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.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

项目反应理论观察分数核等值的影响因素

探究带宽选择方法、样本量、题目数量、等值设计、数据模拟方式对项目反应理论观察分数核等值的影响。通过两种数据模拟方式,获得研究数据,并计算局部与全域评价指标。研究发现,在随机组设计中,带宽选择方法表现相似;考生样本量和题目数量影响甚微。在非等组设计中,惩罚法与Silverman经验准则表现优异;增加题目量可降低百分相对误差和随机误差;增加样本量导致百分相对误差变大,随机误差减小。数据模拟方式可影响等值评价。未来应重点关注等值系统评估。     

Standard errors and confidence intervals for correlations corrected for indirect range restriction: A simulation study comparing analytic and bootstrap methods

A frequent topic of psychological research is the estimation of the correlation between two variables from a sample that underwent a selection process based on a third variable. Due to indirect range restriction, the sample correlation is a biased estimator of the population correlation, and a correction formula is used. In the past, bootstrap standard error and confidence intervals for the corrected correlations were examined with normal data. The present study proposes a large-sample estimate (an analytic method) for the standard error, and a corresponding confidence interval for the corrected correlation. Monte Carlo simulation studies involving both normal and non-normal data were conducted to examine the empirical performance of the bootstrap and analytic methods. Results indicated that with both normal and non-normal data, the bootstrap standard error and confidence interval were generally accurate across simulation conditions (restricted sample size, selection ratio, and population correlations) and outperformed estimates of the analytic method. However, with certain combinations of distribution type and model conditions, the analytic method has an advantage, offering reasonable estimates of the standard error and confidence interval without resorting to the bootstrap procedure's computer-intensive approach. We provide SAS code for the simulation studies.     

Comparing What to What,on What Scale? The Impact of Item Comparisons and Reference Points in Communicating Risk and Uncertainty

The mandated public availability of individual hospital's audit data for children's heart surgery in the UK creates a challenging scenario for communicating these complex and sensitive data to diverse audiences. On the basis of this scenario, we conducted three experiments with the aim of understanding how best to help lay people understand these data and the practical goal of improving the public presentation of these data. The experiments compared different outcome measures for displaying the survival rate (percentage scale versus the ratio of the predicted/observed rates) and presentation formats (individual hospital versus all hospitals shown) for outcomes data presented relative to prediction intervals generated by a risk model that adjusts for case mix. Our data highlight how easily inappropriate comparisons can influence evaluations of complex data: for instance, both a survival ratio of 1 and the presence of other hospitals seemingly provided reference points that resulted in inappropriately harsh evaluations of some hospitals. By drawing on evaluability theory, we demonstrate how to enhance people's understanding of these complex data while also discouraging inappropriate comparisons, which has implications for communicating risk and uncertainty and for choice architecture design in a range of contexts. Copyright © 2018 John Wiley & Sons, Ltd.     

The Academic Advantage of Devotion: Measuring Variation in the Value of Weekly Worship in Late Adolescence on Educational Attainment Using Propensity Score Matching

This study measures the effect of regular worship attendance at age 17 on total years of schooling by age 25, using data from the National Longitudinal Survey of Youth 1997. Expanding on previous work, this study estimates differences in the impact of worship attendance by race and family income status using propensity score matching. Individuals who frequently attend religious services complete .69 more years of schooling than similar individuals who do not frequently attend services. There are significantly greater returns to attendance for low‐income youth and no significant difference in returns by religious affiliation. These findings suggest that religious observance provides greater benefits for low‐income individuals or perhaps provides resources high‐income individuals have access to elsewhere. Moreover, this study extends previous work by examining a more recent and nationally representative sample of youth and by using methods that allow for greater causal inference.     

Why Me? Why Not Me?

The decision to undergo BRCA testing is very complex and emotionally laden. This decision can be further complicated by the loss of a mother at an early age. The following personal account by a genetic counselor discusses the testing process and the struggle to accept the results and reframe one’s self-identity. The sensitive nature of this testing and the implications for other family members is explored.     

Regional brain activity change predicts responsiveness to treatment for stuttering in adults

Developmental stuttering is known to be associated with aberrant brain activity, but there is no evidence that this knowledge has benefited stuttering treatment. This study investigated whether brain activity could predict progress during stuttering treatment for 21 dextral adults who stutter (AWS). They received one of two treatment programs that included periodic H₂¹⁵O PET scanning (during oral reading, monologue, and eyes-closed rest conditions). All participants successfully completed an initial treatment phase and then entered a phase designed to transfer treatment gains; 9/21 failed to complete this latter phase. The 12 pass and 9 fail participants were similar on speech and neural system variables before treatment, and similar in speech performance after the initial phase of their treatment. At the end of the initial treatment phase, however, decreased activation within a single region, L. putamen, in all 3 scanning conditions was highly predictive of successful treatment progress.