Angarita-Valderrama, Andrea Katherine

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    Estudio comparativo entre INLA y MCMC en modelos lineales generalizados mixtos
    (2019-12-09) Angarita-Valderrama, Andrea Katherine; Santana Morant, Dámaris; College of Arts and Sciences - Sciences; Torres Saavedra, Pedro; Macchiavelli, Raúl; Acuña Fernández, Edgar; Department of Mathematics; Ierkic, Henrick M.
    In this work a comparative study is carried out between Integrated Nested Laplace Approximation (INLA) and Markov Chain Monte Carlo (MCMC) for estimation in Generalized Linear Mixed Models (GLMMs) for count data and binary data. The comparison is made through a simulation studies and the analysis of two real data sets. Both methods are used to obtain an approximation of the posterior distributions that arise from the Bayesian inference. INLA uses Laplace approximations to approximate the posterior distributions while the MCMC generates samples from the posterior distributions using Gibbs Sampling. INLA is motivated by the computational challenges of MCMC, in particular Gibbs sampling, when working with large data sets. Besides the high computational demand of MCMC, some practitioners may find the definition of Bayesian models in programs such as JAGS a difficult task to accomplish. INLA offers some computational advantages over MCMC without sacrificing efficiency. Although the commands to fit the models with INLA are not straightforward for a non-expert user, the syntax resembles well-known R packages, and therefore, it could be better assimilated by practitioners. One of disadvantages of INLA is that is restricted to Latent Gaussian Models (LGMs). In the simulation studies, several factors were considered such as the sample size, the number of repeated measures and the precision of the random effect. The comparison of the two methods is done using the following performance measures: BIAS, the Mean Square Error (MSE) and Normalized Root Mean Square Error (NRMSE), and a measure of the time that it takes for the methods to produce estimates. The simulation studies suggest that in general INLA does not differ in terms of BIAS, MSE and NRMSE when compared to MCMC, but INLA is computationally more fast for any sample size, repeated measures and accuracy considered. In some scenarios, INLA does the estimation in a few seconds whereas the MCMC may takes hours to complete that task. The main reason for the good performance of INLA relies on the accuracy of the nested approximations. Finally, the two Bayesian methods for making inference are compared with the maximum likelihood using two real data sets to study the factors that influence the response variable. One data set corresponds to the first cycle of Mathematical Olympiads of Puerto Rico 2016 - 2017. The other data set comprises data for births in Puerto Rico in 2011. Estimates from the three methods led to similar conclusions in both data sets, but INLA is faster computationally than MCMC.