Bayesian Inference for IRT Models with Non-Normal Latent Trait Distributions

2020 ◽  
pp. 1-21
Author(s):  
Xue Zhang ◽  
Chun Wang ◽  
David J. Weiss ◽  
Jian Tao
Keyword(s):  
Bayesian Inference ◽  
Latent Trait ◽  
Irt Models

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

2020 ◽  
pp. 1-12
Author(s):  
Martin Kanovský ◽  
Júlia Halamová ◽  
David C. Zuroff ◽  
Nicholas A. Troop ◽  
Paul Gilbert ◽  
...  
Keyword(s):  
Item Response ◽  
Latent Class ◽  
Latent Trait ◽  
Three Dimensional ◽  
Finite Mixture ◽  
Response Model ◽  
Item Response Model ◽  
Irt Models ◽  
Dimensional Measure ◽  
Different Levels

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.

scholarly journals A study of alternative approaches to non-normal latent trait distributions in item response theory models used for health outcome measurement

2020 ◽  
Vol 29 (4) ◽  
pp. 1030-1048
Author(s):  
Niels Smits ◽  
Oğuzhan Öğreden ◽  
Mauricio Garnier-Villarreal ◽  
Caroline B Terwee ◽  
R Philip Chalmers
Keyword(s):  
Health Outcome ◽  
Item Response Theory ◽  
Health Outcomes ◽  
Item Response ◽  
Outcome Measurement ◽  
Latent Trait ◽  
Parameter Estimates ◽  
Response Theory ◽  
Zero Inflation ◽  
Irt Models

It is often unrealistic to assume normally distributed latent traits in the measurement of health outcomes. If normality is violated, the item response theory (IRT) models that are used to calibrate questionnaires may yield parameter estimates that are biased. Recently, IRT models were developed for dealing with specific deviations from normality, such as zero-inflation (“excess zeros”) and skewness. However, these models have not yet been evaluated under conditions representative of item bank development for health outcomes, characterized by a large number of polytomous items. A simulation study was performed to compare the bias in parameter estimates of the graded response model (GRM), polytomous extensions of the zero-inflated mixture IRT (ZIM-GRM), and Davidian Curve IRT (DC-GRM). In the case of zero-inflation, the GRM showed high bias overestimating discrimination parameters and yielding estimates of threshold parameters that were too high and too close to one another, while ZIM-GRM showed no bias. In the case of skewness, the GRM and DC-GRM showed little bias with the GRM showing slightly better results. Consequences for the development of health outcome measures are discussed.

scholarly journals Refining the assessment of disrupted maternal communication: Using item response models to identify central indicators of disrupted behavior

2017 ◽  
Vol 31 (1) ◽  
pp. 261-277 ◽  
Author(s):  
John D. Haltigan ◽  
Sheri Madigan ◽  
Elisa Bronfman ◽  
Heidi N. Bailey ◽  
Catherine Borland-Kerr ◽  
...  
Keyword(s):  
Item Response ◽  
Discriminant Validity ◽  
Developmental Psychopathology ◽  
Latent Trait ◽  
Maternal Sensitivity ◽  
Coding System ◽  
Infant Attachment ◽  
Irt Models ◽  
Convergent And Discriminant Validity ◽  
Maternal Communication

AbstractThe Atypical Maternal Behavior Instrument for Assessment and Classification (AMBIANCE; Bronfman, Madigan, & Lyons-Ruth, 2009–2014; Bronfman, Parsons, & Lyons-Ruth, 1992–2004) is a widely used and well-validated measure for assessing disrupted forms of caregiver responsiveness within parent–child interactions. However, it requires evaluating approximately 150 behavioral items from videotape and extensive training to code, thus making its use impractical in most clinical contexts. Accordingly, the primary aim of the current study was to identify a reduced set of behavioral indicators most central to the AMBIANCE coding system using latent-trait item response theory (IRT) models. Observed mother–infant interaction data previously coded with the AMBIANCE was pooled from laboratories in both North America and Europe (N = 343). Using 2-parameter logistic IRT models, a reduced set of 45 AMBIANCE items was identified. Preliminary convergent and discriminant validity was evaluated in relation to classifications of maternal disrupted communication assigned using the full set of AMBIANCE indicators, to infant attachment disorganization, and to maternal sensitivity. The results supported the construct validity of the refined item set, opening the way for development of a brief screening measure for disrupted maternal communication. IRT models in clinical scale refinement and their potential for bridging clinical and research objectives in developmental psychopathology are discussed.

scholarly journals A Gibbs Sampler for the Multidimensional Item Response Model

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
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.

scholarly journals Are attitudes toward immigration changing in Europe? An analysis based on latent class IRT models

