Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis

被引：5

作者：

Liu, Ying ^{[1
]}

Culpepper, Steven Andrew ^{[1
]}

Chen, Yuguo ^{[1
]}

机构：

[1] Univ Illinois, Dept Stat, Comp Applicat Bldg,Room 152,605 E Springfield Ave, Champaign, IL 61820 USA

来源：

PSYCHOMETRIKA | 2023年 / 88卷 / 02期

关键词：

cognitive diagnosis model; DINA model; generic identifiability; hidden Markov model; LATENT CLASS MODELS;

D O I：

10.1007/s11336-023-09904-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Hidden Markov models (HMMs) have been applied in various domains, which makes the identifiability issue of HMMs popular among researchers. Classical identifiability conditions shown in previous studies are too strong for practical analysis. In this paper, we propose generic identifiability conditions for discrete time HMMs with finite state space. Also, recent studies about cognitive diagnosis models (CDMs) applied first-order HMMs to track changes in attributes related to learning. However, the application of CDMs requires a known Q matrix to infer the underlying structure between latent attributes and items, and the identifiability constraints of the model parameters should also be specified. We propose generic identifiability constraints for our restricted HMM and then estimate the model parameters, including the Q matrix, through a Bayesian framework. We present Monte Carlo simulation results to support our conclusion and apply the developed model to a real dataset.

引用

页码：361 / 386

页数：26

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