authors are most indebted to Norman D. Verhelst for suggesting Proposition 4 and its proof, to the Law School Admission Council (LSAC) for making available the data set, and to Wim M. M. Tielen for his computational assistance.     

Bayesian item selection criteria for adaptive testing

Owen (1975) proposed an approximate empirical Bayes procedure for item selection in computerized adaptive testing (CAT). The procedure replaces the true posterior by a normal approximation with closed-form expressions for its first two moments. This approximation was necessary to minimize the computational complexity involved in a fully Bayesian approach but is no longer necessary given the computational power currently available for adaptive testing. This paper suggests several item selection criteria for adaptive testing which are all based on the use of the true posterior. Some of the statistical properties of the ability estimator produced by these criteria are discussed and empirically characterized.Portions of this paper were presented at the 60th annual meeting of the Psychometric Society, Minneapolis, Minnesota, June, 1995. The author is indebted to Wim M. M. Tielen for his computational support.     

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate. The findings reported in the literature are actually inconsistent; some studies emphasized the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the coefficient of variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially, however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and non-numerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.