Factor copula models for item response data

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

Modeling the Differences in Counted Outcomes using Bivariate Copula Models: with Application to Mismeasured Counts

This paper makes three contributions. First, it uses copula functions to obtain a flexible bivariate parametric model for nonnegative integer-valued data (counts). Second, it recovers the distribution of the difference in the two counts from a specifed bivariate count distribution. Third, the methods are applied to counts that are measured with error. Specifically we model the determinants of the difference between the self-reported number of doctor visits (measured with error) and true number of doctor visits (also available in the data used).

Quasi-random numbers for copula models

The present work addresses the question how sampling algorithms for commonly applied copula models can be adapted to account for quasi-random numbers. Besides sampling methods such as the conditional distribution method (based on a one-to-one transformation), it is also shown that typically faster sampling methods (based on stochastic representations) can be used to improve upon classical Monte Carlo methods when pseudo-random number generators are replaced by quasi-random number generators. This opens the door to quasi-random numbers for models well beyond independent margins or the multivariate normal distribution. Detailed examples (in the context of finance and insurance), illustrations and simulations are given and software has been developed and provided in the R packages copula and qrng

Size Metrics and Dynamics of Firms Expansion in the European Pharmaceutical Industry

We generalize the growth-of-firm literature by linking alternative metrics of size via a Copula approach. We look at the result of the fitted Copula and justify the metric we base our analysis upon. We employ the Amadeus dataset and investigate the growth dynamics of the European pharmaceutical industry in the Single Market Programme era, 1990–2004. Relying on a set of dynamic panel Probit methods that deal with unobserved heterogeneity and initial conditions, we analyze how our units of investigation, multinationals, capture opportunities over time. We find strong evidence of state dependence and mean reversion, as predicated by the theory of maturation — firms face a period of rapid growth, followed by a slow down, or even a stop, in growth. We finish off our exercise by conditioning the fitted Copula on the predicted measure of size and simulate the remaining measures.Copula, Dynamic Nonlinear Panel Data Models, Entry, Firms Growth, Lower Bound, Pharmaceutical Industry, Single Market Programme, Unobserved Heterogeneity

Comovements in Trading activity: A Multivariate Autoregressive Model of Time Series Count Data Using Copulas

This paper introduces the Multivariate Autoregressive Conditional Poisson model to deal with issues of discreteness, overdispersion and both auto- and cross-correlation, arising with multivariate counts. We model counts with a double Poisson and assume that conditionally on past observations the means follow a Vector Autoregression. We resort to copulas to introduce contemporaneous correlation. We advocate the use of our model as a feasible alternative to multivariate duration models and apply it to the study of sector and stock specific news related to the comovements in the number of trades per unit of time of the most important US department stores traded on the New York Stock Exchange. We show that the market leaders inside an specific sector, in terms of more sectorial information conveyed by their trades, are related to their size measured by their market capitalization.Continuousation; Factor model; Market microstructure.

A Nonparametric Bayesian Approach to Copula Estimation

We propose a novel Dirichlet-based P\'olya tree (D-P tree) prior on the copula and based on the D-P tree prior, a nonparametric Bayesian inference procedure. Through theoretical analysis and simulations, we are able to show that the flexibility of the D-P tree prior ensures its consistency in copula estimation, thus able to detect more subtle and complex copula structures than earlier nonparametric Bayesian models, such as a Gaussian copula mixture. Further, the continuity of the imposed D-P tree prior leads to a more favorable smoothing effect in copula estimation over classic frequentist methods, especially with small sets of observations. We also apply our method to the copula prediction between the S\&P 500 index and the IBM stock prices during the 2007-08 financial crisis, finding that D-P tree-based methods enjoy strong robustness and flexibility over classic methods under such irregular market behaviors