The R Package CDM for Diagnostic Modeling

In this chapter, the R (R Core Team, R: a language and environment for statistical computing. R Foundation for Statistical Computing. Vienna, 2017) pack-age CDM (Robitzsch A, Kiefer T, George AC, Uenlue A, CDM: cognitive diagnosis modeling. R package version 6.0-101. https://CRAN.R-project.org/package=CDM, 2017; George AC, Robitzsch A, Kiefer T, Gros J, Unlu A, J Stat Softw 74(2):1–24. 10.18637/jss.v074.i02, 2016) for estimating diagnostic classification models is introduced. First, the model classes that can be estimated with the CDM package are introduced. Second, the CDM package structure and some of its features are discussed. Third, the usage of the CDM package is demonstrated in a data application. Finally, potential future developments of the CDM package are discussed.

[1]  R. Henson,et al.  Cognitive Diagnostic Attribute-Level Discrimination Indices , 2008 .

[2]  Jingchen Liu,et al.  Regularized Latent Class Analysis with Application in Cognitive Diagnosis , 2017, Psychometrika.

[3]  Ren Liu,et al.  Retrofitting Diagnostic Classification Models to Responses From IRT-Based Assessment Forms , 2018, Educational and psychological measurement.

[4]  Anthony V. Fiacco,et al.  Nonlinear programming;: Sequential unconstrained minimization techniques , 1968 .

[5]  Jian Huang,et al.  COORDINATE DESCENT ALGORITHMS FOR NONCONVEX PENALIZED REGRESSION, WITH APPLICATIONS TO BIOLOGICAL FEATURE SELECTION. , 2011, The annals of applied statistics.

[6]  Alexander Robitzsch,et al.  Multiple group cognitive diagnosis models, with an emphasis on differential item functioning , 2014 .

[7]  Norman Verhelst,et al.  Maximum Likelihood Estimation in Generalized Rasch Models , 1986 .

[8]  Koken Ozaki DINA Models for Multiple-Choice Items With Few Parameters , 2015, Applied psychological measurement.

[9]  Jinxiang Hu,et al.  Evaluation of Model Fit in Cognitive Diagnosis Models , 2016 .

[10]  Matthias von Davier,et al.  Some Notes on the Reinvention of Latent Structure Models as Diagnostic Classification Models , 2009 .

[11]  Matthias von Davier,et al.  COMPARING MULTIPLE-GROUP MULTINOMIAL LOG-LINEAR MODELS FOR MULTIDIMENSIONAL SKILL DISTRIBUTIONS IN THE GENERAL DIAGNOSTIC MODEL , 2008 .

[12]  M. Davier Hierarchical mixtures of diagnostic models , 2010 .

[13]  R. Mislevy,et al.  Marginal maximum likelihood estimation for a psychometric model of discontinuous development , 1996 .

[14]  Achim Zeileis,et al.  On the Estimation of Standard Errors in Cognitive Diagnosis Models , 2018 .

[15]  Marcel A. Croon,et al.  Latent class analysis with ordered latent classe , 1990 .

[16]  Wen-yi Wang,et al.  Attribute-level and pattern-level classification consistency and accuracy indices for cognitive diagnostic assessment , 2015 .

[17]  S. Haberman,et al.  Hierarchical Diagnostic Classification Models Morphing into Unidimensional ‘Diagnostic’ Classification Models—A Commentary , 2014, Psychometrika.

[18]  J. Templin,et al.  Unique Characteristics of Diagnostic Classification Models: A Comprehensive Review of the Current State-of-the-Art , 2008 .

[19]  Youn Seon Lim,et al.  Efficient Models for Cognitive Diagnosis With Continuous and Mixed-Type Latent Variables , 2015, Applied psychological measurement.

[20]  Jimmy de la Torre,et al.  A Cognitive Diagnosis Model for Cognitively Based Multiple-Choice Options. , 2009 .

[21]  Jimmy de la Torre,et al.  An Empirically Based Method of Q‐Matrix Validation for the DINA Model: Development and Applications , 2008 .

[22]  J. D. L. Torre,et al.  DINA Model and Parameter Estimation: A Didactic , 2009 .

[23]  Wenchao Ma,et al.  A sequential cognitive diagnosis model for polytomous responses. , 2016, The British journal of mathematical and statistical psychology.

[24]  Joshua N. Pritikin A comparison of parameter covariance estimation methods for item response models in an expectation-maximization framework , 2017 .

[25]  Zhiliang Ying,et al.  Latent Variable Selection for Multidimensional Item Response Theory Models via $$L_{1}$$L1 Regularization , 2016 .

[26]  Pui-Wa Lei,et al.  The selection of cognitive diagnostic models for a reading comprehension test , 2016 .

[27]  A. Formann Linear Logistic Latent Class Analysis for Polytomous Data , 1992 .

[28]  Hung-Yu Huang,et al.  The Random‐Effect DINA Model , 2014 .

[29]  H. White Maximum Likelihood Estimation of Misspecified Models , 1982 .

