A general diagnostic model applied to language testing data
Abstract
Probabilistic models with one or more latent variables are designed to report on a corresponding number of skills or cognitive attributes. Multidimensional skill profiles offer additional information beyond what a single test score can provide, if the reported skills can be identified and distinguished reliably. Many recent approaches to skill profile models are limited to dichotomous data and have made use of computationally intensive estimation methods such as Markov chain Monte Carlo, since standard maximum likelihood (ML) estimation techniques were deemed infeasible. This paper presents a general diagnostic model (GDM) that can be estimated with standard ML techniques and applies to polytomous response variables as well as to skills with two or more proficiency levels. The paper uses one member of a larger class of diagnostic models, a compensatory diagnostic model for dichotomous and partial credit data. Many well‐known models, such as univariate and multivariate versions of the Rasch model and the two‐parameter logistic item response theory model, the generalized partial credit model, as well as a variety of skill profile models, are special cases of this GDM. In addition to an introduction to this model, the paper presents a parameter recovery study using simulated data and an application to real data from the field test for TOEFL® Internet‐based testing.
Citing Literature
Number of times cited according to CrossRef: 182
- Wenyi Wang, Lihong Song, Teng Wang, Peng Gao, Jian Xiong, A Note on the Relationship of the Shannon Entropy Procedure and the Jensen–Shannon Divergence in Cognitive Diagnostic Computerized Adaptive Testing, SAGE Open, 10.1177/2158244019899046, 10, 1, (215824401989904), (2020).
- Matthias von Davier, Psychometrics, Encyclopedia of Personality and Individual Differences, 10.1007/978-3-319-24612-3, (4157-4161), (2020).
- Wenchao Ma, Nathan Minchen, Jimmy de la Torre, Choosing between CDM and Unidimensional IRT: The Proportional Reasoning Test Case, Measurement: Interdisciplinary Research and Perspectives, 10.1080/15366367.2019.1697122, 18, 2, (87-96), (2020).
- Wenyi Wang, Lihong Song, Shuliang Ding, Teng Wang, Peng Gao, Jian Xiong, A Semi-supervised Learning Method for Q-Matrix Specification Under the DINA and DINO Model With Independent Structure, Frontiers in Psychology, 10.3389/fpsyg.2020.02120, 11, (2020).
- Xi-tian Chen, Zhengjia Dai, Ying Lin, undefined, 2020 International Joint Conference on Neural Networks (IJCNN), 10.1109/IJCNN48605.2020.9207587, (1-8), (2020).
- Hamdollah Ravand, Purya Baghaei, Philip Doebler, Examining Parameter Invariance in a General Diagnostic Classification Model, Frontiers in Psychology, 10.3389/fpsyg.2019.02930, 10, (2020).
- Kazuhiro Yamaguchi, Variational Bayesian inference for the multiple-choice DINA model, Behaviormetrika, 10.1007/s41237-020-00104-w, (2020).
- Zhaoyuan Zhang, Jiwei Zhang, Jing Lu, Jian Tao, Bayesian Estimation of the DINA Model With Pólya-Gamma Gibbs Sampling, Frontiers in Psychology, 10.3389/fpsyg.2020.00384, 11, (2020).
- Lei Guo, Jing Yang, Naiqing Song, Spectral Clustering Algorithm for Cognitive Diagnostic Assessment, Frontiers in Psychology, 10.3389/fpsyg.2020.00944, 11, (2020).
- Chun Wang, Jing Lu, Learning Attribute Hierarchies From Data: Two Exploratory Approaches, Journal of Educational and Behavioral Statistics, 10.3102/1076998620931094, (107699862093109), (2020).
- Kazuhiro Yamaguchi, Kensuke Okada, Hybrid cognitive diagnostic model, Behaviormetrika, 10.1007/s41237-020-00111-x, (2020).
- Michela Gnaldi, Silvia Bacci, Thiemo Kunze, Samuel Greiff, Students’ Complex Problem Solving Profiles, Psychometrika, 10.1007/s11336-020-09709-2, (2020).
