Explanatory Secondary Dimension Modeling of Latent Differential Item Functioning

2011 ◽  
Vol 35 (8) ◽  
pp. 583-603 ◽  
Author(s):  
Paul De Boeck ◽  
Sun-Joo Cho ◽  
Mark Wilson
Keyword(s):  
Differential Item Functioning ◽  
Mixture Models ◽  
Latent Class ◽  
The Other ◽  
Model Parameters ◽  
Latent Classes ◽  
Property A ◽  
Arithmetic Operations ◽  
Item Functioning ◽  
Time Specific

The models used in this article are secondary dimension mixture models with the potential to explain differential item functioning (DIF) between latent classes, called latent DIF. The focus is on models with a secondary dimension that is at the same time specific to the DIF latent class and linked to an item property. A description of the models is provided along with a means of estimating model parameters using easily available software and a description of how the models behave in two applications. One application concerns a test that is sensitive to speededness and the other is based on an arithmetic operations test where the division items show latent DIF.

Bayesian nonparametric latent class model for longitudinal data

2020 ◽  
Vol 29 (11) ◽  
pp. 3381-3395
Author(s):  
Wonmo Koo ◽  
Heeyoung Kim
Keyword(s):  
Longitudinal Data ◽  
Latent Class ◽  
Latent Class Model ◽  
Latent Class Models ◽  
Model Parameters ◽  
Latent Classes ◽  
Bayesian Nonparametric ◽  
Class Model ◽  
Proposed Model ◽  
Class Models

Latent class models have been widely used in longitudinal studies to uncover unobserved heterogeneity in a population and find the characteristics of the latent classes simultaneously using the class allocation probabilities dependent on predictors. However, previous latent class models for longitudinal data suffer from uncertainty in the choice of the number of latent classes. In this study, we propose a Bayesian nonparametric latent class model for longitudinal data, which allows the number of latent classes to be inferred from the data. The proposed model is an infinite mixture model with predictor-dependent class allocation probabilities; an individual longitudinal trajectory is described by the class-specific linear mixed effects model. The model parameters are estimated using Markov chain Monte Carlo methods. The proposed model is validated using a simulated example and a real-data example for characterizing latent classes of estradiol trajectories over the menopausal transition using data from the Study of Women’s Health Across the Nation.

scholarly journals The Q-Matrix Anchored Mixture Rasch Model

2021 ◽  
Vol 12 ◽  
Author(s):  
Ming-Chi Tseng ◽  
Wen-Chung Wang
Keyword(s):  
Rasch Model ◽  
Latent Variable ◽  
Latent Class ◽  
Parameter Estimates ◽  
Model Parameters ◽  
Latent Classes ◽  
Modeling Framework ◽  
Class Invariant ◽  
Common Scale ◽  
Q Matrix

Mixture item response theory (IRT) models include a mixture of latent subpopulations such that there are qualitative differences between subgroups but within each subpopulation the measure model based on a continuous latent variable holds. Under this modeling framework, students can be characterized by both their location on a continuous latent variable and by their latent class membership according to Students’ responses. It is important to identify anchor items for constructing a common scale between latent classes beforehand under the mixture IRT framework. Then, all model parameters across latent classes can be estimated on the common scale. In the study, we proposed Q-matrix anchored mixture Rasch model (QAMRM), including a Q-matrix and the traditional mixture Rasch model. The Q-matrix in QAMRM can use class invariant items to place all model parameter estimates from different latent classes on a common scale regardless of the ability distribution. A simulation study was conducted, and it was found that the estimated parameters of the QAMRM recovered fairly well. A real dataset from the Certificate of Proficiency in English was analyzed with the QAMRM, LCDM. It was found the QAMRM outperformed the LCDM in terms of model fit indices.

scholarly journals Regularized Latent Class Analysis for Polytomous Item Responses: An Application to SPM-LS Data

2020 ◽  
Vol 8 (3) ◽  
pp. 30 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Latent Class ◽  
Latent Class Model ◽  
Simulated Data ◽  
Latent Class Models ◽  
Latent Classes ◽  
Polytomous Item ◽  
Item Functioning ◽  
Item Responses ◽  
Polytomous Item Responses ◽  
Raven's Standard Progressive Matrices

The last series of Raven’s standard progressive matrices (SPM-LS) test was studied with respect to its psychometric properties in a series of recent papers. In this paper, the SPM-LS dataset is analyzed with regularized latent class models (RLCMs). For dichotomous item response data, an alternative estimation approach based on fused regularization for RLCMs is proposed. For polytomous item responses, different alternative fused regularization penalties are presented. The usefulness of the proposed methods is demonstrated in a simulated data illustration and for the SPM-LS dataset. For the SPM-LS dataset, it turned out the regularized latent class model resulted in five partially ordered latent classes. In total, three out of five latent classes are ordered for all items. For the remaining two classes, violations for two and three items were found, respectively, which can be interpreted as a kind of latent differential item functioning.

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