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Factor copula models for item response data are more interpretable and fit better than (truncated) vine copula models when dependence can be explained through latent variables, but are not robust to violations of conditional independence. To circumvent these issues, truncated vines and factor copula models for item response data are joined to define a combined model, the so-called factor tree copula model, with individual benefits from each of the two approaches. Rather than adding factors and causing computational problems and difficulties in interpretation and identification, a truncated vine structure is assumed on the residuals conditional on one or two latent variables. This structure can be better explained as a conditional dependence given a few interpretable latent variables. On the one hand, the parsimonious feature of factor models remains intact and any residual dependencies are being taken into account on the other. We discuss estimation along with model selection. In particular, we propose model selection algorithms to choose a plausible factor tree copula model to capture the (residual) dependencies among the item responses. Our general methodology is demonstrated with an extensive simulation study and illustrated by analyzing Post Traumatic Stress Disorder.

There is an extensive literature on methods for meta-analysis of diagnostic studies, but it mainly focuses on a single test. However, the better understanding of a particular disease has led to the development of multiple tests. A multinomial generalized linear mixed model (GLMM) is recently proposed for the joint meta-analysis of studies comparing multiple tests. We propose a novel model for the joint meta-analysis of multiple tests, which assumes independent multinomial distributions for the counts of each combination of test results in diseased and non-diseased patients, conditional on the latent vector of probabilities of each combination of test results in diseased and non-diseased patients. For the random effects distribution of the latent proportions, we employ a truncated drawable vine copula that can cover flexible dependence structures. The proposed model includes the multinomial GLMM as a special case, but can also operate on the original scale of the latent proportions. Our methodology is demonstrated with a simulation study and using a meta-analysis of screening for Down syndrome with two tests: shortened humerus and shortened femur. The comparison of our method with the multinomial GLMM yields findings in the real data meta-analysis that change the current conclusions., arXiv admin note: text overlap with arXiv:2006.09278

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)

Supplemental material, Supplementary Material for A D-vine copula mixed model for joint meta-analysis and comparison of diagnostic tests by Aristidis K Nikoloulopoulos in Statistical Methods in Medical Research

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: firstly, a copula-based Markov model is used to relate the marginal distribution of the response in different time periods, separately for males and females; secondly, 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 favour 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.

A novel copula-based multivariate panel ordinal model is developed to estimate structural relations among components of well-being. Each ordinal time-series is modelled using a copula-based Markov model to relate the marginal distributions of the response at each time of observation and then, at each observation time, the conditional distributions of each ordinal time-series are joined using a multivariate t copula. Maximum simulated likelihood based on evaluating the multidimensional integrals of the likelihood with randomized quasi Monte Carlo methods is used for the estimation. Asymptotic calculations show that our method is nearly as efficient as maximum likelihood for fully specified multivariate copula models. Our findings highlight the importance of one's relative position in evaluating their well-being with no direct effects of socio-economic characteristics on well-being but strong indirect effects through their impact on components of well-being. Temporal resilience, habit formation and behavioural traits can explain the dependence in the joint tails over time and across well-being components.

Extending generalized estimating equations (GEE) to ordinal response data requires a conversion of the ordinal response to a vector of binary category indicators. That leads to a rather complicated association structure, and the introduction of large matrices when the number of categories and dimension of the cluster are large. To allow a richer specification of working correlation assumptions, we adopt the weighted scores method which is essentially an extension of the GEE approach, since it can also be applied to families that are not in the GLM class. The weighted scores method stems from the lack of a theoretically sound methodology for analyzing multivariate discrete data based only on moments up to second order and it is robust to dependence and nearly as efficient as maximum likelihood. There is no need to convert the ordinal response to binary indicators, thus the weight matrices have smaller dimensions and it is not necessary to guess the correlations of indicator variables for different categories. We focus on important issues that would interest the data analyst, such as choice of the structure of the correlation matrix and of explanatory variables, comparison of results obtained from our methods versus GEE, and insights provided by our method that would be missed with the GEE method. Our modelling framework is implemented in the package weightedScores within the open source statistical environment R., Comment: arXiv admin note: text overlap with arXiv:1510.06852