- Chen-Wei Liu, Björn Andersson, Anders Skrondal, A Constrained Metropolis–Hastings Robbins–Monro Algorithm for Q Matrix Estimation in DINA Models, Psychometrika, 10.1007/s11336-020-09707-4, (2020).
- Alexander Robitzsch, Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data, Journal of Intelligence, 10.3390/jintelligence8030030, 8, 3, (30), (2020).
- Shiyu Wang, Yinghan Chen, Using Response Times and Response Accuracy to Measure Fluency Within Cognitive Diagnosis Models, Psychometrika, 10.1007/s11336-020-09717-2, (2020).
- Qiao Lin, Kuan Xing, Yoon Soo Park, Measuring Skill Growth and Evaluating Change: Unconditional and Conditional Approaches to Latent Growth Cognitive Diagnostic Models, Frontiers in Psychology, 10.3389/fpsyg.2020.02205, 11, (2020).
- Xuliang Gao, Wenchao Ma, Daxun Wang, Yan Cai, Dongbo Tu, A Class of Cognitive Diagnosis Models for Polytomous Data, Journal of Educational and Behavioral Statistics, 10.3102/1076998620951986, (107699862095198), (2020).
- Yinghan Chen, Steven Andrew Culpepper, A Multivariate Probit Model for Learning Trajectories: A Fine-Grained Evaluation of an Educational Intervention, Applied Psychological Measurement, 10.1177/0146621620920928, (014662162092092), (2020).
- Luca Stefanutti, Debora de Chiusole, Pasquale Anselmi, Andrea Spoto, Extending the Basic Local Independence Model to Polytomous Data, Psychometrika, 10.1007/s11336-020-09722-5, (2020).
- Xin Xu, Jimmy de la Torre, Jiwei Zhang, Jinxin Guo, Ningzhong Shi, Estimating CDMs Using the Slice-Within-Gibbs Sampler, Frontiers in Psychology, 10.3389/fpsyg.2020.02260, 11, (2020).
- Xue Zhang, Juntao Wang, On the Sequential Hierarchical Cognitive Diagnostic Model, Frontiers in Psychology, 10.3389/fpsyg.2020.579018, 11, (2020).
- Wenchao Ma, Jimmy Torre, An empirical Q‐matrix validation method for the sequential generalized DINA model, British Journal of Mathematical and Statistical Psychology, 10.1111/bmsp.12156, 73, 1, (142-163), (2019).
- Chongqin Xi, Yan Cai, Siwei Peng, Jie Lian, Dongbo Tu, A diagnostic classification version of Schizotypal Personality Questionnaire using diagnostic classification models, International Journal of Methods in Psychiatric Research, 10.1002/mpr.1807, 29, 1, (2019).
- Xiang Liu, Matthew S. Johnson, Estimating CDMs Using MCMC, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_31, (629-646), (2019).
- Yoon Soo Park, Young-Sun Lee, Explanatory Cognitive Diagnostic Models, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_10, (207-222), (2019).
- Xue-Lan Qiu, Xiaomin Li, Wen-Chung Wang, Differential Item Functioning in Diagnostic Classification Models, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_18, (379-393), (2019).
- Sandip Sinharay, Matthew S. Johnson, Measures of Agreement: Reliability, Classification Accuracy, and Classification Consistency, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_17, (359-377), (2019).
- Gongjun Xu, Identifiability and Cognitive Diagnosis Models, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_16, (333-357), (2019).
- Yunxiao Chen, Xiaoou Li, Exploratory Data Analysis for Cognitive Diagnosis: Stochastic Co-blockmodel and Spectral Co-clustering, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_14, (287-306), (2019).
- Wenchao Ma, Cognitive Diagnosis Modeling Using the GDINA R Package, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_29, (593-601), (2019).
- Chia-Yi Chiu, Hans-Friedrich Köhn, Nonparametric Methods in Cognitively Diagnostic Assessment, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_5, (107-132), (2019).
- Zhihui Fu, Ya-Hui Su, Jian Tao, A Copula Model for Residual Dependency in DINA Model, Quantitative Psychology, 10.1007/978-3-030-01310-3_14, (145-156), (2019).
