Defining a Family of Cognitive Diagnosis Models Using Log-Linear Models with Latent Variables

Psychometrika ◽  
2008 ◽  
Vol 74 (2) ◽  
pp. 191-210 ◽  
Author(s):  
Robert A. Henson ◽  
Jonathan L. Templin ◽  
John T. Willse
Keyword(s):  
Latent Variables ◽  
Linear Models ◽  
Cognitive Diagnosis ◽  
Cognitive Diagnosis Models ◽  
Log Linear

scholarly journals Using JAGS for Bayesian Cognitive Diagnosis Modeling: A Tutorial

2019 ◽  
Vol 44 (4) ◽  
pp. 473-503 ◽  
Author(s):  
Peida Zhan ◽  
Hong Jiao ◽  
Kaiwen Man ◽  
Lijun Wang
Keyword(s):  
Gibbs Sampler ◽  
Logistic Model ◽  
Structural Model ◽  
Higher Order ◽  
Unified Model ◽  
Cognitive Diagnosis ◽  
Cognitive Diagnosis Models ◽  
Log Linear ◽  
Linear Logistic Model ◽  
Or Gate

In this article, we systematically introduce the just another Gibbs sampler (JAGS) software program to fit common Bayesian cognitive diagnosis models (CDMs) including the deterministic inputs, noisy “and” gate model; the deterministic inputs, noisy “or” gate model; the linear logistic model; the reduced reparameterized unified model; and the log-linear CDM (LCDM). Further, we introduce the unstructured latent structural model and the higher order latent structural model. We also show how to extend these models to consider polytomous attributes, the testlet effect, and longitudinal diagnosis. Finally, we present an empirical example as a tutorial to illustrate how to use JAGS codes in R.

scholarly journals Assessing Change in Latent Skills Across Time With Longitudinal Cognitive Diagnosis Modeling: An Evaluation of Model Performance

2016 ◽  
Vol 77 (3) ◽  
pp. 369-388 ◽  
Author(s):  
Yasemin Kaya ◽  
Walter L. Leite
Keyword(s):  
Latent Variables ◽  
Model Performance ◽  
Repeated Measurements ◽  
Cognitive Diagnosis ◽  
Longitudinal Models ◽  
Monte Carlo Simulation Study ◽  
Transition Analysis ◽  
Cognitive Diagnosis Models ◽  
Study Results ◽  
Cognitive Diagnosis Modeling

Cognitive diagnosis models are diagnostic models used to classify respondents into homogenous groups based on multiple categorical latent variables representing the measured cognitive attributes. This study aims to present longitudinal models for cognitive diagnosis modeling, which can be applied to repeated measurements in order to monitor attribute stability of individuals and to account for respondent dependence. Models based on combining latent transition analysis modeling and the DINA and DINO cognitive diagnosis models were developed and then evaluated through a Monte Carlo simulation study. The study results indicate that the proposed models provide adequate convergence and correct classification rates.

On Permissible Attribute Classes in Noncompensatory Cognitive Diagnosis Models

Methodology ◽  
2014 ◽  
Vol 10 (3) ◽  
pp. 100-107 ◽  
Author(s):  
Jürgen Groß ◽  
Ann Cathrice George
Keyword(s):  
Diagnostic Information ◽  
Cognitive Diagnosis ◽  
Latent Classes ◽  
Psychometric Test ◽  
Cognitive Diagnosis Models ◽  
Dina Model

When a psychometric test has been completed by a number of examinees, an afterward analysis of required skills or attributes may improve the extraction of diagnostic information. Relying upon the retrospectively specified item-by-attribute matrix, such an investigation may be carried out by classifying examinees into latent classes, consisting of subsets of required attributes. Specifically, various cognitive diagnosis models may be applied to serve this purpose. In this article it is shown that the permission of all possible attribute combinations as latent classes can have an undesired effect in the classification process, and it is demonstrated how an appropriate elimination of specific classes may improve the classification results. As an easy example, the popular deterministic input, noisy “and” gate (DINA) model is applied to Tatsuoka’s famous fraction subtraction data, and results are compared to current discussions in the literature.

When and why are log-linear models self-normalizing?

2015 ◽  
Author(s):  
Jacob Andreas ◽  
Dan Klein
Keyword(s):  
Linear Models ◽  
Log Linear

Log-Linear Models with Dependent Spatial Data

1983 ◽  
Vol 15 (6) ◽  
pp. 801-813 ◽  
Author(s):  
B Fingleton
Keyword(s):  
Spatial Data ◽  
Statistical Models ◽  
Linear Models ◽  
Square Lattice ◽  
Categorical Variables ◽  
Systematic Sampling ◽  
Pairwise Correlations ◽  
Independent Observations ◽  
Intersection Points ◽  
Log Linear

Log-linear models are an appropriate means of determining the magnitude and direction of interactions between categorical variables that in common with other statistical models assume independent observations. Spatial data are often dependent rather than independent and thus the analysis of spatial data by log-linear models may erroneously detect interactions between variables that are spurious and are the consequence of pairwise correlations between observations. A procedure is described in this paper to accommodate these effects that requires only very minimal assumptions about the nature of the autocorrelation process given systematic sampling at intersection points on a square lattice.

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