Copula Functions for Residual Dependency

Braeken, Johan; Tuerlinckx, Francis; Boeck, Paul De

doi:10.1007/s11336-007-9005-4

Cited by 53 publications

(61 citation statements)

References 45 publications

(45 reference statements)

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“…In psychometric and SEM literature, the use of copulas is relatively limited. Braeken et al (2007) used copulas for modeling residual dependencies in Rasch models. Mair et al (2012) propose to use copulas to generate data with a pre-specified covariance matrix, offering an alternative to the VM method.…”

Section: Introductionmentioning

confidence: 99%

How General is the Vale–Maurelli Simulation Approach?

Foldnes

Grønneberg

2014

Psychometrika

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Abstract. The Vale-Maurelli (VM) approach to generating non-normal multivariate data involves the use of Fleishman polynomials applied to an underlying Gaussian random vector. This method has been extensively used in Monte Carlo studies during the last three decades to investigate the finite-sample performance of estimators under non-Gaussian conditions. The validity of conclusions drawn from these studies clearly depends on the range of distributions obtainable with the VM method. We deduce the distribution and the copula for a vector generated by a generalized VM transformation, and show that it is fundamentally linked to the underlying Gaussian distribution and copula. In the process we derive the distribution of the Fleishman polynomial in full generality. While data generated with the VM approach appears to be highly non-normal, its truly multivariate properties are close to the Gaussian case. A Monte Carlo study illustrates that generating data with a different copula than that implied by the VM approach severely weakens the performance of normal-theory based ML estimates.

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Section: Introductionmentioning

confidence: 99%

How General is the Vale–Maurelli Simulation Approach?

Foldnes

Grønneberg

2014

Psychometrika

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“…Another direction of future research is to extend our factor model to capture the residual dependence as in Braeken et al (2007). Therein multivariate Archimedean copulas have been used for subgroups of items that are chosen from the context.…”

Section: Discussionmentioning

confidence: 99%

“…A copula approach in psychometrics was recently proposed by Braeken et al (2007) and Braeken (2011) who explored the use of Archimedean copulas or a mixture of the independence and comonotonicity copulas to capture the residual dependence of the Rasch model. The multivariate probit or discretized MVN model has been in use for a considerable length of time in psychometrics (Muthén, 1978), and it can be considered as a special case of the MVN copula with univariate probit marginals.…”

Section: Introductionmentioning

confidence: 99%

Factor Copula Models for Item Response Data

Nikoloulopoulos

Joe

2013

Psychometrika

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university of east anglia Harry Joe university of british columbia Factor or conditional independence models based on copulas are proposed for multivariate discrete data such as item responses. The factor copula models have interpretations of latent maxima/minima (in comparison with latent means) and can lead to more probability in the joint upper or lower tail compared with factor models based on the discretized multivariate normal distribution (or multidimensional normal ogive model). Details on maximum likelihood estimation of parameters for the factor copula model are given, as well as analysis of the behavior of the log-likelihood. Our general methodology is illustrated with several item response data sets, and it is shown that there is a substantial improvement on existing models both conceptually and in fit to data.

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“…To handle deviations from the conditional independence assumption, the toolbox includes recent copula IRT models (Braeken, Tuerlinckx, & De Boeck, 2007), which are not yet implemented elsewhere. With IRTm, we offer practitioners a small, integrated IRT toolbox for explanatory research and for exploring the potential of the copula approach within IRT.…”

Section: The 2pl Modelmentioning

confidence: 99%

“…A convenient way of accounting for these residual dependencies within an item subset can be found in the use of copula functions (Braeken et al, 2007). A copula is a type of function that is able to connect sets of marginal distributions to form a multivariate distribution that preserves these margins (for reference works on copula theory, see Joe, 1997, andNelsen, 1999).…”

Section: Accounting For Deviations Of Common Assumptionsmentioning

confidence: 99%

Investigating latent constructs with item response models: A MATLAB IRTm toolbox

Braeken

Tuerlinckx

2009

Behavior Research Methods

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Item response theory (IRT) models are the central tools in modern measurement and advanced psychometrics. We offer a MATLAB IRT modeling (IRTm) toolbox that is freely available and that follows an explicit design matrix approach, giving the end user control and flexibility in building a model that goes beyond standard models, such as the Rasch model (Rasch, 1960) and the two-parameter logistic model. As such, IRTm allows for a large variety of unidimensional IRT models for binary responses, the incorporation of additional person and item information, and deviations from common model assumptions. An exclusive key feature of the toolbox is the inclusion of copula IRT models to handle local item dependencies. Two appendixes for this report, containing example code and information on the general copula IRT in IRTm, may be downloaded from brm.psychonomic -journals.org/content/supplemental.

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Copula Functions for Residual Dependency

Abstract: item response theory, local item dependency, copula,

Cited by 53 publications

References 45 publications

How General is the Vale–Maurelli Simulation Approach?

How General is the Vale–Maurelli Simulation Approach?

Factor Copula Models for Item Response Data

Investigating latent constructs with item response models: A MATLAB IRTm toolbox

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