The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

A critical review of theS/L reliability index

The meaning and properties of a commonly used index of reliability, S/L,were examined critically. It was found that the index does not reflect any conventional concept of reliability. When used for an identical behavioral observation session, it is not statistically correlated with other reliability indices. Within an observation session, the standardizing measure of Lis beyond the control of the investigator. Furthermore, the reason for the choice of Las the standard is unclear. The role of chance agreement in S/Lis not known. The exact interpretation of the index depends on which observer reports L.Overall the conceptual and mathematical meaning of S/Lis dubious. It is suggested that the S/Lindex should not be used until its nature is shown to be a measure of reliability. Other approaches such as the intraclass correlations and generalizability coefficients should be used instead.The authors are indebted to Johnny Matson for his critique of an earlier version of this paper.     

AN INDEX FOR ASSESSING WEIGHT CHANGE IN CHILDREN: WEIGHT/HEIGHT RATIOS1

Weight and height data from two studies were recomputed, and original data were computed using a Weight Index formula that accounts for the interaction of actual weight/height changes in growing children and compares this ratio with that of normed weight/height ratios for equal-aged children. Recomputing the data of one study showed that the Weight Index is a more sensitive procedure for assessing long-term behavioral treatment of obesity for girls than weight alone. Recomputing the data of a second study showed that the Weight Index formula is consistent for boys and girls and is a more sensitive procedure for assessing long-term effects of a variety of medical treatments for obesity than the Ponderal Index or weight alone. Computation of the data for 17 “normal” children in a preschool class showed a zero Weight Index score before and after a six-month interval elapsed without treatment. The procedure may be useful in assessing ponderosity or anorexia over intervals of six months or more with growing children or difference between actual and normed weight over shorter intervals.     

On the optimality of the simultaneous redundancy transformations

The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.     

不同空间构型下邻近性对视觉工作记忆中相似性效应的影响

相似性对视觉工作记忆表征的促进被称为相似性效应。以相似项目间的距离和是否插入其他项目改变邻近性,并操纵记忆项空间构型有序性,探讨邻近性对相似性效应的影响。结果发现,不同空间构型和邻近性条件下相似项目的记忆正确率高于非相似项目;在空间构型有序下,相似项目距离远时,插入其他项目时的相似性效应值低于不插入,而空间构型无序下未发现显著差异。这表明相似性促进视觉工作记忆表征,空间构型在邻近性对相似性效应的影响中起重要作用。     

Processes of similarity judgment

Similarity underlies fundamental cognitive capabilities such as memory, categorization, decision making, problem solving, and reasoning. Although recent approaches to similarity appreciate the structure of mental representations, they differ in the processes posited to operate over these representations. We present an experiment that differentiates among extant structural accounts of similarity in their ability to account for patterns of similarity ratings. These data pose a challenge for transformation-based models and all but one mapping-based model, the Similarity as Interactive Activation and Mapping (SIAM) model of similarity.     

Female physical attractiveness in Britain and Malaysia: a cross-cultural study

Two purported cues to perceived female physical attractiveness are body mass index (BMI) and body shape as measured by the waist-to-hip ratio (WHR). This study examined the relative contribution of both cues in several culturally socio-economically distinct populations. Six hundred and eighty-two participants from Britain and Malaysia were asked to rate a set of images of real women with known BMI and WHR. The results showed that BMI is the primary determinant of female physical attractiveness, whereas WHR failed to emerge as a significant predictor. The results also showed that there were significant differences in preferences for physical attractiveness along a gradient of socio-economic development, with urban participants preferring images of women with significantly lower BMIs than their rural counterparts. The findings are discussed in terms of evolutionary psychological explanations of mate selection, and sociocultural theory, which emphasises the learning of preferences for body sizes in social and cultural contexts.     

内隐联想测验中他人重要性对自我心理表征的影响

联合采用联想匹配任务和内隐联想测验（IAT）任务,考察了自我—他人分类中的他人重要性对自我—高奖赏相似性的影响。研究将中性的几何图形与自我、不同重要性的他人（实验一为陌生人,实验二为朋友）建立联结,并将自我（暂时建立联结的图形）高奖赏联合任务与自我低奖赏联合任务下的反应差异（即IAT值）作为自我—高奖赏相似性的指标,结果表明：（1）联想匹配任务中自我和朋友以及自我和陌生人之间都存在显著的自我优势效应;（2）IAT任务中,自我和高奖赏只在他人为朋友的自我—他人分类判断时才具有相似性,而他人为陌生人时二者不具有相似性。这说明他人重要性改变了自我的心理表征。     

Nonparametric IRT: Testing the bi-isotonicity of isotonic probabilistic models (ISOP)

Nonparametric tests for testing the validity of polytomous ISOP-models (unidimensional ordinal probabilistic polytomous IRT-models) are presented. Since the ISOP-model is a very general nonparametric unidimensional rating scale model the test statistics apply to a great multitude of latent trait models. A test for the comonotonicity of item sets of two or more items is suggested. Procedures for testing the comonotonicity of two item sets and for item selection are developed. The tests are based on Goodman-Kruskal's gamma index of ordinal association and are generalizations thereof. It is an essential advantage of polytomous ISOP-models within probabilistic IRT-models that the tests of validity of the model can be performed before and without the model being fitted to the data. The new test statistics have the further advantage that no prior order of items or subjects needs to be known.     

Risk and Prisoner's Dilemma: A Reinterpretation of Coombs' Re‐parameterization

We propose a model to measure risk in a prisoner's dilemma based on Coombs' (1973) re‐parameterization of the game as an individual risk decision‐making task that chooses between a gamble of cooperation and another gamble of defection. Specifically, we propose an index, r, to represent the risk associated with cooperation relative to defection. In conjunction with Rapoport's (1967) index of cooperation (K), our formulation of risk allows us to construct games that vary in risk (as indexed by r) while controlling for cooperativeness (as indexed by K). Following utility analysis that models risk seeking as a convex utility function and risk averse as a concave function, we predict that risk‐seeking people cooperate more in games that the cooperation choice is more risky, whereas risk‐averse people cooperate more in games that the cooperation choice is less risky. In the three studies that we varied game parameters, used different measures of risk orientation and prosocial orientation and used different experimental procedures, we found robust results supporting our predictions. Theoretical analysis of our formulation further suggests that risk and cooperativeness of a prisoner's dilemma game is not entirely independent. Games that have a higher cooperativeness index are necessarily more risky. Copyright © 2011 John Wiley & Sons, Ltd.