Factor Copula Models for Item Response Data

2015

Statistics in Medicine

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Diagnostic test accuracy studies typically report the number of true positives, false positives, true negatives and false negatives. There usually exists a negative association between the number of true positives and true negatives, because studies that adopt less stringent criterion for declaring a test positive invoke higher sensitivities and lower specificities. A generalized linear mixed model (GLMM) is currently recommended to synthesize diagnostic test accuracy studies. We propose a copula mixed model for bivariate meta-analysis of diagnostic test accuracy studies. Our general model includes the GLMM as a special case and can also operate on the original scale of sensitivity and specificity. Summary receiver operating characteristic curves are deduced for the proposed model through quantile regression techniques and different characterizations of the bivariate random effects distribution. Our general methodology is demonstrated with an extensive simulation study and illustrated by re-analysing the data of two published meta-analyses. Our study suggests that there can be an improvement on GLMM in fit to data and makes the argument for moving to copula random effects models. Our modelling framework is implemented in the package CopulaREMADA within the open source statistical environment R.

“…If C (·; θ ) is a parametric family of copulas and F j (·; η j ) is a parametric model for the j th univariate margin, then

C (F_{1} (x_{1}; η_{1}), F_{2} (x_{2}; η_{2}); θ)

is a bivariate parametric model with univariate margins F 1 , F 2 . For copula models, the variables can be continuous or discrete .…”

Section: The Copula Mixed Model For Diagnostic Test Accuracy Studiesmentioning

confidence: 99%

A mixed effect model for bivariate meta‐analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution

2015

Statistics in Medicine

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“…where F −1 j are inverse cdfs (Nikoloulopoulos and Joe, 2015). For example, if Φ d (·; R) is the MVN cdf with correlation matrix R = (ρ jk : 1 ≤ j < k ≤ d) and N(0,1) margins, and Φ is the univariate standard normal cdf, then the MVN copula is C(u 1 , .…”

Section: Overview and Relevant Background For Copulasmentioning

confidence: 99%

Hybrid copula mixed models for combining case-control and cohort studies in meta-analysis of diagnostic tests

2016

Stat Methods Med Res

Copula mixed models for trivariate (or bivariate) meta-analysis of diagnostic test accuracy studies accounting (or not) for disease prevalence have been proposed in the biostatistics literature to synthesize information. However, many systematic reviews often include case-control and cohort studies, so one can either focus on the bivariate meta-analysis of the case-control studies or the trivariate meta-analysis of the cohort studies, as only the latter contains information on disease prevalence. In order to remedy this situation of wasting data we propose a hybrid copula mixed model via a combination of the bivariate and trivariate copula mixed model for the data from the case-control studies and cohort studies, respectively. Hence, this hybrid model can account for study design and also due to its generality can deal with dependence in the joint tails. We apply the proposed hybrid copula mixed model to a review of the performance of contemporary diagnostic imaging modalities for detecting metastases in patients with melanoma.

“…If C (·; θ ) is a parametric family of copulas and F j (·; η j ) is a parametric model for the j th univariate margin, then

C (F_{1} (y_{1}; η_{1}), F_{2} (y_{2}, η_{2}), θ)

is a bivariate parametric model with univariate margins F 1 , F 2 . For copula models, the variables can be continuous or discrete (Nikoloulopoulos ; Nikoloulopoulos and Joe ).…”

Section: Overview and Relevant Background For Copulasmentioning

confidence: 99%

“…In our candidate set, families that have different strengths of tail behavior (see e.g., Nikoloulopoulos, Joe, and Li ; Nikoloulopoulos and Joe ) are included. In the descriptions below, a bivariate copula C is reflection symmetric if its density satisfies c ( u 1 , u 2 ) = c (1 − u 1 , 1 − u 2 ) for all 0 ≤ u 1 , u 2 ≤ 1.…”

Section: Choices Of Parametric Families Of Copulasmentioning

confidence: 99%

See 1 more Smart Citation

Coupling Couples With Copulas: Analysis of Assortative Matching on Risk Attitude

Moffatt

2018

Economic Inquiry

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We investigate patterns of assortative matching on risk attitude, using self‐reported (ordinal) data on risk attitudes for males and females within married couples, from the German Socio‐Economic Panel over the period 2004–2012. We apply a novel copula‐based bivariate panel ordinal model. Estimation is in two steps: first, a copula‐based Markov model is used to relate the marginal distribution of the response in different time periods, separately for males and females; second, another copula is used to couple the males' and females' conditional (on the past) distributions. We find positive dependence, both in the middle of the distribution, and in the joint tails, and we interpret this as positive assortative matching (PAM). Hence we reject standard assortative matching theories based on risk‐sharing assumptions, and favor models based on alternative assumptions such as the ability of agents to control income risk. We also find evidence of “assimilation”; that is, PAM appearing to increase with years of marriage. (JEL C33, C51, D81)