scholarly journals Partially and Fully Noncompensatory Response Models for Dichotomous and Polytomous Items

2020 ◽  
Vol 44 (6) ◽  
pp. 415-430
Author(s):  
R. Philip Chalmers
Keyword(s):  
Item Response ◽  
Response Model ◽  
Polytomous Items ◽  
Response Models ◽  
Parameter Recovery ◽  
Response Data ◽  
Empirical Performance ◽  
Small Set ◽  
Ordered Response ◽  
Performance Results

This article extends Sympson’s partially noncompensatory dichtomous response model to ordered response data, and introduces a set of fully noncompensatory models for dichotomous and polytomous response data. The theoretical properties of the partially and fully noncompensatory response models are contrasted, and a small set of Monte Carlo simulations are presented to evaluate their parameter recovery performance. Results indicate that the respective models fit the data similarly when correctly matched to their respective population generating model. The fully noncompensatory models, however, demonstrated lower sampling variability and smaller degrees of bias than the partially noncompensatory counterparts. Based on the theoretical properties and empirical performance, it is argued that the fully noncompensatory models should be considered in item response theory applications when investigating conjunctive response processes.

scholarly journals Extreme Response Style: A Simulation Study Comparison of Three Multidimensional Item Response Models

2018 ◽  
Vol 43 (4) ◽  
pp. 322-335 ◽  
Author(s):  
Brian C. Leventhal
Keyword(s):  
Item Response ◽  
Partial Credit Model ◽  
Response Model ◽  
Multidimensional Item Response ◽  
Generalized Partial Credit Model ◽  
Response Models ◽  
Item Response Models ◽  
Nominal Response Model ◽  
Extreme Response ◽  
Generalized Partial Credit

Several multidimensional item response models have been proposed for survey responses affected by response styles. Through simulation, this study compares three models designed to account for extreme response tendencies: the IRTree Model, the multidimensional nominal response model, and the modified generalized partial credit model. The modified generalized partial credit model results in the lowest item mean squared error (MSE) across simulation conditions of sample size (500, 1,000), survey length (10, 20), and number of response options (4, 6). The multidimensional nominal response model is equally suitable for surveys measuring one substantive trait using responses to 10 four-option, forced-choice Likert-type items. Based on data validation, comparison of item MSE, and posterior predictive model checking, the IRTree Model is hypothesized to account for additional sources of construct-irrelevant variance.

scholarly journals A Note on the D-Scoring Method Adapted for Polytomous Test Items

2018 ◽  
Vol 79 (3) ◽  
pp. 545-557 ◽  
Author(s):  
Dimiter M. Dimitrov ◽  
Yong Luo
Keyword(s):  
Item Response ◽  
Psychological Assessment ◽  
Response Model ◽  
Response Functions ◽  
Graded Response Model ◽  
Unified Framework ◽  
Polytomous Items ◽  
Scoring Method ◽  
Test Items ◽  
Graded Response

An approach to scoring tests with binary items, referred to as D-scoring method, was previously developed as a classical analog to basic models in item response theory (IRT) for binary items. As some tests include polytomous items, this study offers an approach to D-scoring of such items and parallels the results with those obtained under the graded response model (GRM) for ordered polytomous items in the framework of IRT. The proposed design of using D-scoring with “virtual” binary items generated from polytomous items provides (a) ability scores that are consistent with their GRM counterparts and (b) item category response functions analogous to those obtained under the GRM. This approach provides a unified framework for D-scoring and psychometric analysis of tests with binary and/or polytomous items that can be efficient in different scenarios of educational and psychological assessment.

scholarly journals Ignoring a Multilevel Structure in Mixture Item Response Models: Impact on Parameter Recovery and Model Selection

