Estimation of a four‐parameter item response theory model

We explore the justification and formulation of a four‐parameter item response theory model (4PM) and employ a Bayesian approach to recover successfully parameter estimates for items and respondents. For data generated using a 4PM item response model, overall fit is improved when using the 4PM rather than the 3PM or the 2PM. Furthermore, although estimated trait scores under the various models correlate almost perfectly, inferences at the high and low ends of the trait continuum are compromised, with poorer coverage of the confidence intervals when the wrong model is used. We also show in an empirical example that the 4PM can yield new insights into the properties of a widely used delinquency scale. We discuss the implications for building appropriate measurement models in education and psychology to model more accurately the underlying response process.     

I've Fallen and I Can't Get Up: Can High Ability Students Recover From Early Mistakes in CAT?

A difficult result to interpret in Computerized Adaptive Tests (CATs) occurs when an ability estimate initially drops and then ascends continuously until the test ends, suggesting that the true ability may be higher than implied by the final estimate. We explain why this asymmetry occurs and show that early mistakes by high ability students can lead to considerable underestimation, even in tests with 45 items. The opposite response pattern, where low ability students start with lucky guesses, leads to much less bias. We show that using Barton and Lord's (1981) four-parameter model and a less informative prior can lower bias and RMSE for high ability students with a poor start, as the CAT algorithm ascends more quickly after initial underperformance. We also show that the 4PM slightly outperforms a CAT in which less discriminating items are initially used. The practical implications and relevance for psychological measurement more generally are discussed.     

A reputation for success (or failure): the association of peer academic reputations with academic self-concept, effort, and performance across the upper elementary grades

The associations between children's academic reputations among peers and their academic self-concept, effort, and performance were examined in a longitudinal study of 427 students initially enrolled in Grades 3, 4, and 5. Assessments were completed in the fall and spring of 2 consecutive school years and in the fall of a 3rd school year. Peer academic reputation (PAR) correlated moderately strongly with teacher-rated skills and changed over time as a function of grades earned at the prior assessment. Path-analytic models indicated bidirectional associations between PAR and academic self-concept, teacher-rated academic effort, and grade point average. There was little evidence that changes in self-concept mediated the association between PAR and effort and GPA or that changes in effort mediated the association between PAR and GPA. Results suggest that peers may possess unique information about classmates' academic functioning, that children's PARs are psychologically meaningful, and that these reputations may serve as a useful marker of processes that forecast future academic engagement and performance.     

Tie strength and family formation: Which personal relationships are influential?

On the basis of the analysis of qualitative interviews in Western Germany, it has been argued that personal relationships have a strong impact on individuals' family formation processes and childbearing intentions. Persons who influence individuals' childbearing choices were identified. Strong ties, such as among core family members (i.e., parents and siblings), are an important contributing factor, but the authors are also able to show that weak ties, such as those among colleagues and acquaintances, need to be considered when examining social influence on family formation processes. Apart from single network partners, influential groups of persons have been identified. Such groups serve as a comparative standard regarding the timing of having one's first child and subsequent children.