2021 ◽  
Author(s):  
Ewa Genge ◽  
Francesco Bartolucci
Keyword(s):  
Latent Class ◽  
Temporal Dynamics ◽  
Latent Trait ◽  
European Social Survey ◽  
Host Countries ◽  
Irt Models ◽  
Specific Interpretation ◽  
Changing Attitudes ◽  
Time Varying Covariates ◽  
Attitudes Toward Immigration

AbstractWe analyze the changing attitudes toward immigration in EU host countries in the last few years (2010–2018) on the basis of the European Social Survey data. These data are collected by the administration of a questionnaire made of items concerning different aspects related to the immigration phenomenon. For this analysis, we rely on a latent class approach considering a variety of models that allow for: (1) multidimensionality; (2) discreteness of the latent trait distribution; (3) time-constant and time-varying covariates; and (4) sample weights. Through these models we find latent classes of Europeans with similar levels of immigration acceptance and we study the effect of different socio-economic covariates on the probability of belonging to these classes for which we provide a specific interpretation. In this way we show which countries tend to be more or less positive toward immigration and we analyze the temporal dynamics of the phenomenon under study.

Examining the Robustness of the Graded Response and 2-Parameter Logistic Models to Violations of Construct Normality

2022 ◽  
pp. 001316442110634
Author(s):  
Patrick D. Manapat ◽  
Michael C. Edwards
Keyword(s):  
Logistic Model ◽  
Population Distribution ◽  
Latent Trait ◽  
Logistic Models ◽  
Skewed Distribution ◽  
Parameter Recovery ◽  
Irt Models ◽  
Psychological Theories ◽  
Graded Response ◽  
Computationally Intensive

When fitting unidimensional item response theory (IRT) models, the population distribution of the latent trait (θ) is often assumed to be normally distributed. However, some psychological theories would suggest a nonnormal θ. For example, some clinical traits (e.g., alcoholism, depression) are believed to follow a positively skewed distribution where the construct is low for most people, medium for some, and high for few. Failure to account for nonnormality may compromise the validity of inferences and conclusions. Although corrections have been developed to account for nonnormality, these methods can be computationally intensive and have not yet been widely adopted. Previous research has recommended implementing nonnormality corrections when θ is not “approximately normal.” This research focused on examining how far θ can deviate from normal before the normality assumption becomes untenable. Specifically, our goal was to identify the type(s) and degree(s) of nonnormality that result in unacceptable parameter recovery for the graded response model (GRM) and 2-parameter logistic model (2PLM).

Item Response Theory Models Applied to Data Allowing Examinee Choice

1998 ◽  
Vol 23 (3) ◽  
pp. 236-243 ◽  
Author(s):  
Eric T. Bradlow ◽  
Neal Thomas
Keyword(s):  
Bayesian Inference ◽  
Item Response Theory ◽  
Item Response ◽  
Estimation Methods ◽  
Response Theory ◽  
Standard Methods ◽  
Irt Models ◽  
Item Responses ◽  
Low Dimensional ◽  
Item Response Theory Models

Examinations that permit students to choose a subset of the items are popular despite the potential that students may take examinations of varying difficulty as a result of their choices. We provide a set of conditions for the validity of inference for Item Response Theory (IRT) models applied to data collected from choice-based examinations. Valid likelihood and Bayesian inference using standard estimation methods require (except in extraordinary circumstances) that there is no dependence, after conditioning on the observed item responses, between the examinees choices and their (potential but unobserved) responses to omitted items, as well as their latent abilities. These independence assumptions are typical of those required in much more general settings. Common low-dimensional IRT models estimated by standard methods, though potentially useful tools for educational data, do not resolve the difficult problems posed by choice-based data.

Item response theory and the measurement of psychiatric constructs: some empirical and conceptual issues and challenges

2016 ◽  
Vol 46 (10) ◽  
pp. 2025-2039 ◽  
Author(s):  
S. P. Reise ◽  
A. Rodriguez
Keyword(s):  
Item Response Theory ◽  
Item Response ◽  
Latent Trait ◽  
Response Theory ◽  
Outcomes Measurement ◽  
Measurement Models ◽  
Irt Models ◽  
Trait Distribution ◽  
Item Pools ◽  
Latent Trait Distribution

Item response theory (IRT) measurement models are now commonly used in educational, psychological, and health-outcomes measurement, but their impact in the evaluation of measures of psychiatric constructs remains limited. Herein we present two, somewhat contradictory, theses. The first is that, when skillfully applied, IRT has much to offer psychiatric measurement in terms of scale development, psychometric analysis, and scoring. The second argument, however, is that psychiatric measurement presents some unique challenges to the application of IRT – challenges that may not be easily addressed by application of conventional IRT models and methods. These challenges include, but are not limited to, the modeling of conceptually narrow constructs and their associated limited item pools, and unipolar constructs where the expected latent trait distribution is highly skewed.

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