Passage-related local item dependence and spurious latent classes in the mixture Rasch model : a simulation study

The Andersen LRT uses sample characteristics as split criteria to evaluate Rasch model fit, or theory driven hypothesis testing for a test. The power and Type I error of a random split criterion was evaluated with a simulation study. Results consistently show a random split criterion lacks power.

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The Q-Matrix Anchored Mixture Rasch Model

Frontiers in Psychology ◽

10.3389/fpsyg.2021.564976 ◽

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.

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Agreement on the Classification of Latent Class Membership Between Different Identification Constraint Approaches in the Mixture Rasch Model

Methodology ◽

10.1027/1614-2241/a000148 ◽

2018 ◽

Vol 14 (2) ◽

pp. 82-93

Author(s):

Yi-Jhen Wu ◽

Insu Paek

Keyword(s):

Rasch Model ◽

Latent Class ◽

Model Identification ◽

Real Data ◽

Latent Classes ◽

Class Membership ◽

High Agreement ◽

Common Scale ◽

Constraint Approach

Abstract. When using the mixture Rasch model, the model identification constraints are either to set the equal means for all classes in the assumed normal ability distributions (equal ability mean constraint in short), or to set the sum of item difficulties to be zero for each class. In real data analysis, however, both constraints are not always sufficient to establish a common scale across latent classes unless some items are specified as anchor items in the estimation. If these two conventional constraint approaches recover the class membership as good as the anchor item constraint approach, the conventional constraint approaches may be considered useful for the purpose of class membership classification. This study investigated agreement on class membership between one conventional constraint (the equal ability mean) and the anchor item constraint approaches. Results showed high agreement between these two constraint approaches, indicating that the conventional constraint of the equal mean ability approach may be used to recover the latent class membership although item profiles are not correctly estimated across latent classes.

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Spurious Latent Classes in the Mixture Rasch Model

Journal of Educational Measurement ◽

10.1111/j.1745-3984.2011.00146.x ◽

2011 ◽

Vol 48 (3) ◽

pp. 313-332 ◽

Cited By ~ 16

Author(s):

Natalia Alexeev ◽

Jonathan Templin ◽

Allan S. Cohen

Keyword(s):

Rasch Model ◽

Latent Classes

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A Longitudinal Higher-Order Diagnostic Classification Model

Journal of Educational and Behavioral Statistics ◽

10.3102/1076998619827593 ◽

2019 ◽

Vol 44 (3) ◽

pp. 251-281 ◽

Cited By ~ 14

Author(s):

Peida Zhan ◽

Hong Jiao ◽

Dandan Liao ◽

Feiming Li

Keyword(s):

Parameter Estimation ◽

Simulation Study ◽

Higher Order ◽

Latent Structure ◽

Classification Model ◽

Individual Growth ◽

Diagnostic Classification ◽

Modeling Approach ◽

Local Item Dependence ◽

Diagnostic Classification Model

Providing diagnostic feedback about growth is crucial to formative decisions such as targeted remedial instructions or interventions. This article proposed a longitudinal higher-order diagnostic classification modeling approach for measuring growth. The new modeling approach is able to provide quantitative values of overall and individual growth by constructing a multidimensional higher-order latent structure to take into account the correlations among multiple latent attributes that are examined across different occasions. In addition, potential local item dependence among anchor (or repeated) items can be taken into account. Model parameter estimation is explored in a simulation study. An empirical example is analyzed to illustrate the applications and advantages of the proposed modeling approach.

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The Andersen likelihood ratio test with a random split criterion lacks power

10.31219/osf.io/gu8sq ◽

2019 ◽

Author(s):

Georg Krammer

Keyword(s):

Hypothesis Testing ◽

Likelihood Ratio Test ◽

Simulation Study ◽

Rasch Model ◽

Type I Error ◽

Model Fit ◽

Ratio Test ◽

Type I ◽

Sample Characteristics ◽

Split Criterion

The Andersen LRT uses sample characteristics as split criteria to evaluate Rasch model fit, or theory driven hypothesis testing for a test. This simulation study is the first to evaluate power and Type I error of a random split criterion. Results consistently show that a random split criterion lacks power.

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A Comprehensive Simulation Study of Estimation Methods for the Rasch Model

Stats ◽

10.3390/stats4040048 ◽

2021 ◽

Vol 4 (4) ◽

pp. 814-836

Author(s):

Alexander Robitzsch

Keyword(s):

Maximum Likelihood ◽

Simulation Study ◽

Rasch Model ◽

Item Parameter ◽

Estimation Methods ◽

Limited Information ◽

Marginal Maximum Likelihood ◽

Chi Square ◽

Parameter Estimation Methods ◽

The Rasch Model

The Rasch model is one of the most prominent item response models. In this article, different item parameter estimation methods for the Rasch model are systematically compared through a comprehensive simulation study: Different alternatives of joint maximum likelihood (JML) estimation, different alternatives of marginal maximum likelihood (MML) estimation, conditional maximum likelihood (CML) estimation, and several limited information methods (LIM). The type of ability distribution (i.e., nonnormality), the number of items, sample size, and the distribution of item difficulties were systematically varied. Across different simulation conditions, MML methods with flexible distributional specifications can be at least as efficient as CML. Moreover, in many situations (i.e., for long tests), penalized JML and JML with ε adjustment resulted in very efficient estimates and might be considered alternatives to JML implementations currently used in statistical software. Moreover, minimum chi-square (MINCHI) estimation was the best-performing LIM method. These findings demonstrate that JML estimation and LIM can still prove helpful in applied research.

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