2017 ◽  
Vol 42 (2) ◽  
pp. 136-154 ◽  
Author(s):  
Woo-yeol Lee ◽  
Sun-Joo Cho ◽  
Sonya K. Sterba
Keyword(s):  
Model Selection ◽  
Item Response ◽  
Cluster Size ◽  
Response Model ◽  
Item Response Model ◽  
Number Of Clusters ◽  
Parameter Recovery ◽  
Single Level ◽  
Multilevel Structure ◽  
Level Data

The current study investigated the consequences of ignoring a multilevel structure for a mixture item response model to show when a multilevel mixture item response model is needed. Study 1 focused on examining the consequence of ignoring dependency for within-level latent classes. Simulation conditions that may affect model selection and parameter recovery in the context of a multilevel data structure were manipulated: class-specific ICC, cluster size, and number of clusters. The accuracy of model selection (based on information criteria) and quality of parameter recovery were used to evaluate the impact of ignoring a multilevel structure. Simulation results indicated that, for the range of class-specific ICCs examined here (.1 to .3), mixture item response models which ignored a higher level nesting structure resulted in less accurate estimates and standard errors ( SEs) of item discrimination parameters when the number of clusters was larger than 24 and the cluster size was larger than six. Class-varying ICCs can have compensatory effects on bias. Also, the results suggested that a mixture item response model which ignored multilevel structure was not selected over the multilevel mixture item response model based on Bayesian information criterion (BIC) if the number of clusters and cluster size was at least 50, respectively. In Study 2, the consequences of unnecessarily fitting a multilevel mixture item response model to single-level data were examined. Reassuringly, in the context of single-level data, a multilevel mixture item response model was not selected by BIC, and its use would not distort the within-level item parameter estimates or SEs when the cluster size was at least 20. Based on these findings, it is concluded that, for class-specific ICC conditions examined here, a multilevel mixture item response model is recommended over a single-level item response model for a clustered dataset having cluster size [Formula: see text] and the number of clusters [Formula: see text].

DSM criteria for major depression: evaluating symptom patterns using latent-trait item response models

2004 ◽  
Vol 35 (4) ◽  
pp. 475-487 ◽  
Author(s):  
STEVEN H. AGGEN ◽  
MICHAEL C. NEALE ◽  
KENNETH S. KENDLER
Keyword(s):  
Major Depression ◽  
Item Response ◽  
Latent Trait ◽  
Risk Measurement ◽  
Measurement Properties ◽  
Model Parameters ◽  
Response Model ◽  
Item Response Model ◽  
Response Models ◽  
Item Response Models

Background. Expert committees of clinicians have chosen diagnostic criteria for psychiatric disorders with little guidance from measurement theory or modern psychometric methods. The DSM-III-R criteria for major depression (MD) are examined to determine the degree to which latent trait item response models can extract additional useful information.Method. The dimensionality and measurement properties of the 9 DSM-III-R criteria plus duration are evaluated using dichotomous factor analysis and the Rasch and 2 parameter logistic item response models. Quantitative liability scales are compared with a binary DSM-III-R diagnostic algorithm variable to determine the ramifications of using each approach.Results. Factor and item response model results indicated the 10 MD criteria defined a reasonably coherent unidimensional scale of liability. However, person risk measurement was not optimal. Criteria thresholds were unevenly spaced leaving scale regions poorly measured. Criteria varied in discriminating levels of risk. Compared to a binary MD diagnosis, item response model (IRM) liability scales performed far better in (i) elucidating the relationship between MD symptoms and liability, (ii) predicting the personality trait of neuroticism and future depressive episodes and (iii) more precisely estimating heritability parameters.Conclusions. Criteria for MD largely defined a single dimension of disease liability although the quality of person risk measurement was less clear. The quantitative item response scales were statistically superior in predicting relevant outcomes and estimating twin model parameters. Item response models that treat symptoms as ordered indicators of risk rather than as counts towards a diagnostic threshold more fully exploit the information available in symptom endorsement data patterns.