- Matthias von Davier, Psychometrics, Encyclopedia of Personality and Individual Differences, 10.1007/978-3-319-28099-8, (1-5), (2019).
- Zhuangzhuang Han, Matthew S. Johnson, Global- and Item-Level Model Fit Indices, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_13, (265-285), (2019).
- Jingchen Liu, Hyeon-Ah Kang, Q-Matrix Learning via Latent Variable Selection and Identifiability, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_12, (247-263), (2019).
- Lawrence T. DeCarlo, Insights from Reparameterized DINA and Beyond, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_11, (223-243), (2019).
- Susan E. Embretson, Diagnostic Modeling of Skill Hierarchies and Cognitive Processes with MLTM-D, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_9, (187-205), (2019).
- Robert Henson, Jonathan L. Templin, Loglinear Cognitive Diagnostic Model (LCDM), Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_8, (171-185), (2019).
- Jimmy de la Torre, Nathan D. Minchen, The G-DINA Model Framework, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_7, (155-169), (2019).
- Alexander Robitzsch, Ann Cathrice George, The R Package CDM for Diagnostic Modeling, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_26, (549-572), (2019).
- Stephan Abele, Matthias von Davier, CDMs in Vocational Education: Assessment and Usage of Diagnostic Problem-Solving Strategies in Car Mechatronics, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_22, (461-488), (2019).
- L. Andries van der Ark, Gina Rossi, Klaas Sijtsma, Nonparametric Item Response Theory and Mokken Scale Analysis, with Relations to Latent Class Models and Cognitive Diagnostic Models, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_2, (21-45), (2019).
- Wenchao Ma, Wenjing Guo, Cognitive diagnosis models for multiple strategies, British Journal of Mathematical and Statistical Psychology, 10.1111/bmsp.12155, 72, 2, (370-392), (2019).
- Matthias von Davier, The General Diagnostic Model, Handbook of Diagnostic Classification Models, 10.1007/978-3-030-05584-4_6, (133-153), (2019).
- Jianbin Fu, Maximum Marginal Likelihood Estimation With an Expectation–Maximization Algorithm for Multigroup/Mixture Multidimensional Item Response Theory Models, ETS Research Report Series, 10.1002/ets2.12272, 2019, 1, (1-16), (2019).
- Farshad Effatpanah, Purya Baghaei, Ali Akbar Boori, Diagnosing EFL learners’ writing ability: a diagnostic classification modeling analysis, Language Testing in Asia, 10.1186/s40468-019-0090-y, 9, 1, (2019).
- Yanlou Liu, Hao Yin, Tao Xin, Laicheng Shao, Lu Yuan, A Comparison of Differential Item Functioning Detection Methods in Cognitive Diagnostic Models, Frontiers in Psychology, 10.3389/fpsyg.2019.01137, 10, (2019).
- Peida Zhan, Hong Jiao, Dandan Liao, Feiming Li, A Longitudinal Higher-Order Diagnostic Classification Model, Journal of Educational and Behavioral Statistics, 10.3102/1076998619827593, (107699861982759), (2019).
- Peida Zhan, Hong Jiao, Kaiwen Man, Lijun Wang, Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial, Journal of Educational and Behavioral Statistics, 10.3102/1076998619826040, (107699861982604), (2019).
- Mehmet Kaplan, Jimmy de la Torre, A Blocked-CAT Procedure for CD-CAT, Applied Psychological Measurement, 10.1177/0146621619835500, (014662161983550), (2019).
- Roy Levy, Dynamic Bayesian Network Modeling of Game-Based Diagnostic Assessments, Multivariate Behavioral Research, 10.1080/00273171.2019.1590794, (1-24), (2019).
- Xuliang Gao, Daxun Wang, Yan Cai, Dongbo Tu, Cognitive Diagnostic Computerized Adaptive Testing for Polytomously Scored Items, Journal of Classification, 10.1007/s00357-019-09357-x, (2019).
