In a signal detection theory (SDT) approach to multiple choice exams, examinees are viewed as choosing, for each item, the alternative that is perceived as being the most plausible, with perceived plausibility depending in part on whether or not an item is known. The SDT model is a process model and provides measures of item difficulty, item…

The goal of this study is to model pauses extracted from writing keystroke logs as a way of characterizing the processes students use in essay composition. Low-level timing data were modeled, the interkey interval and its subtype, the intraword duration, thought to reflect processes associated with keyboarding skills and composition fluency.…

In observed-score equipercentile equating, the goal is to make scores on two scales or tests measuring the same construct comparable by matching the percentiles of the respective score distributions. If the tests consist of different items with multiple categories for each item, a suitable model for the responses is a polytomous item response…

This article addresses performance assessments that involve collaboration among students. We apply the Hawkes process to infer whether the actions of one student are associated with increased probability of further actions by his/her partner(s) in the near future. This leads to an intuitive notion of engagement among collaborators, and we consider…

The DINA (deterministic input, noisy, and gate) model has been widely used in cognitive diagnosis tests and in the process of test development. The outcomes known as slip and guess are included in the DINA model function representing the responses to the items. This study aimed to extend the DINA model by using the random-effect approach to allow…

Testlet effects can be taken into account by incorporating specific dimensions in addition to the general dimension into the item response theory model. Three such multidimensional models are described: the bi-factor model, the testlet model, and a second-order model. It is shown how the second-order model is formally equivalent to the testlet…

Within the theoretical framework of knowledge space theory, a probabilistic skill multimap model for assessing learning processes is proposed. The learning process of a student is modeled as a function of the student's knowledge and of an educational intervention on the attainment of specific skills required to solve problems in a knowledge…

The purpose of this study is to apply the attribute hierarchy method (AHM) to a subset of SAT critical reading items and illustrate how the method can be used to promote cognitive diagnostic inferences. The AHM is a psychometric procedure for classifying examinees' test item responses into a set of attribute mastery patterns associated with…

This article demonstrates the use of a new class of model-free cumulative sum (CUSUM) statistics to detect person fit given the responses to a linear test. The fundamental statistic being accumulated is the likelihood ratio of two probabilities. The detection performance of this CUSUM scheme is compared to other model-free person-fit statistics…

This article addresses issues in model building and statistical inference in the context of student modeling. The use of probability-based reasoning to explicate hypothesized and empirical relationships and to structure inference in the context of proportional reasoning tasks is discussed. Ideas are illustrated with an example concerning…

To assess item dimensionality, the following two approaches are described and compared: hierarchical generalized linear model (HGLM) and multidimensional item response theory (MIRT) model. Two generating models are used to simulate dichotomous responses to a 17-item test: the unidimensional and compensatory two-dimensional (C2D) models. For C2D…