Procedural fairness and self-esteem

We argue that people's self-esteem is affected by the fairness of procedures to which they are subjected; unfair treatment will lower self-esteem. Moreover, since this influence on self-esteem is presumably due to the implicit evaluation expressed by the choice of procedure and hence by the evaluation expressed by the person implementing the procedure, people's concern with the fairness of treatment will be focused on the interactional aspects of the procedure. In two experiments designed to test these hypotheses subjects received either a high or a low grade on an ability test on the basis of either fair or unfair grading procedures. The results of Experiment 1 indicated that subjects' self-esteem was lower after unfair treatment, and this influence was only apparent when subjects received high test feedback. Additionally, ratings of the fairness of the interaction were lower following unfair grading procedures. Experiment 2 also manipulated level of involvement with the test. Self-esteem was affected by procedural fairness and procedural fairness influenced perceived fairness of the interaction only in the high involvement condition.     

Regression Mixture Models: Does Modeling the Covariance Between Independent Variables and Latent Classes Improve the Results?

Regression mixture models are increasingly used as an exploratory approach to identify heterogeneity in the effects of a predictor on an outcome. In this simulation study, we tested the effects of violating an implicit assumption often made in these models; that is, independent variables in the model are not directly related to latent classes. Results indicate that the major risk of failing to model the relationship between predictor and latent class was an increase in the probability of selecting additional latent classes and biased class proportions. In addition, we tested whether regression mixture models can detect a piecewise relationship between a predictor and outcome. Results suggest that these models are able to detect piecewise relations but only when the relationship between the latent class and the predictor is included in model estimation. We illustrate the implications of making this assumption through a reanalysis of applied data examining heterogeneity in the effects of family resources on academic achievement. We compare previous results (which assumed no relation between independent variables and latent class) to the model where this assumption is lifted. Implications and analytic suggestions for conducting regression mixture based on these findings are noted.     

K-means may perform as well as mixture model clustering but may also be much worse: comment on Steinley and Brusco (2011)

Steinley and Brusco (2011) presented the results of a huge simulation study aimed at evaluating cluster recovery of mixture model clustering (MMC) both for the situation where the number of clusters is known and is unknown. They derived rather strong conclusions on the basis of this study, especially with regard to the good performance of K-means (KM) compared with MMC. I agree with the authors' conclusion that the performance of KM may be equal to MMC in certain situations, which are primarily the situations investigated by Steinley and Brusco. However, a weakness of the paper is the failure to investigate many important real-world situations where theory suggests that MMC should outperform KM. This article elaborates on the KM-MMC comparison in terms of cluster recovery and provides some additional simulation results that show that KM may be much worse than MMC. Moreover, I show that KM is equivalent to a restricted mixture model estimated by maximizing the classification likelihood and comment on Steinley and Brusco's recommendation regarding the use of mixture models for clustering.     

Fairness Evaluations of Encounters With Police Officers and Correctional Officers1

The fairness of treatment can be inferred from 2 aspects of the relationship between authority and other party: the person-related aspect and the role-related aspect. One hundred seventy-five American detainees were interviewed about their encounters with police officers and correctional officers. The role-related aspect affected procedural fairness judgments most when first-time incarcerated detainees evaluated the encounter with police officers. The person-related aspect affected procedural fairness judgments most when first-time detainees and repeatedly incarcerated detainees evaluated encounters with correctional officers. Consequences for the group value model of procedural fairness as well as for the legal practice are discussed.     

Hidden Markov Item Response Theory Models for Responses and Response Times

Current approaches to model responses and response times to psychometric tests solely focus on between-subject differences in speed and ability. Within subjects, speed and ability are assumed to be constants. Violations of this assumption are generally absorbed in the residual of the model. As a result, within-subject departures from the between-subject speed and ability level remain undetected. These departures may be of interest to the researcher as they reflect differences in the response processes adopted on the items of a test. In this article, we propose a dynamic approach for responses and response times based on hidden Markov modeling to account for within-subject differences in responses and response times. A simulation study is conducted to demonstrate acceptable parameter recovery and acceptable performance of various fit indices in distinguishing between different models. In addition, both a confirmatory and an exploratory application are presented to demonstrate the practical value of the modeling approach.     

A semi-parametric within-subject mixture approach to the analyses of responses and response times

In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.     

Latent class models for testing monotonicity and invariant item ordering for polytomous items

Two assumptions that are relevant to many applications using item response theory are the assumptions of monotonicity (M) and invariant item ordering (IIO). A latent class model is proposed for ordinal items with inequality constraints on the class-specific item means. This model is used as a tool for testing for violations of M and IIO. A Gibbs sampling scheme is used for estimating the model parameters. It is shown that the deviance information criterion can be used as an overall test of M and IIO, while posterior predictive checks can be used to test these assumptions at the item level. A real data application illustrates a model-fitting strategy for detecting items that violate M and IIO.     

The development of verbal and visual working memory processes: a latent variable approach

Working memory (WM) processing in children has been studied with different approaches, focusing on either the organizational structure of WM processing during development (factor analytic) or the influence of different task conditions on WM processing (experimental). The current study combined both approaches, aiming to distinguish verbal and visual processing in order to investigate WM development. We investigated recall performance under different task conditions in a sample of 5- to 13-year-olds, applying latent class regression analysis. In this analysis, we examined latent classes (subgroups) within the sample that differed in terms of processing type. The interpretations of the latent classes were validated internally using characteristics of the latent classes and externally using recall performance of words and figures. The results showed that children of different developmental stages used the same type of processing under the same conditions. However, due to developmental differences, their overall performances differed, showing groups of children who were successful in verbal or visual processing and groups of children who were not. This study shows and discusses the importance of disentangling the influence of task conditions from the influence of WM development when interpreting recall performance in children.