Laine Bradshaw

Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies

Although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment, current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies. This paper introduces the Hierarchical Diagnostic Classification Model (HDCM), which adapts the Log-linear Cognitive Diagnosis Model to cases where attribute hierarchies are present. The utility of the HDCM is demonstrated through simulation and by an empirical example. Simulation study results show the HDCM is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically, a feature not possible when using more commonly used DCMs. Empirically, the HDCM is used to test for the presence of a suspected attribute hierarchy in a test of English grammar, confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed, or nonhierarchical structure.

Measuring the Reliability of Diagnostic Classification Model Examinee Estimates

Over the past decade, diagnostic classification models (DCMs) have become an active area of psychometric research. Despite their use, the reliability of examinee estimates in DCM applications has seldom been reported. In this paper, a reliability measure for the categorical latent variables of DCMs is defined. Using theory-and simulation-based results, we show how DCMs uniformly provide greater examinee estimate reliability than IRT models for tests of the same length, a result that is a consequence of the smaller range of latent variable values examinee estimates can take in DCMs. We demonstrate this result by comparing DCM and IRT reliability for a series of models estimated with data from an end-of-grade test, culminating with a discussion of how DCMs can be used to change the character of large scale testing, either by shortening tests that measure examinees unidimensionally or by providing more reliable multidimensional measurement for tests of the same length.

Combining item response theory and diagnostic classification models: a psychometric model for scaling ability and diagnosing misconceptions.

Traditional testing procedures typically utilize unidimensional item response theory (IRT) models to provide a single, continuous estimate of a student’s overall ability. Advances in psychometrics have focused on measuring multiple dimensions of ability to provide more detailed feedback for students, teachers, and other stakeholders. Diagnostic classification models (DCMs) provide multidimensional feedback by using categorical latent variables that represent distinct skills underlying a test that students may or may not have mastered. The Scaling Individuals and Classifying Misconceptions (SICM) model is presented as a combination of a unidimensional IRT model and a DCM where the categorical latent variables represent misconceptions instead of skills. In addition to an estimate of ability along a latent continuum, the SICM model provides multidimensional, diagnostic feedback in the form of statistical estimates of probabilities that students have certain misconceptions. Through an empirical data analysis, we show how this additional feedback can be used by stakeholders to tailor instruction for students’ needs. We also provide results from a simulation study that demonstrate that the SICM MCMC estimation algorithm yields reasonably accurate estimates under large-scale testing conditions.

The Effects of Q-Matrix Design on Classification Accuracy in the Log-Linear Cognitive Diagnosis Model

Diagnostic classification models are psychometric models that aim to classify examinees according to their mastery or non-mastery of specified latent characteristics. These models are well-suited for providing diagnostic feedback on educational assessments because of their practical efficiency and increased reliability when compared with other multidimensional measurement models. A priori specifications of which latent characteristics or attributes are measured by each item are a core element of the diagnostic assessment design. This item–attribute alignment, expressed in a Q-matrix, precedes and supports any inference resulting from the application of the diagnostic classification model. This study investigates the effects of Q-matrix design on classification accuracy for the log-linear cognitive diagnosis model. Results indicate that classification accuracy, reliability, and convergence rates improve when the Q-matrix contains isolated information from each measured attribute.

An Illustration of Diagnostic Classification Modeling in Student Learning Outcomes Assessment

The assessment of higher-education student learning outcomes is an important component in understanding the strengths and weaknesses of academic and general education programs. This study illustrates the application of diagnostic classification models, a burgeoning set of statistical models, in assessing student learning outcomes. To facilitate understanding and future applications of diagnostic modeling, the log-linear cognitive diagnosis model used in this study is presented in a didactic manner. The model is applied in a context where undergraduate students were assessed along four learning outcomes related to psychosocial research across two time points. Results focus on implications and methods to aid stakeholders’ interpretation of the analyses. Contrasts to traditional measurement models and potential future applications are also discussed.

Invariance Properties for General Diagnostic Classification Models

In item response theory (IRT), the invariance property states that item parameter estimates are independent of the examinee sample, and examinee ability estimates are independent of the test items. While this property has long been established and understood by the measurement community for IRT models, the same cannot be said for diagnostic classification models (DCMs). DCMs are a newer class of psychometric models that are designed to classify examinees according to levels of categorical latent traits. We examined the invariance property for general DCMs using the log-linear cognitive diagnosis model (LCDM) framework. We conducted a simulation study to examine the degree to which theoretical invariance of LCDM classifications and item parameter estimates can be observed under various sample and test characteristics. Results illustrated that LCDM classifications and item parameter estimates show clear invariance when adequate model data fit is present. To demonstrate the implications of this important property, we conducted additional analyses to show that using pre-calibrated tests to classify examinees provided consistent classifications across calibration samples with varying mastery profile distributions and across tests with varying difficulties.

