2,570 research outputs found
Variational Bayes Estimation of Discrete-Margined Copula Models with Application to Time Series
We propose a new variational Bayes estimator for high-dimensional copulas
with discrete, or a combination of discrete and continuous, margins. The method
is based on a variational approximation to a tractable augmented posterior, and
is faster than previous likelihood-based approaches. We use it to estimate
drawable vine copulas for univariate and multivariate Markov ordinal and mixed
time series. These have dimension , where is the number of observations
and is the number of series, and are difficult to estimate using previous
methods. The vine pair-copulas are carefully selected to allow for
heteroskedasticity, which is a feature of most ordinal time series data. When
combined with flexible margins, the resulting time series models also allow for
other common features of ordinal data, such as zero inflation, multiple modes
and under- or over-dispersion. Using six example series, we illustrate both the
flexibility of the time series copula models, and the efficacy of the
variational Bayes estimator for copulas of up to 792 dimensions and 60
parameters. This far exceeds the size and complexity of copula models for
discrete data that can be estimated using previous methods
Mixed Marginal Copula Modeling
This article extends the literature on copulas with discrete or continuous
marginals to the case where some of the marginals are a mixture of discrete and
continuous components. We do so by carefully defining the likelihood as the
density of the observations with respect to a mixed measure. The treatment is
quite general, although we focus focus on mixtures of Gaussian and Archimedean
copulas. The inference is Bayesian with the estimation carried out by Markov
chain Monte Carlo. We illustrate the methodology and algorithms by applying
them to estimate a multivariate income dynamics model.Comment: 46 pages, 8 tables and 4 figure
A mixed effect model for bivariate meta-analysis of diagnostic test accuracy studies using a copula representation of the random effects distribution
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
On the estimation of normal copula discrete regression models using the continuous extension and simulated likelihood
The continuous extension of a discrete random variable is amongst the
computational methods used for estimation of multivariate normal copula-based
models with discrete margins. Its advantage is that the likelihood can be
derived conveniently under the theory for copula models with continuous
margins, but there has not been a clear analysis of the adequacy of this
method. We investigate the asymptotic and small-sample efficiency of two
variants of the method for estimating the multivariate normal copula with
univariate binary, Poisson, and negative binomial regressions, and show that
they lead to biased estimates for the latent correlations, and the univariate
marginal parameters that are not regression coefficients. We implement a
maximum simulated likelihood method, which is based on evaluating the
multidimensional integrals of the likelihood with randomized quasi Monte Carlo
methods. Asymptotic and small-sample efficiency calculations show that our
method is nearly as efficient as maximum likelihood for fully specified
multivariate normal copula-based models. An illustrative example is given to
show the use of our simulated likelihood method
Penalized EM algorithm and copula skeptic graphical models for inferring networks for mixed variables
In this article, we consider the problem of reconstructing networks for
continuous, binary, count and discrete ordinal variables by estimating sparse
precision matrix in Gaussian copula graphical models. We propose two
approaches: penalized extended rank likelihood with Monte Carlo
Expectation-Maximization algorithm (copula EM glasso) and copula skeptic with
pair-wise copula estimation for copula Gaussian graphical models. The proposed
approaches help to infer networks arising from nonnormal and mixed variables.
We demonstrate the performance of our methods through simulation studies and
analysis of breast cancer genomic and clinical data and maize genetics data
A vine copula mixed effect model for trivariate meta-analysis of diagnostic test accuracy studies accounting for disease prevalence
A bivariate copula mixed model has been recently proposed to synthesize diagnostic test accuracy studies and it has been shown that it is superior to the standard generalized linear mixed model in this context. Here, we call trivariate vine copulas to extend the bivariate meta-analysis of diagnostic test accuracy studies by accounting for disease prevalence. Our vine copula mixed model includes the trivariate generalized linear mixed model as a special case and can also operate on the original scale of sensitivity, specificity, and disease prevalence. Our general methodology is illustrated by re-analyzing the data of two published meta-analyses. Our study suggests that there can be an improvement on trivariate generalized linear mixed model in fit to data and makes the argument for moving to vine copula random effects models especially because of their richness, including reflection asymmetric tail dependence, and computational feasibility despite their three dimensionality
- …