[30]  Hung-Hsuan Chen,et al.  A Penalized Likelihood Method for Structural Equation Modeling , 2017, Psychometrika.

[31]  Gerhard Tutz,et al.  Sequential Models for Ordered Responses , 1997 .

[32]  Julio Olea,et al.  Inferential Item-Fit Evaluation in Cognitive Diagnosis Modeling , 2017, Applied psychological measurement.

[33]  Michel C. Desmarais,et al.  A Matrix Factorization Method for Mapping Items to Skills and for Enhancing Expert-Based Q-Matrices , 2013, AIED.

[34]  Gongjun Xu,et al.  Identifying Latent Structures in Restricted Latent Class Models , 2018, Journal of the American Statistical Association.

[35]  Francesco Bartolucci,et al.  A class of multidimensional IRT models for testing unidimensionality and clustering items , 2007 .

[36]  Gerhard Tutz,et al.  A Penalty Approach to Differential Item Functioning in Rasch Models , 2015, Psychometrika.

[37]  ANTON K. FORMANN,et al.  Structural Latent Class Models , 1998 .

[38]  Jeroen K. Vermunt,et al.  The Use of Restricted Latent Class Models for Defining and Testing Nonparametric and Parametric Item Response Theory Models , 2001 .

[39]  Paul De Boeck,et al.  IRT Models for Ability-Based Guessing , 2006 .

[40]  Alexander Robitzsch,et al.  The R Package CDM for Cognitive Diagnosis Models , 2016 .

[41]  Chia-Yi Chiu Statistical Refinement of the Q-Matrix in Cognitive Diagnosis , 2013 .

[42]  Richard D. Roberts,et al.  Factorial Versus Typological Models: A Comparison of Methods for Personality Data , 2012 .

[43]  Wenchao Ma,et al.  Model Similarity, Model Selection, and Attribute Classification , 2016, Applied psychological measurement.

[44]  Matthias von Davier,et al.  A General Diagnostic Model Applied to Language Testing Data. Research Report. ETS RR-05-16. , 2005 .

[45]  Alexander Robitzsch,et al.  Focusing on Interactions Between Content and Cognition: A New Perspective on Gender Differences in Mathematical Sub-Competencies , 2018 .

[46]  J. D. L. Torre,et al.  Evaluating the Wald Test for Item‐Level Comparison of Saturated and Reduced Models in Cognitive Diagnosis , 2013 .

[47]  Steven Andrew Culpepper,et al.  An Improved Strategy for Bayesian Estimation of the Reduced Reparameterized Unified Model , 2018, Applied psychological measurement.

[48]  Jung Yeon Park,et al.  An efficient standard error estimator of the DINA model parameters when analysing clustered data , 2017 .

[49]  L. A. van der Ark,et al.  Nonparametric Item Response Theory and Mokken Scale Analysis, with Relations to Latent Class Models and Cognitive Diagnostic Models , 2019, Handbook of Diagnostic Classification Models.

[50]  R Philip Chalmers,et al.  Numerical approximation of the observed information matrix with Oakes' identity , 2018, The British journal of mathematical and statistical psychology.

[51]  J. Templin,et al.  Measurement of psychological disorders using cognitive diagnosis models. , 2006, Psychological methods.

[52]  Sedat Sen,et al.  Comparison of Relative Fit Indices for Diagnostic Model Selection , 2017, Applied psychological measurement.

[53]  D. Oakes Direct calculation of the information matrix via the EM , 1999 .

[54]  Mark Gierl,et al.  Estimating Classification Consistency and Accuracy for Cognitive Diagnostic Assessment. , 2012 .

[55]  Alexander Robitzsch,et al.  Cognitive Diagnostic Modeling Using R. , 2015 .

[56]  D. Thissen,et al.  Likelihood-Based Item-Fit Indices for Dichotomous Item Response Theory Models , 2000 .

[57]  Ann Cathrice George,et al.  On Permissible Attribute Classes in Noncompensatory Cognitive Diagnosis Models , 2014 .

[58]  Eunice Eunhee Jang,et al.  Cognitive diagnostic assessment of L2 reading comprehension ability: Validity arguments for Fusion Model application to LanguEdge assessment , 2009 .

[59]  Alain Berlinet,et al.  Acceleration of the EM algorithm: P-EM versus epsilon algorithm , 2012, Comput. Stat. Data Anal..

[60]  R. P. McDonald,et al.  Goodness of Fit in Item Response Models. , 1995, Multivariate behavioral research.

[61]  André A. Rupp,et al.  A practical illustration of multidimensional diagnostic skills profiling: Comparing results from confirmatory factor analysis and diagnostic classification models , 2009 .

[62]  Jeffrey A Douglas,et al.  Higher-order latent trait models for cognitive diagnosis , 2004 .

[63]  A. C. George,et al.  Cognitive Diagnosis Models in R: A didactic , 2015 .

[64]  M. Davier The Log‐Linear Cognitive Diagnostic Model (LCDM) as a Special Case of the General Diagnostic Model (GDM) , 2014 .

