Cluster Analysis for Cognitive Diagnosis: Theory and Applications

Chiu, Chia Yi; Douglas, Jeffrey A.; Li, Xiaodong

doi:10.1007/s11336-009-9125-0

Cited by 206 publications

(222 citation statements)

References 31 publications

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“…It is usually recommended to use a complete Q-matrix. More discussions regarding this issue can be found in Chiu et al (2009) and Liu et al (2013).…”

Section: The Identifiability Resultsmentioning

confidence: 99%

Statistical Analysis ofQ-Matrix Based Diagnostic Classification Models

Chen

Liu

et al. 2015

Journal of the American Statistical Association

164

160

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Diagnostic classification models have recently gained prominence in educational assessment, psychiatric evaluation, and many other disciplines. Central to the model specification is the so-called Q-matrix that provides a qualitative specification of the item-attribute relationship. In this paper, we develop theories on the identifiability for the Q-matrix under the DINA and the DINO models. We further propose an estimation procedure for the Q-matrix through the regularized maximum likelihood. The applicability of this procedure is not limited to the DINA or the DINO model and it can be applied to essentially all Q-matrix based diagnostic classification models. Simulation studies are conducted to illustrate its performance. Furthermore, two case studies are presented. The first case is a data set on fraction subtraction (educational application) and the second case is a subsample of the National Epidemiological Survey on Alcohol and Related Conditions concerning the social anxiety disorder (psychiatric application).

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“…It is usually recommended to use a complete Q-matrix. More discussions regarding this issue can be found in Chiu et al (2009) and Liu et al (2013).…”

Section: The Identifiability Resultsmentioning

confidence: 99%

Statistical Analysis ofQ-Matrix Based Diagnostic Classification Models

Chen

Liu

et al. 2015

Journal of the American Statistical Association

164

160

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“…In the case of dichotomous data, one family of special-purpose methods includes those procedures that are grounded in set theory (Curry, 1976; Restle, 1959), such as methods found in the diverse family of hierarchical classes (HICLAS) models that are designed for structural analysis of multi-mode, multi-way dichotomous data (Ceulemans & Van Mechelen, 2005, 2008; Ceulemans, Van Mechelen, & Leenen, 2007; DeBoeck & Rosenberg, 1988; Vande Gaer, Ceulemans, Van Mechelen, & Kuppens, 2012; Wilderjans, Ceulemans, & Van Mechelen, 2008, 2012). A second category corresponds to the literature stream pertaining to cognitive diagnosis methods to assess mastery (or non-mastery) of a collection of items in educational testing (Chiu et al, 2009; Macready & Dayton, 1977; Templin & Henson, 2006; Templin, Henson, & Douglas, 2007). Blockmodeling methods for social network analysis represent yet another class of special-purpose methods for dichotomous data (see Doreian, Batagelj, & Ferligoj, 2005 for an extensive review).…”

Section: Introductionmentioning

confidence: 99%

A comparison of latent class, K-means, and K-median methods for clustering dichotomous data.

Brusco

Shireman

Steinley

2017

Psychological Methods

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The problem of partitioning a collection of objects based on their measurements on a set of dichotomous variables is a well-established problem in psychological research, with applications including clinical diagnosis, educational testing, cognitive categorization, and choice analysis. Latent class analysis and K-means clustering are popular methods for partitioning objects based on dichotomous measures in the psychological literature. The K-median clustering method has recently been touted as a potentially useful tool for psychological data and might be preferable to its close neighbor, K-means, when the variable measures are dichotomous. We conducted simulation-based comparisons of the latent class, K-means, and K-median approaches for partitioning dichotomous data. Although all three methods proved capable of recovering cluster structure, K-median clustering yielded the best average performance, followed closely by latent class analysis. We also report results for the three methods within the context of an application to transitive reasoning data, where it was found that the three approaches can exhibit profound differences when applied to real data.

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“…The research cited and discussed focuses on the DINA model, a model that has long been understood to have identification problems that are not present in more general diagnostic models (see Chiu, Douglas, & Li, 2009 and subsequent forthcoming research). In our paper we showed how if attributes with compensatory behavior followed a linear hierarchy, a DINA model version of the HDCM with strict assumptions of conjunctive attribute behavior could not uncover the attribute structure.…”

Section: On the Conjunctive Nature Of Attributes In A Hierarchymentioning

confidence: 99%

The Use and Misuse of Psychometric Models

Templin

Bradshaw

2014

Psychometrika

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The purpose of our paper entitled Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies 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

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Cluster Analysis for Cognitive Diagnosis: Theory and Applications

Abstract: cluster analysis, cognitive diagnosis, latent class analysis,

Cited by 206 publications

References 31 publications

Statistical Analysis ofQ-Matrix Based Diagnostic Classification Models

Statistical Analysis ofQ-Matrix Based Diagnostic Classification Models

A comparison of latent class, K-means, and K-median methods for clustering dichotomous data.

The Use and Misuse of Psychometric Models

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