Constructing the exact significance level for a person fit statistic

This paper uses an extension of the network algorithm originally introduced by Mehta and Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. By assuming that item difficulties are known, the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score. A simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less.     

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.     

需求和接受的授权型领导匹配对下属工作结果的影响：情绪耗竭的中介作用

基于人-环境匹配理论和压力认知交互作用理论, 本文探讨了下属需求和接受的授权型领导匹配性对下属态度、行为和绩效的影响及情绪耗竭的中介作用。本文分别通过对150位领导与150位下属(研究1)、50位领导与243位下属(研究2)的配对样本开展两项多时点、多来源的问卷数据收集, 并采用跨层次多项式回归和响应面分析方法得出以下结论: (1)下属需求和接受的授权型领导失配会导致下属情绪耗竭; (2)相对于授权不足, 领导的过度授权更会导致下属情绪耗竭; (3)下属需求和接受的授权型领导匹配性通过作用于下属情绪耗竭进而影响下属对领导的满意度、组织公民行为和工作绩效。     

How our work influences who we are: Testing a theory of vocational and personality development over fifty years

This study examines the developmental influences of occupational environments on personality traits from childhood to adulthood. We test aspects of a theory of vocational and personality development, proposing that traits develop in response to work experience following corresponsive and noncorresponsive mechanisms. We describe these pathways in the context of situations of vocational gravitation and inhabitation. In a sample from the Hawaii personality and health cohort (N = 596), we examined associations of childhood and adulthood personality traits, with occupational environments profiled on the RIASEC model. Mediations tests confirmed that work influenced personality development from childhood to adulthood for Openness/Intellect. We observed multiple reactivity effects of occupation environments on adulthood traits that were not associated with corresponding selection effects.     

Assertive Ads for Want or Should? It Depends on Consumers’ Power

Advertisements using assertive language are commonly seen in marketing communications, yet assertive language has often been shown to be ineffective in communication and even decrease compliance. Recent research began to examine factors that influence the effectiveness of assertive advertising messages, but little research has studied the potential moderating role of consumer‐related factors. The current research fills this gap by investigating the moderating role of consumers’ power. Across five studies, the authors find that for high‐power consumers, assertive ads are effective in promoting want products but ineffective in promoting should products. For low‐power consumers, however, assertive ads are effective in promoting should products but ineffective in promoting want products. Moreover, the authors show that this pattern of results is driven (mediated) by consumers’ perception of the fit between the advertising message and the advertised product. Theoretical and practical implications of the findings are discussed.     

A gender perspective on Person-Manager fit and managerial advancement

This article presents two studies examining (1) the relationship between Person-Manager (P-M) fit and managerial advancement of women and men with, and without managerial aspirations and (2) the P-M fit as related to managerial and non-managerial women. The P-M fit was assessed by computing the congruence between participants' self-rated personality profile and the perceived personality profile of a manager. Sex (men show a higher P-M fit than women), gender (the higher the individual's masculine gender-role, the higher the P-M fit) and group (managers and managerial aspirants show a higher P-M fit than non-managerial aspirants and non-managers) hypotheses were tested. There was no support for the sex difference hypothesis. However, the group and gender hypotheses were confirmed showing that managers and managerial aspirants had a higher P-M fit than non-managers and non-aspirants. Further, analyses revealed that the higher the participants' masculinity scores, the higher the P-M fit. Implications of these findings are discussed in relation to the gendered image of the managerial role and adaptation theory.     

Checking the Assumptions of Rasch's Model for Speed Tests

Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.