Regularized Latent Class Analysis with Application in Cognitive Diagnosis

Yunxiao Chen, Xiaoou Li, Jingchen Liu, Zhiliang Ying

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each component of the model usually having a practical meaning. However, parameterized diagnostic classification models are sometimes too simple to capture all the data patterns, resulting in significant model lack of fit. In this paper, we attempt to obtain a compromise between interpretability and goodness of fit by regularizing a latent class model. Our approach starts with minimal assumptions on the data structure, followed by suitable regularization to reduce complexity, so that readily interpretable, yet flexible model is obtained. An expectation–maximization-type algorithm is developed for efficient computation. It is shown that the proposed approach enjoys good theoretical properties. Results from simulation studies and a real application are presented.

Original languageEnglish (US)
Pages (from-to)660-692
Number of pages33
JournalPsychometrika
Volume82
Issue number3
DOIs
StatePublished - Sep 1 2017

Fingerprint

Latent Class Analysis
Diagnostics
Model
Lack of Fit
Latent Class Model
Expectation Maximization
Interpretability
Goodness of fit
Regularization
Data Structures
Data structures
Attribute
Simulation Study

Keywords

  • EM algorithm
  • consistency
  • diagnostic classification models
  • latent class analysis
  • regularization

Cite this

Regularized Latent Class Analysis with Application in Cognitive Diagnosis. / Chen, Yunxiao; Li, Xiaoou; Liu, Jingchen; Ying, Zhiliang.

In: Psychometrika, Vol. 82, No. 3, 01.09.2017, p. 660-692.

Research output: Contribution to journalArticle

Chen, Yunxiao ; Li, Xiaoou ; Liu, Jingchen ; Ying, Zhiliang. / Regularized Latent Class Analysis with Application in Cognitive Diagnosis. In: Psychometrika. 2017 ; Vol. 82, No. 3. pp. 660-692.
@article{eb7fa269f5bd49fa8a97c5cb6efee45b,
title = "Regularized Latent Class Analysis with Application in Cognitive Diagnosis",
abstract = "Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each component of the model usually having a practical meaning. However, parameterized diagnostic classification models are sometimes too simple to capture all the data patterns, resulting in significant model lack of fit. In this paper, we attempt to obtain a compromise between interpretability and goodness of fit by regularizing a latent class model. Our approach starts with minimal assumptions on the data structure, followed by suitable regularization to reduce complexity, so that readily interpretable, yet flexible model is obtained. An expectation–maximization-type algorithm is developed for efficient computation. It is shown that the proposed approach enjoys good theoretical properties. Results from simulation studies and a real application are presented.",
keywords = "EM algorithm, consistency, diagnostic classification models, latent class analysis, regularization",
author = "Yunxiao Chen and Xiaoou Li and Jingchen Liu and Zhiliang Ying",
year = "2017",
month = "9",
day = "1",
doi = "10.1007/s11336-016-9545-6",
language = "English (US)",
volume = "82",
pages = "660--692",
journal = "Psychometrika",
issn = "0033-3123",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - Regularized Latent Class Analysis with Application in Cognitive Diagnosis

AU - Chen, Yunxiao

AU - Li, Xiaoou

AU - Liu, Jingchen

AU - Ying, Zhiliang

PY - 2017/9/1

Y1 - 2017/9/1

N2 - Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each component of the model usually having a practical meaning. However, parameterized diagnostic classification models are sometimes too simple to capture all the data patterns, resulting in significant model lack of fit. In this paper, we attempt to obtain a compromise between interpretability and goodness of fit by regularizing a latent class model. Our approach starts with minimal assumptions on the data structure, followed by suitable regularization to reduce complexity, so that readily interpretable, yet flexible model is obtained. An expectation–maximization-type algorithm is developed for efficient computation. It is shown that the proposed approach enjoys good theoretical properties. Results from simulation studies and a real application are presented.

AB - Diagnostic classification models are confirmatory in the sense that the relationship between the latent attributes and responses to items is specified or parameterized. Such models are readily interpretable with each component of the model usually having a practical meaning. However, parameterized diagnostic classification models are sometimes too simple to capture all the data patterns, resulting in significant model lack of fit. In this paper, we attempt to obtain a compromise between interpretability and goodness of fit by regularizing a latent class model. Our approach starts with minimal assumptions on the data structure, followed by suitable regularization to reduce complexity, so that readily interpretable, yet flexible model is obtained. An expectation–maximization-type algorithm is developed for efficient computation. It is shown that the proposed approach enjoys good theoretical properties. Results from simulation studies and a real application are presented.

KW - EM algorithm

KW - consistency

KW - diagnostic classification models

KW - latent class analysis

KW - regularization

UR - http://www.scopus.com/inward/record.url?scp=85000394581&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85000394581&partnerID=8YFLogxK

U2 - 10.1007/s11336-016-9545-6

DO - 10.1007/s11336-016-9545-6

M3 - Article

C2 - 27905058

AN - SCOPUS:85000394581

VL - 82

SP - 660

EP - 692

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 3

ER -