This study investigates polytomous item explanatory item response theory models under the multivariate generalized linear mixed modeling framework, using the linear logistic test model approach. Building on the original ideas of the many-facet Rasch model and the linear partial credit model, a polytomous Rasch model is extended to the item…

Scores estimated from multidimensional item response theory (IRT) models are not necessarily comparable across dimensions. In this article, the concept of aligned dimensions is formalized in the context of Rasch models, and two methods are described--delta dimensional alignment (DDA) and logistic regression alignment (LRA)--to transform estimated…

With the adoption by most states of the Common Core State Standards (CCSS) for English language arts and literacy and for mathematics (CCSS Initiative, 2010a, 2010b) comes major changes in public education that will affect instructional practice, curriculum, and assessment across the nation. Heritage, Walqui, and Linquanti (2015) argued that the…

This paper builds on the current literature base about learning progressions in science to address the question, "What is the nature of the learning progression in the content domain of the structure of matter?" We introduce a learning progression in response to that question and illustrate a methodology, the Construct Modeling (Wilson,…

This paper presents the Latent Class Level-PCM as a method for identifying and interpreting latent classes of respondents according to empirically estimated performance levels. The model, which combines elements from latent class models and reparameterized partial credit models for polytomous data, can simultaneously (a) identify empirical…

This study proposes a structured constructs model (SCM) to examine measurement in the context of a multidimensional learning progression (LP). The LP is assumed to have features that go beyond a typical multidimentional IRT model, in that there are hypothesized to be certain cross-dimensional linkages that correspond to requirements between the…

This article summarizes assessment of cognitive skills through collaborative tasks, using field test results from the Assessment and Teaching of 21st Century Skills (ATC21S) project. This project, sponsored by Cisco, Intel, and Microsoft, aims to help educators around the world enable students with the skills to succeed in future career and…

The Rasch rating (or partial credit) model is a widely applied item response model that is used to model ordinal observed variables that are assumed to collectively reflect a common latent variable. In the application of the model there is considerable controversy surrounding the assessment of fit. This controversy is most notable when the set of…

Interpretations for licensure tests involve a series of inferences or a validity argument, leading from the test score to decisions about who is accepted or denied entry into a profession. Utilizing an argument-based framework for validation based on the Standards for Educational and Psychological Testing, we explore the evidence for the ongoing…

This paper provides a summary of a novel and integrated way to think about the item response models (most often used in measurement applications in social science areas such as psychology, education, and especially testing of various kinds) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. In addition,…

Introduces the Rater Bundle Model, an item response model for repeated ratings of student work. Applies the model to real and simulated data to illustrate the approach, which was motivated by the observation that when repeated ratings occur, the assumption of conditional independence is violated, and current item response models can then…

The Rasch testlet model for both dichotomous and polytomous items in testlet-based tests is proposed. It can be viewed as a special case of the multidimensional random coefficients multinomial logit model (MRCMLM). Therefore, the estimation procedures for the MRCMLM can be directly applied. Simulations were conducted to examine parameter recovery…

The random-effects facet model that deals with local item dependence in many-facet contexts is presented. It can be viewed as a special case of the multidimensional random coefficients multinomial logit model (MRCMLM) so that the estimation procedures for the MRCMLM can be directly applied. Simulations were conducted to examine parameter recovery…

An approach to the measurement of knowledge content, knowledge access, and knowledge learning is developed. First a theoretical view of cognition is described, and then a class of measurement models, based on Rasch modeling, is presented. Knowledge access and content are viewed as determining the observable actions selected by an agent to achieve…

Marginal maximum likelihood estimation equations are derived for the structural parameters of the Saltus model, and a computing approximation is suggested based on the EM algorithm. The solution is illustrated with simulated data and an example from the domain of mixed number subtraction. (SLD)