[65]  Louis V. DiBello,et al.  31A Review of Cognitively Diagnostic Assessment and a Summary of Psychometric Models , 2006 .

[66]  Jimmy de la Torre,et al.  Estimating a Cognitive Diagnostic Model for Multiple Strategies via the EM Algorithm , 2014 .

[67]  Jimmy de la Torre,et al.  Differential Item Functioning Assessment in Cognitive Diagnostic Modeling: Application of the Wald Test to Investigate DIF in the DINA Model. , 2014 .

[68]  Trevor Hastie,et al.  Statistical Learning with Sparsity: The Lasso and Generalizations , 2015 .

[69]  Travis T. York,et al.  Defining and Measuring Academic Success. , 2015 .

[70]  I. W. Molenaar,et al.  A multidimensional item response model: Constrained latent class analysis using the gibbs sampler and posterior predictive checks , 1997 .

[71]  J. D. L. Torre,et al.  The Generalized DINA Model Framework. , 2011 .

[72]  Jingchen Liu,et al.  Theory of the Self-learning Q-Matrix. , 2010, Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability.

[73]  Thomas Kohlmann,et al.  Applied Latent Class Analysis: Three-Parameter Linear Logistic Latent Class Analysis , 2002 .

[74]  Jingchen Liu,et al.  A Fused Latent and Graphical Model for Multivariate Binary Data , 2016, 1606.08925.

[75]  Jianqing Fan,et al.  A Selective Overview of Variable Selection in High Dimensional Feature Space. , 2009, Statistica Sinica.

[76]  Harry Joe,et al.  Assessing Approximate Fit in Categorical Data Analysis , 2014, Multivariate behavioral research.

[77]  Hong Jiao,et al.  Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial , 2017, Journal of Educational and Behavioral Statistics.

[78]  Anton K. Formann Almost) Equivalence Between Conditional and Mixture Maximum Likelihood Estimates for Some Models of the Rasch Type , 2007 .

[79]  Michael Eid,et al.  Multimethod latent class analysis , 2015, Front. Psychol..

[80]  David Magis,et al.  Taking Atypical Response Patterns Into Account , 2012 .

[81]  Laine Bradshaw,et al.  Hierarchical Diagnostic Classification Models: A Family of Models for Estimating and Testing Attribute Hierarchies , 2014, Psychometrika.

[82]  Z. Ying,et al.  Statistical Analysis of Q-Matrix Based Diagnostic Classification Models , 2015, Journal of the American Statistical Association.

[83]  Mark Wilson,et al.  Measuring Progressions: Assessment Structures Underlying a Learning Progression , 2009 .

[84]  Hyo Jeong Shin,et al.  Structured Constructs Models Based on Change-Point Analysis , 2017 .

[85]  Jimmy de la Torre,et al.  Model Evaluation and Multiple Strategies in Cognitive Diagnosis: An Analysis of Fraction Subtraction Data , 2008 .

[86]  Mark J. Gierl,et al.  The Attribute Hierarchy Method for Cognitive Assessment: A Variation on Tatsuoka's Rule-Space Approach , 2004 .

[87]  Xiaotong Shen,et al.  Journal of the American Statistical Association Likelihood-based Selection and Sharp Parameter Estimation Likelihood-based Selection and Sharp Parameter Estimation , 2022 .

[88]  Tao Xin,et al.  Information matrix estimation procedures for cognitive diagnostic models. , 2019, The British journal of mathematical and statistical psychology.

[89]  Jimmy de la Torre,et al.  Relative and Absolute Fit Evaluation in Cognitive Diagnosis Modeling. , 2013 .

[90]  Wen-Chung Wang,et al.  Assessment of Differential Item Functioning Under Cognitive Diagnosis Models: The DINA Model Example , 2015 .

[91]  Matthias von Davier,et al.  Variance Estimation for NAEP Data Using a Resampling-Based Approach: An Application of Cognitive Diagnostic Models. Research Report. ETS RR-10-26. , 2010 .

[92]  Bor-Chen Kuo,et al.  A Cognitive Diagnosis Model for Identifying Coexisting Skills and Misconceptions , 2018, Applied psychological measurement.

[93]  Matthias von Davier,et al.  FITTING THE STRUCTURED GENERAL DIAGNOSTIC MODEL TO NAEP DATA , 2008 .

[94]  Ying Liu,et al.  Testing Person Fit in Cognitive Diagnosis , 2009 .

[95]  Lesa Hoffman,et al.  Obtaining Diagnostic Classification Model Estimates Using Mplus , 2013 .

[96]  L. T. DeCarlo Recognizing Uncertainty in the Q-Matrix via a Bayesian Extension of the DINA Model , 2012 .

[97]  Hui Zhou,et al.  Test designs and modeling under the general nominal diagnosis model framework , 2017, PloS one.

[98]  Anton K. Formann,et al.  Constrained latent class models: Theory and applications , 1985 .