scholarly journals Cognitive Diagnostic Models With Attribute Hierarchies: Model Estimation With a Restricted Q-Matrix Design

2018 ◽  
Vol 43 (4) ◽  
pp. 255-271 ◽  
Author(s):  
Dongbo Tu ◽  
Shiyu Wang ◽  
Yan Cai ◽  
Jeff Douglas ◽  
Hua-Hua Chang
Keyword(s):  
Classification Accuracy ◽  
Latent Class ◽  
Estimation Procedure ◽  
Syllogistic Reasoning ◽  
Estimation Methods ◽  
Diagnostic Models ◽  
Cognitive Diagnostic Models ◽  
Attribute Hierarchy ◽  
Q Matrix ◽  
Matrix Design

Attribute hierarchy is a common assumption in the educational context, where the mastery of one attribute is assumed to be a prerequisite to the mastery of another one. The attribute hierarchy can be incorporated through a restricted Q matrix that implies the specified structure. The latent class–based cognitive diagnostic models (CDMs) usually do not assume a hierarchical structure among attributes, which means all profiles of attributes are possible in a population of interest. This study investigates different estimation methods to the classification accuracy for a family of CDMs when they are combined with a restricted Q-matrix design. A simulation study is used to explain the misclassification caused by an unrestricted estimation procedure. The advantages of the restricted estimation procedure utilizing attribute hierarchies for increased classification accuracy are also further illustrated through a real data analysis on a syllogistic reasoning diagnostic assessment. This research can provide guidelines for educational and psychological researchers and practitioners when they use CDMs to analyze the data with a restricted Q-matrix design and make them be aware of the potentially contaminated classification results if ignoring attribute hierarchies.

scholarly journals Examining the Impact of Differential Item Functioning on Classification Accuracy in Cognitive Diagnostic Models

2019 ◽  
Vol 44 (4) ◽  
pp. 267-281 ◽  
Author(s):  
Justin Paulsen ◽  
Dubravka Svetina ◽  
Yanan Feng ◽  
Montserrat Valdivia
Keyword(s):  
Differential Item Functioning ◽  
Classification Accuracy ◽  
Simple Structure ◽  
Future Directions ◽  
Content Areas ◽  
Item Functioning ◽  
Diagnostic Models ◽  
Cognitive Diagnostic Models ◽  
The Impact ◽  
Item Types

Cognitive diagnostic models (CDMs) are of growing interest in educational research because of the models’ ability to provide diagnostic information regarding examinees’ strengths and weaknesses suited to a variety of content areas. An important step to ensure appropriate uses and interpretations from CDMs is to understand the impact of differential item functioning (DIF). While methods of detecting DIF in CDMs have been identified, there is a limited understanding of the extent to which DIF affects classification accuracy. This simulation study provides a reference to practitioners to understand how different magnitudes and types of DIF interact with CDM item types and group distributions and sample sizes to influence attribute- and profile-level classification accuracy. The results suggest that attribute-level classification accuracy is robust to DIF of large magnitudes in most conditions, while profile-level classification accuracy is negatively influenced by the inclusion of DIF. Conditions of unequal group distributions and DIF located on simple structure items had the greatest effect in decreasing classification accuracy. The article closes by considering implications of the results and future directions.

Use of simulation–extrapolation estimation in catch–effort analyses

1999 ◽  
Vol 56 (7) ◽  
pp. 1234-1240
Author(s):  
W R Gould ◽  
L A Stefanski ◽  
K H Pollock
Keyword(s):  
Measurement Error ◽  
Measurement Errors ◽  
Mean Squared Error ◽  
Estimation Procedure ◽  
Bias Reduction ◽  
Estimation Methods ◽  
Effort Estimation ◽  
Stat Assoc ◽  
General Terms ◽  
Naive Estimator

All catch-effort estimation methods implicitly assume catch and effort are known quantities, whereas in many cases, they have been estimated and are subject to error. We evaluate the application of a simulation-based estimation procedure for measurement error models (J.R. Cook and L.A. Stefanski. 1994. J. Am. Stat. Assoc. 89: 1314-1328) in catch-effort studies. The technique involves a simulation component and an extrapolation step, hence the name SIMEX estimation. We describe SIMEX estimation in general terms and illustrate its use with applications to real and simulated catch and effort data. Correcting for measurement error with SIMEX estimation resulted in population size and catchability coefficient estimates that were substantially less than naive estimates, which ignored measurement errors in some cases. In a simulation of the procedure, we compared estimators from SIMEX with "naive" estimators that ignore measurement errors in catch and effort to determine the ability of SIMEX to produce bias-corrected estimates. The SIMEX estimators were less biased than the naive estimators but in some cases were also more variable. Despite the bias reduction, the SIMEX estimator had a larger mean squared error than the naive estimator for one of two artificial populations studied. However, our results suggest the SIMEX estimator may outperform the naive estimator in terms of bias and precision for larger populations.

A Two-Stage Conditional Estimation Procedure for Unrestricted Latent Class Models

1980 ◽  
Vol 5 (2) ◽  
pp. 129-156 ◽  
Author(s):  
George B. Macready ◽  
C. Mitchell Dayton
Keyword(s):  
General Class ◽  
Latent Class ◽  
Estimation Procedure ◽  
Error Rates ◽  
Latent Class Models ◽  
Parameter Estimates ◽  
Probability Models ◽  
Two Stage ◽  
Conditional Estimation ◽  
Class Models

A variety of latent class models has been presented during the last 10 years which are restricted forms of a more general class of probability models. Each of these models involves an a priori dependency structure among a set of dichotomously scored tasks that define latent class response patterns across the tasks. In turn, the probabilities related to these latent class patterns along with a set of “Omission” and “intrusion” error rates for each task are the parameters used in defining models within this general class. One problem in using these models is that the defining parameters for a specific model may not be “identifiable.” To deal with this problem, researchers have considered curtailing the form of the model of interest by placing restrictions on the defining parameters. The purpose of this paper is to describe a two-stage conditional estimation procedure which results in reasonable estimates of specific models even though they may be nonidentifiable. This procedure involves the following stages: (a) establishment of initial parameter estimates and (b) step-wise maximum likelihood solutions for latent class probabilities and classification errors with iteration of this process until stable parameter estimates across successive iterations are obtained.

Assessing Fit of Cognitive Diagnostic Models A Case Study

2007 ◽  
Vol 67 (2) ◽  
pp. 239-257 ◽  
Author(s):  
Sandip Sinharay ◽  
Russell G. Almond
Keyword(s):  
Diagnostic Models ◽  
Cognitive Diagnostic Models
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