- Matthew S. Johnson, Sandip Sinharay, The Reliability of the Posterior Probability of Skill Attainment in Diagnostic Classification Models, Journal of Educational and Behavioral Statistics, 10.3102/1076998619864550, (107699861986455), (2019).
- Wenchao Ma, Evaluating the Fit of Sequential G-DINA Model Using Limited-Information Measures, Applied Psychological Measurement, 10.1177/0146621619843829, (014662161984382), (2019).
- Bo Hu, Jonathan Templin, Using Diagnostic Classification Models to Validate Attribute Hierarchies and Evaluate Model Fit in Bayesian Networks, Multivariate Behavioral Research, 10.1080/00273171.2019.1632165, (1-12), (2019).
- Susu Zhang, Hua-Hua Chang, A multilevel logistic hidden Markov model for learning under cognitive diagnosis, Behavior Research Methods, 10.3758/s13428-019-01238-w, (2019).
- Chia-Yi Chiu, Hans-Friedrich Köhn, Consistency Theory for the General Nonparametric Classification Method, Psychometrika, 10.1007/s11336-019-09660-x, (2019).
- Jing Yang, Hua-Hua Chang, Jian Tao, Ningzhong Shi, Stratified Item Selection Methods in Cognitive Diagnosis Computerized Adaptive Testing, Applied Psychological Measurement, 10.1177/0146621619893783, (014662161989378), (2019).
- Peida Zhan, Wen-Chung Wang, Xiaomin Li, A Partial Mastery, Higher-Order Latent Structural Model for Polytomous Attributes in Cognitive Diagnostic Assessments, Journal of Classification, 10.1007/s00357-019-09323-7, (2019).
- Kevin Carl P. Santos, Jimmy de la Torre, Matthias von Davier, Adjusting Person Fit Index for Skewness in Cognitive Diagnosis Modeling, Journal of Classification, 10.1007/s00357-019-09325-5, (2019).
- Steven Andrew Culpepper, An Exploratory Diagnostic Model for Ordinal Responses with Binary Attributes: Identifiability and Estimation, Psychometrika, 10.1007/s11336-019-09683-4, (2019).
- Feiya Xiao, Lucy Barnard-Brak, William Lan, Hansel Burley, Examining problem-solving skills in technology-rich environments as related to numeracy and literacy, International Journal of Lifelong Education, 10.1080/02601370.2019.1598507, (1-12), (2019).
- Silvia Bacci, Bruno Bertaccini, Alessandra Petrucci, Beliefs and needs of academic teachers: a latent class analysis, Statistical Methods & Applications, 10.1007/s10260-019-00495-5, (2019).
- Dongbo Tu, Shiyu Wang, Yan Cai, Jeff Douglas, Hua-Hua Chang, Cognitive Diagnostic Models With Attribute Hierarchies: Model Estimation With a Restricted Q-Matrix Design, Applied Psychological Measurement, 10.1177/0146621618765721, 43, 4, (255-271), (2018).
- Peida Zhan, Hong Jiao, Manqian Liao, Yufang Bian, Bayesian DINA Modeling Incorporating Within-Item Characteristic Dependency, Applied Psychological Measurement, 10.1177/0146621618781594, 43, 2, (143-158), (2018).
- Steven Andrew Culpepper, Yinghan Chen, Development and Application of an Exploratory Reduced Reparameterized Unified Model, Journal of Educational and Behavioral Statistics, 10.3102/1076998618791306, 44, 1, (3-24), (2018).
- Yanlou Liu, Tao Xin, Björn Andersson, Wei Tian, Information matrix estimation procedures for cognitive diagnostic models, British Journal of Mathematical and Statistical Psychology, 10.1111/bmsp.12134, 72, 1, (18-37), (2018).
- Wenchao Ma, A diagnostic tree model for polytomous responses with multiple strategies, British Journal of Mathematical and Statistical Psychology, 10.1111/bmsp.12137, 72, 1, (61-82), (2018).
- Xueying Tang, Yunxiao Chen, Xiaoou Li, Jingchen Liu, Zhiliang Ying, A reinforcement learning approach to personalized learning recommendation systems, British Journal of Mathematical and Statistical Psychology, 10.1111/bmsp.12144, 72, 1, (108-135), (2018).
