Ordinary least squares (OLS) regression and orthogonal regression (OR) address different questions and make different assumptions about errors. The OLS regression of Y on X yields predictions of a dependent variable (Y) contingent on an independent variable (X) and minimizes the sum of squared errors of prediction. It assumes that the independent…

This report presents results on a parallel implementation of the expectation-maximization (EM) algorithm for multidimensional latent variable models. The developments presented here are based on code that parallelizes both the E step and the M step of the parallel-E parallel-M algorithm. Examples presented in this report include item response…

We propose a crowdsourcing-based framework to iteratively and rapidly bootstrap a dialog system from scratch for a new domain. We leverage the open-source modular HALEF dialog system to deploy dialog applications. We illustrate the usefulness of this framework using four different prototype dialog items with applications in the educational domain…

Many aspects of the geometry of linear statistical models and least squares estimation are well known. Discussions of the geometry may be found in many sources. Some aspects of the geometry relating to the partitioning of variation that can be explained using a little-known theorem of Pappus and have not been discussed previously are the topic of…

The report is the first systematic evaluation of the sentence equivalence item type introduced by the "GRE"® revised General Test. We adopt a validity framework to guide our investigation based on Kane's approach to validation whereby a hierarchy of inferences that should be documented to support score meaning and interpretation is…

Graduate school recommendations are an important part of admissions in higher education, and natural language processing may be able to provide objective and consistent analyses of recommendation texts to complement readings by faculty and admissions staff. However, these sorts of high-stakes, personal recommendations are different from the…

To assess the value of individual students' subscores on the Major Field Test in Business (MFT Business), I examined the test's internal structure with factor analysis and structural equation model methods, and analyzed the subscore reliabilities using the augmented scores method. Analyses of the internal structure suggested that the MFT Business…

In this research, we investigated the feasibility of implementing the "e-rater"® scoring engine as a check score in place of all-human scoring for the "Graduate Record Examinations"® ("GRE"®) revised General Test (rGRE) Analytical Writing measure. This report provides the scientific basis for the use of e-rater as a…

Collaboration is generally recognized as a core competency of today's knowledge economy and has taken a central role in recent theoretical and technological developments in education research. Yet, the methodology for assessing the learning benefits of collaboration continues to rely on educational tests designed for isolated individuals. Thus,…

This simulation study evaluated the potential of alternative loglinear smoothing strategies for improving equipercentile equating function accuracy. These alternative strategies use cues from the sample data to make automatable and efficient improvements to model fit, either through the use of indicator functions for fitting large residuals or by…

The reporting methods used in large-scale educational assessments such as the National Assessment of Educational Progress (NAEP) rely on a "latent regression model". There is a lack of research on the assessment of fit of latent regression models. This paper suggests a simulation-based model-fit technique to assess the fit of such…

This study addressed 2 issues of using loglinear models for smoothing univariate test score distributions and for enhancing the stability of equipercentile equating functions. One issue was a comparative assessment of several statistical strategies that have been proposed for selecting 1 from several competing model parameterizations. Another…

Monotonicity properties of a general diagnostic model (GDM) are considered in this paper. Simple data summaries are identified to inform about the ordered categories of latent traits. The findings are very much in accordance with the statements made about the GPCM (Hemker, Sijtsma, Molenaar, & Junker, 1996, 1997). On the one hand, by fitting a…

This paper introduces the mixture general diagnostic model (MGDM), an extension of the general diagnostic model (GDM). The MGDM extension allows one to estimate diagnostic models for multiple known populations as well as discrete unknown, or not directly observed mixtures of populations. The GDM is based on developments that integrate located…

Quantitative item models are item structures that may be expressed in terms of mathematical variables and constraints. An item model may be developed as a computer program from which large numbers of items are automatically generated. Item models can be used to produce large numbers of items for use in traditional, large-scale assessments. But…