Learning Latent and Hierarchical Structures in Cognitive Diagnosis Models

04/05/2021
by   Chenchen Ma, et al.
0

Cognitive Diagnosis Models (CDMs) are a special family of discrete latent variable models that are widely used in modern educational, psychological, social and biological sciences. A key component of CDMs is a binary Q-matrix characterizing the dependence structure between the items and the latent attributes. Additionally, researchers also assume in many applications certain hierarchical structures among the latent attributes to characterize their dependence. In most CDM applications, the attribute-attribute hierarchical structures, the item-attribute Q-matrix, the item-level diagnostic model, as well as the number of latent attributes, need to be fully or partially pre-specified, which however may be subjective and misspecified as noted by many recent studies. This paper considers the problem of jointly learning these latent and hierarchical structures in CDMs from observed data with minimal model assumptions. Specifically, a penalized likelihood approach is proposed to select the number of attributes and estimate the latent and hierarchical structures simultaneously. An efficient expectation-maximization (EM) algorithm and a latent structure recovery algorithm are developed, and statistical consistency theory is also established under mild conditions. The good performance of the proposed method is illustrated by simulation studies and a real data application in educational assessment.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 33

page 34

04/08/2019

Learning Attribute Patterns in High-Dimensional Structured Latent Attribute Models

Structured latent attribute models (SLAMs) are a special family of discr...
06/19/2019

Identification and Estimation of Hierarchical Latent Attribute Models

Hierarchical Latent Attribute Models (HLAMs) are a popular family of dis...
06/06/2021

Hypothesis Testing for Hierarchical Structures in Cognitive Diagnosis Models

Cognitive Diagnosis Models (CDMs) are a special family of discrete laten...
09/09/2020

A Joint MLE Approach to Large-Scale Structured Latent Attribute Analysis

Structured Latent Attribute Models (SLAMs) are a family of discrete late...
11/05/2019

A Latent Topic Model with Markovian Transition for Process Data

We propose a latent topic model with a Markovian transition for process ...
12/22/2020

Identifiability of Bifactor Models

The bifactor model and its extensions are multidimensional latent variab...
10/09/2018

Sufficient and Necessary Conditions for the Identifiability of the Q-matrix

Restricted latent class models (RLCMs) have recently gained prominence i...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.