de Leon, AlexanderYan, YingRen, Mingchen2016-09-202016-09-2020162016Ren, M. (2016). Likelihood Analysis of Gaussian Copula Distributions for Mixed Data via a Parameter-Expanded Monte Carlo EM (PX-MCEM) Algorithm (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/26765http://hdl.handle.net/11023/3316Mixed discrete and continuous data arise in a variety of settings. In this thesis, we adopt so-called Gaussian copula distributions (GCDs) as a general model for binary and continuous variables. The attractive feature of GCDs is their use of Gaussian copulas to separately model dependencies between variables, thereby preserving the variables' distinct marginal properties. We employ an efficient approach to maximum likelihood estimation for the model via a parameter-expanded Monte Carlo EM (MCEM) algorithm. By doing so, we not only avoid the direct evaluation of the likelihood function, which involves computing multivariate normal probabilities, but also improve the computational efficiency of the algorithm. Another advantage of the PX-MCEM algorithm is that it has an analytically tractable M-step, and hence does not require numerical optimization techniques. Based on simulations and an application to a breast cancer dataset, we show that the estimates are reasonably unbiased and their sampling variabilities can be accurately estimated by their bootstrapped standard errors.engUniversity of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.StatisticsGaussian Copula distributionParameter-ExpandedMixed datamaster thesis10.11575/PRISM/26765