A Multilevel Multidimensional Finite Mixture Item Response Model to Cluster Respondents and Countries

Abstract. The aim of this study was to test the multilevel multidimensional finite mixture item response model of the Forms of Self-Criticising/Attacking and Self-Reassuring Scale (FSCRS) to cluster respondents and countries from 13 samples ( N = 7,714) and from 12 countries. The practical goal was to learn how many discrete classes there are on the level of individuals (i.e., how many cut-offs are to be used) and countries (i.e., the magnitude of similarities and dissimilarities among them). We employed the multilevel multidimensional finite mixture approach which is based on an extended class of multidimensional latent class Item Response Theory (IRT) models. Individuals and countries are partitioned into discrete latent classes with different levels of self-criticism and self-reassurance, taking into account at the same time the multidimensional structure of the construct. This approach was applied to the analysis of the relationships between observed characteristics and latent trait at different levels (individuals and countries), and across different dimensions using the three-dimensional measure of the FSCRS. Results showed that respondents’ scores were dependent on unobserved (latent class) individual and country membership, the multidimensional structure of the instrument, and justified the use of a multilevel multidimensional finite mixture item response model in the comparative psychological assessment of individuals and countries. Latent class analysis of the FSCRS showed that individual participants and countries could be divided into discrete classes. Along with the previous findings that the FSCRS is psychometrically robust we can recommend using the FSCRS for measuring self-criticism.

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A Gibbs Sampler for the Multidimensional Item Response Model

ISRN Applied Mathematics ◽

10.5402/2012/269385 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 10

Author(s):

Yanyan Sheng ◽

Todd C. Headrick

Keyword(s):

Item Response ◽

Latent Trait ◽

Multidimensional Item Response Theory ◽

Relative Importance ◽

Response Model ◽

Item Response Model ◽

Mcmc Algorithm ◽

Multidimensional Item Response ◽

Irt Models ◽

Latent Traits

Current procedures for estimating compensatory multidimensional item response theory (MIRT) models using Markov chain Monte Carlo (MCMC) techniques are inadequate in that they do not directly model the interrelationship between latent traits. This limits the implementation of the model in various applications and further prevents the development of other types of IRT models that offer advantages not realized in existing models. In view of this, an MCMC algorithm is proposed for MIRT models so that the actual latent structure is directly modeled. It is demonstrated that the algorithm performs well in modeling parameters as well as intertrait correlations and that the MIRT model can be used to explore the relative importance of a latent trait in answering each test item.

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A multilevel finite mixture item response model to cluster examinees and schools

Advances in Data Analysis and Classification ◽

10.1007/s11634-014-0196-0 ◽

2015 ◽

Vol 10 (1) ◽

pp. 53-70 ◽

Cited By ~ 14

Author(s):

Michela Gnaldi ◽

Silvia Bacci ◽

Francesco Bartolucci

Keyword(s):

Item Response ◽

Finite Mixture ◽

Response Model ◽

Item Response Model

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

Psychological Medicine ◽

10.1017/s0033291704003563 ◽

2004 ◽

Vol 35 (4) ◽

pp. 475-487 ◽

Cited By ~ 71

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.

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A Zero-Inflated Box-Cox Normal Unipolar Item Response Model for Measuring Constructs of Psychopathology

Applied Psychological Measurement ◽

10.1177/0146621618758291 ◽

2018 ◽

Vol 42 (7) ◽

pp. 571-589 ◽

Cited By ~ 1

Author(s):

Brooke E. Magnus ◽

Yang Liu

Keyword(s):

Item Response ◽

Latent Variable ◽

Model Comparison ◽

Latent Class ◽

Normal Population ◽

Empirical Support ◽

Variable Density ◽

Parameter Estimates ◽

Response Model ◽

Item Response Model

This research introduces a latent class item response theory (IRT) approach for modeling item response data from zero-inflated, positively skewed, and arguably unipolar constructs of psychopathology. As motivating data, the authors use 4,925 responses to the Patient Health Questionnaire (PHQ-9), a nine Likert-type item depression screener that inquires about a variety of depressive symptoms. First, Lucke’s log-logistic unipolar item response model is extended to accommodate polytomous responses. Then, a nontrivial proportion of individuals who do not endorse any of the symptoms are accounted for by including a nonpathological class that represents those who may be absent on or at some floor level of the latent variable that is being measured by the PHQ-9. To enhance flexibility, a Box-Cox normal distribution is used to empirically determine a transformation parameter that can help characterize the degree of skewness in the latent variable density. A model comparison approach is used to test the necessity of the features of the proposed model. Results suggest that (a) the Box-Cox normal transformation provides empirical support for using a log-normal population density, and (b) model fit substantially improves when a nonpathological latent class is included. The parameter estimates from the latent class IRT model are used to interpret the psychometric properties of the PHQ-9, and a method of computing IRT scale scores that reflect unipolar constructs is described, focusing on how these scores may be used in clinical contexts.

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About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model

10.20944/preprints202105.0699.v1 ◽

2021 ◽

Author(s):

Alexander Robitzsch

Keyword(s):

Item Response ◽

Logistic Model ◽

Latent Trait ◽

Response Model ◽

Item Response Model ◽

Numerical Illustration ◽

Scoring Model ◽

Estimation Techniques ◽

Pisa Data ◽

Two Parameter

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation.

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