The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.

Item response theory has become an essential component in the toolkit of every researcher in the behavioral sciences. It provides a powerful means to study individual responses to a variety of stimuli, and the methodology has been extended and developed to cover many different models of interaction. This volume presents a wide-ranging handbook to item response theory - and its applications to educational and psychological testing. It will serve as both an introduction to the subject and also as a comprehensive reference volume for practitioners and researchers. It is organized into six major sections: the nominal categories model, models for response time or multiple attempts on items, models for multiple abilities or cognitive components, nonparametric models, models for nonmonotone items, and models with special assumptions. Each chapter in the book has been written by an expert of that particular topic, and the chapters have been carefully edited to ensure that a uniform style of notation and presentation is used throughout. As a result, all researchers whose work uses item response theory will find this an indispensable companion to their work and it will be the subject's reference volume for many years to come.

Item response theory (IRT) is currently the dominant methodological paradigm in educational and psychological measurement. IRT models are based on assumptions about the relationship between latent traits and observed responses, so the accuracy of the methodology depends heavily on the reasonableness of these assumptions. This dissertation consists of three studies, all of which focus on different scenarios where existing IRT models do not agree closely with reality and thus may provide misleading or insufficient characterizations of measurement phenomena. In the first study, I discuss anchoring, the tendency for respondents to select categories near the rating category used for the immediately preceding item in self-report rating scale assessments. I propose a psychometric model based on a multidimensional nominal model for response style that also simultaneously accommodates a respondent-level anchoring tendency. This model is applied to a real dataset measuring extraversion, and empirical results support attending to both anchoring and midpoint response styles as ways of assessing respondent engagement. In the second study, I examine the simultaneous relevance of content trait level and response styles as predictive factors of response time on noncognitive assessments, and the potential for omitted variable bias when ignoring either factor. Using response time data from several noncognitive assessments, I demonstrate how a multilevel model leads to consistent findings that support the simultaneous relevance of both factors. The average effects of response style consistently emerge as stronger, although also show greater respondent-level variability, than those of content traits. In the third study, test items whose scores reflect sequential or IRTree modeling outcomes are considered. For such items, I argue that item specific factors, although not empirically measurable, are often present across stages of the same item. A conceptual model that incorporates such factors is proposed and used to demonstrate how they create ambiguity in the interpretations of item and person parameters beyond the first stage. Various empirical applications show patterns of violations of item parameter invariance across stages that are highly suggestive of item specific factors. These studies reflect some recent advances in IRT modeling applied to practical issues, which hopefully will benefit both methodologists and practitioners.

Introduction to measurement -- The one-parameter model -- Joint maximum likelihood parameter estimation -- Marginal maximum likelihood parameter estimation -- The two-parameter model -- The three-parameter model -- Rasch models for ordered polytomous data -- Non-Rasch models for ordered polytomous data -- Models for nominal polytomous data -- Models for multidimensional data -- Linking and equating -- Differential item functioning -- Multilevel IRT models.

This volume guides its reader through the basics of Item Response Theory, with an emphasis on what and how to include relevant information in the methods and results sections of professional papers. The author offers examples of good and bad write-ups.

Recently, researchers have reformulated Item Response Theory (IRT) models into multilevel models to evaluate clustered data appropriately. Using a multilevel model to obtain item difficulty and person ability parameter estimates that correspond directly with IRT models' parameters is often referred to as multilevel measurement modeling. Unlike conventional IRT models, multilevel measurement models (MMM) can handle, the addition of predictor variables, appropriate modeling of clustered data, and can be estimated using non-specialized computer software, including SAS. For example, a three-level model can model the repeated measures (level one) of individuals (level two) who are clustered within schools (level three). Limitations in terms of the minimum sample size and number of test items that permit reasonable one-parameter logistic (1-PL) IRT model's parameters have not been examined for either the two- or three-level MMM. Researchers (Wright and Stone, 1979; Lord, 1983; Hambleton and Cook, 1983) have found that sample sizes under 200 and fewer than 20 items per test result in poor model fit and poor parameter recovery for dichotomous 1-PL IRT models with data that meet model assumptions. This simulation study tested the performance of the two-level and three-level MMM under various conditions that included three sample sizes (100, 200, and 400), three test lengths (5, 10, and 20), three level-3 cluster sizes (10, 20, and 50), and two generated intraclass correlations (.05 and .15). The study demonstrated that use of the two- and three-level MMMs lead to somewhat divergent results for item difficulty and person-level ability estimates. The mean relative item difficulty bias was lower for the three-level model than the two-level model. The opposite was true for the person-level ability estimates, with a smaller mean relative parameter bias for the two-level model than the three-level model. There was no difference between the two- and three-level MMMs in the school-level ability estimates. Modeling clustered data appropriately; having a minimum total sample size of 100 to accurately estimate level-2 residuals and a minimum total sample size of 400 to accurately estimate level-3 residuals; and having at least 20 items will help ensure valid statistical test results.