- Nathan Minchen, Jimmy de la Torre, A General Cognitive Diagnosis Model for Continuous-Response Data, Measurement: Interdisciplinary Research and Perspectives, 10.1080/15366367.2018.1436817, 16, 1, (30-44), (2018).
- Yunxiao Chen, Yang Liu, Shuangshuang Xu, Mutual Information Reliability for Latent Class Analysis, Applied Psychological Measurement, 10.1177/0146621617748324, 42, 6, (460-477), (2018).
- Hans-Friedrich Köhn, Chia-Yi Chiu, How to Build a Complete Q-Matrix for a Cognitively Diagnostic Test, Journal of Classification, 10.1007/s00357-018-9255-0, 35, 2, (273-299), (2018).
- Jesper Tijmstra, Maria Bolsinova, Minjeong Jeon, General mixture item response models with different item response structures: Exposition with an application to Likert scales, Behavior Research Methods, 10.3758/s13428-017-0997-0, 50, 6, (2325-2344), (2018).
- Robert Henson, Lou DiBello, Bill Stout, A Generalized Approach to Defining Item Discrimination for DCMs, Measurement: Interdisciplinary Research and Perspectives, 10.1080/15366367.2018.1436855, 16, 1, (18-29), (2018).
- Hans-Friedrich Köhn, Chia-Yi Chiu, Identifiability of the Latent Attribute Space and Conditions of Q-Matrix Completeness for Attribute Hierarchy Models, Quantitative Psychology, 10.1007/978-3-319-77249-3_30, (363-375), (2018).
- Matthias von Davier, Diagnosing Diagnostic Models: From Von Neumann’s Elephant to Model Equivalencies and Network Psychometrics, Measurement: Interdisciplinary Research and Perspectives, 10.1080/15366367.2018.1436827, 16, 1, (59-70), (2018).
- Shiyu Wang, Susu Zhang, Jeff Douglas, Steven Culpepper, Using Response Times to Assess Learning Progress: A Joint Model for Responses and Response Times, Measurement: Interdisciplinary Research and Perspectives, 10.1080/15366367.2018.1435105, 16, 1, (45-58), (2018).
- Daniel M. Bolt, Jee‐Seon Kim, Parameter Invariance and Skill Attribute Continuity in the DINA Model, Journal of Educational Measurement, 10.1111/jedm.12175, 55, 2, (264-280), (2018).
- Matthew S. Johnson, Sandip Sinharay, Measures of Agreement to Assess Attribute‐Level Classification Accuracy and Consistency for Cognitive Diagnostic Assessments, Journal of Educational Measurement, 10.1111/jedm.12196, 55, 4, (635-664), (2018).
- Yuqi Gu, Jingchen Liu, Gongjun Xu, Zhiliang Ying, Hypothesis Testing of the Q-matrix, Psychometrika, 10.1007/s11336-018-9629-6, 83, 3, (515-537), (2018).
- Jianbin Fu, Yuling Feng, A Comparison of Score Aggregation Methods for Unidimensional Tests on Different Dimensions, ETS Research Report Series, 10.1002/ets2.12194, 2018, 1, (1-16), (2018).
- Jianbin Fu, Yanxuan Qu, A Review of Subscore Estimation Methods, ETS Research Report Series, 10.1002/ets2.12203, 2018, 1, (1-15), (2018).
- Gongjun Xu, Zhuoran Shang, Identifying Latent Structures in Restricted Latent Class Models, Journal of the American Statistical Association, 10.1080/01621459.2017.1340889, 113, 523, (1284-1295), (2018).
- Yanlou Liu, Björn Andersson, Tao Xin, Haiyan Zhang, Lingling Wang, Improved Wald Statistics for Item-Level Model Comparison in Diagnostic Classification Models, Applied Psychological Measurement, 10.1177/0146621618798664, (014662161879866), (2018).
- Minjeong Jeon, A Constrained Confirmatory Mixture IRT Model: Extensions and Estimation of the Saltus model using Mplus, The Quantitative Methods for Psychology, 10.20982/tqmp.14.2.p120, 14, 2, (120-136), (2018).