The Rater Bundle Model

2001 ◽  
Vol 26 (3) ◽  
pp. 283-306 ◽  
Author(s):  
Mark Wilson ◽  
Machteld Hoskens
Keyword(s):  
Item Response ◽  
Conditional Independence ◽  
State Of The Art ◽  
Simulated Data ◽  
Response Model ◽  
Item Response Model ◽  
Student Work ◽  
Response Models ◽  
Item Response Models ◽  
Current State

In this article an item response model is introduced for repeated ratings of student work, which we have called the Rater Bundle Model (RBM). Development of this model was motivated by the observation that when repeated ratings occur, the assumption of conditional independence is violated, and hence current state-of-the-art item response models, such as the rater facets model, that ignore this violation, underestimate measurement error, and overestimate reliability. In the rater bundle model these dependencies are explicitly parameterized. The model is applied to both real and simulated data to illustrate the approach.

scholarly journals Robust Haebara Linking for Many Groups in the Case of Partial Invariance

2020 ◽  
Author(s):  
Alexander Robitzsch
Keyword(s):  
Present Article ◽  
Item Response ◽  
Empirical Research ◽  
Simulation Study ◽  
Response Models ◽  
Item Response Models ◽  
Empirical Application ◽  
Response Data ◽  
Partial Invariance ◽  
Pisa Data

The comparison of group means in item response models constitutes an important issue in empirical research. The present article discusses an extension of Haebara linking by proposing a flexible class of robust linking functions for comparisons of many groups. These robust linking functions are particularly suited to item response data that are generated under partial invariance. In a simulation study, it is shown that the newly proposed robust Haebara linking approach outperforms existing approaches of Haebara linking. In an empirical application using PISA data, it is illustrated that country means can be sensitive to the choice of linking functions.

Using Data Augmentation and Markov Chain Monte Carlo for the Estimation of Unfolding Response Models

2003 ◽  
Vol 28 (3) ◽  
pp. 195-230 ◽  
Author(s):  
Matthew S. Johnson ◽  
Brian W. Junker
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Item Response ◽  
Data Augmentation ◽  
Estimation Procedure ◽  
Model Parameters ◽  
Response Model ◽  
Response Models ◽  
Mcmc Estimation

Unfolding response models, a class of item response theory (IRT) models that assume a unimodal item response function (IRF), are often used for the measurement of attitudes. Verhelst and Verstralen (1993) and Andrich and Luo (1993) independently developed unfolding response models by relating the observed responses to a more common monotone IRT model using a latent response model (LRM; Maris, 1995 ). This article generalizes their approach, and suggests a data augmentation scheme for the estimation of any unfolding response model. The article introduces two Markov chain Monte Carlo (MCMC) estimation procedures for the Bayesian estimation of unfolding model parameters; one is a direct implementation of MCMC, and the second utilizes the data augmentation method. We use the estimation procedure to analyze three data sets, one simulated, and two from real attitudinal surveys.

scholarly journals Item-Focused Trees for the Detection of Differential Item Functioning in Partial Credit Models

2017 ◽  
Vol 78 (5) ◽  
pp. 781-804 ◽  
Author(s):  
Stella Bollmann ◽  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Differential Item Functioning ◽  
Present Article ◽  
Item Response ◽  
Partial Credit Model ◽  
Partial Credit ◽  
Response Models ◽  
Item Response Models ◽  
Item Functioning ◽  
Alternative Approaches ◽  
Ordered Response

Various methods to detect differential item functioning (DIF) in item response models are available. However, most of these methods assume that the responses are binary, and so for ordered response categories available methods are scarce. In the present article, DIF in the widely used partial credit model is investigated. An item-focused tree is proposed that allows the detection of DIF items, which might affect the performance of the partial credit model. The method uses tree methodology, yielding a tree for each item that is detected as DIF item. The visualization as trees makes the results easily accessible, as the obtained trees show which variables induce DIF and in which way. In the present paper, the new method is compared with alternative approaches and simulations demonstrate the performance of the method.

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