The Use and Misuse of Psychometric Models

The purpose of our paper entitled Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies (Templin & Bradshaw, 2014) was two-fold: to create a psychometric model and framework that would enable attribute hierarchies to be parameterized as dependent binary latent traits, and to formulate an empirically driven hypothesis test for the purpose of falsifying proposed attribute hierarchies. The methodological contributions of this paper were motivated by a curious result in the analysis of a real data set using the log-linear cognitive diagnosis model, or LCDM (Henson, Templin, & Willse, 2009). In the analysis of the Examination for Certification of Proficiency in English (ECPE; Templin & Hoffman, 2013), results indicated that few, if any, examinees were classified into four of the possible eight attribute profiles that are hypothesized in the LCDM for a test of three binary latent attributes. Further, when considering the four profiles lacking examinees, it appeared that some attributes must be mastered before others, suggesting what is commonly called an attribute hierarchy (e.g., Leighton, Gierl, & Hunka, 2004). Although the data analysis alerted us to the notion that such a data structure might be present, we lacked the methodological tools to falsify the presence of such an attribute hierarchy. As such, we developed the Hierarchical Diagnostic Classification Model, or HDCM, in an attempt to fill the need for such tools. We note that the driving force behind the HDCM is one of seeking a simpler, or more parsimonious, solution when model data misfit is either evident from LCDM results or implied by the hypothesized theories underlying the assessed constructs. As a consequence of the ECPE data results, we worked to develop a more broadly defined set of models that would allow for empirical evaluation of hypothesized attribute hierarchies. We felt our work was timely, as a number of methods, both new and old, are now using implied attribute hierarchies to assess examinees in many large scale analyses—from so-called intelligent tutoring systems (e.g., Cen, Koedinger, & Junker, 2006) to large scale state assessment systems for alternative assessments using instructionally imbedded items (e.g. the Dynamic Learning Maps Alternate Assessment System Consortium Grant, 2010–2015). Moreover, such large scale analyses are based on tremendously large data sets, many of which simply cannot fit with the types of (mainly unidimensional) models often used in current large scale testing situations. Furthermore, newly developed standards in education have incorporated ideas of learning progressions which indirectly imply the existence of hierarchically structured attributes (e.g., Progressions for the Common Core State Standards in Mathematics, Common Core State Standards Writing Team, 2012). In short, the current and

Development and Psychometric Evaluation of the Autism Stigma and Knowledge Questionnaire (ASK-Q).

ASD knowledge deficits contribute to disparities in the timing and quality of ASD services. To address the limitations with existing measures of ASD knowledge, we developed and examined the Autism Stigma and Knowledge Questionnaire (ASK-Q), which comprehensively assesses multiple subdomains of ASD knowledge while maintaining strong psychometric support and cross-cultural utility. ASK-Q items derived from the published research are organized into four subscales: (i) diagnosis, (ii) etiology, (iii) treatment, and (iv) stigma. ASK-Q items were selected based on ratings of face, construct, and cross-cultural validity by a group of 16 international researchers. Using Diagnostic Classification Modeling we confirmed the proposed factor structure and evaluated the statistical validity of each item among a lay sample of 617 participants.

Assessing Growth in a Diagnostic Classification Model Framework

A common assessment research design is the single-group pre-test/post-test design in which examinees are administered an assessment before instruction and then another assessment after instruction. In this type of study, the primary objective is to measure growth in examinees, individually and collectively. In an item response theory (IRT) framework, longitudinal IRT models can be used to assess growth in examinee ability over time. In a diagnostic classification model (DCM) framework, assessing growth translates to measuring changes in attribute mastery status over time, thereby providing a categorical, criterion-referenced interpretation of growth. This study introduces the Transition Diagnostic Classification Model (TDCM), which combines latent transition analysis with the log-linear cognitive diagnosis model to provide methodology for analyzing growth in a general DCM framework. Simulation study results indicate that the proposed model is flexible, provides accurate and reliable classifications, and is quite robust to violations to measurement invariance over time. The TDCM is used to analyze pre-test/post-test data from a diagnostic mathematics assessment.

Attribute-level Item Selection Method for DCM-CAT

ABSTRACT Diagnostic classification models (DCMs) can provide multidimensional diagnostic feedback about students’ mastery levels of knowledge components or attributes. One advantage of using DCMs is the ability to accurately and reliably classify students into mastery levels with a relatively small number of items per attribute. Combining DCMs with computerized adaptive testing can further shorten a test by strategically administering different items to different examinees. Current studies about item selection methods select the next item to increase the classification accuracy for the overall attribute profile and have been explored with item pools that have equal attribute information for all attributes on the assessment. In practice, the attribute information for diagnostic assessment is usually not balanced in the item pool. We propose a new attribute-level item selection method based on Cognitive Diagnostic Index at the Attribute Level (CDI_A; Henson et al., 2008) that helps balance classification accuracies among attributes on an assessment when item pools are not balanced across attributes. We conducted simulation studies to compare the performance of the CDI_A to other leading item selection methods; a pair of studies was theoretically based, and the last study was empirically based. Results showed that the new method can increase the classification accuracy and the reliability for attributes with weaker items in the item pool by administering more items to measure the attribute. Although using fewer items, the method retains reasonable accuracies for the attributes with stronger items in the pool. Thus, the CDI_A provides a trade-off to maintain an acceptable level of estimation accuracy for all attributes.