- Ren Liu, Zhehan Jiang, Diagnostic Classification Models for Ordinal Item Responses, Frontiers in Psychology, 10.3389/fpsyg.2018.02512, 9, (2018).
- Yuan-Pei Chang, Chia-Yi Chiu, Rung-Ching Tsai, Nonparametric CAT for CD in Educational Settings With Small Samples, Applied Psychological Measurement, 10.1177/0146621618813113, (014662161881311), (2018).
- Susu Zhang, Shiyu Wang, Modeling Learner Heterogeneity: A Mixture Learning Model With Responses and Response Times, Frontiers in Psychology, 10.3389/fpsyg.2018.02339, 9, (2018).
- Wenchao Ma, Jimmy de la Torre, Category-Level Model Selection for the Sequential G-DINA Model, Journal of Educational and Behavioral Statistics, 10.3102/1076998618792484, (107699861879248), (2018).
- Edward Rock Davis, Rachel Wilson, ‘Not so globalised’: contrasting media discourses on education and competitiveness in four countries., Journal of Asia Business Studies, 10.1108/JABS-08-2016-0108, (00-00), (2018).
- Chanjin Zheng, Xiangbin Meng, Shaoyang Guo, Zhengguang Liu, Expectation-Maximization-Maximization: A Feasible MLE Algorithm for the Three-Parameter Logistic Model Based on a Mixture Modeling Reformulation, Frontiers in Psychology, 10.3389/fpsyg.2017.02302, 8, (2018).
- Peida Zhan, Manqian Liao, Yufang Bian, Joint Testlet Cognitive Diagnosis Modeling for Paired Local Item Dependence in Response Times and Response Accuracy, Frontiers in Psychology, 10.3389/fpsyg.2018.00607, 9, (2018).
- Dubravka Svetina, Yanan Feng, Justin Paulsen, Montserrat Valdivia, Arturo Valdivia, Shenghai Dai, Examining DIF in the Context of CDMs When the Q-Matrix Is Misspecified, Frontiers in Psychology, 10.3389/fpsyg.2018.00696, 9, (2018).
- Jinsong Chen, Jimmy de la Torre, Introducing the General Polytomous Diagnosis Modeling Framework, Frontiers in Psychology, 10.3389/fpsyg.2018.01474, 9, (2018).
- Yan Cai, Dongbo Tu, Shuliang Ding, Theorems and Methods of a Complete Q Matrix With Attribute Hierarchies Under Restricted Q-Matrix Design, Frontiers in Psychology, 10.3389/fpsyg.2018.01413, 9, (2018).
- Hans-Friedrich Köhn, Chia-Yi Chiu, Attribute Hierarchy Models in Cognitive Diagnosis: Identifiability of the Latent Attribute Space and Conditions for Completeness of the Q-Matrix, Journal of Classification, 10.1007/s00357-018-9278-6, (2018).
- Steven Andrew Culpepper, Estimating the Cognitive Diagnosis $$\varvec{Q}$$Q Matrix with Expert Knowledge: Application to the Fraction-Subtraction Dataset, Psychometrika, 10.1007/s11336-018-9643-8, (2018).
- Marit Kristine List, Olaf Köller, Gabriel Nagy, A Semiparametric Approach for Modeling Not-Reached Items, Educational and Psychological Measurement, 10.1177/0013164417749679, 79, 1, (170-199), (2017).
- Janine Buchholz, Johannes Hartig, Comparing Attitudes Across Groups: An IRT-Based Item-Fit Statistic for the Analysis of Measurement Invariance, Applied Psychological Measurement, 10.1177/0146621617748323, 43, 3, (241-250), (2017).
- Shiyu Wang, Yan Yang, Steven Andrew Culpepper, Jeffrey A. Douglas, Tracking Skill Acquisition With Cognitive Diagnosis Models: A Higher-Order, Hidden Markov Model With Covariates, Journal of Educational and Behavioral Statistics, 10.3102/1076998617719727, 43, 1, (57-87), (2017).
- See more
