MIXED-EFFECT MODELS WITH RESTRICTED MAXIMUM LIKELIHOOD (REML), BOOT-STRAPPED REML AND BAYESIAN INFERENCE IN APPLICATION OF GAPMINDER DATA

Abstract

Mixed effects model combines fixed effects and random effects, allowing for the analysis of data with both fixed and random variations. This modeling approach is widely utilized across various fields. In R, the lme4 package is commonly employed to estimate mixed effects models using Restricted Maximum Likelihood (REML). There are several methods for estimating model parameters, including Bayesian inference, which has gained prominence with ongoing research advancements. Bayesian inference using Markov Chain Monte Carlo (MCMC) is among the most widely used Bayesian methods. Bayesian inference leverages probabilistic distributions to estimate parameters.to understand the general overview of life expectancy, serving as an indicator of survival time across different continents in the Gapminder dataset, it's essential to identify relevant variables after computing mixed effects predictions using Maximum Likelihood and REML estimation. This involves predicting life expectancy by integrating both random and fixed effects, determining relevant variables after estimating the Mixed Effects Model using REML Bootstrap estimation, and identifying influential variables after estimating the Mixed Effects Model using Bayesian MCMC inference. The methods employed include REML, Bootstrapped-REML, and Bayesian MCMC. The results indicate that all inference methods can be utilized to estimate parameters, with all predictor variables influencing life expectancy, except for the population variable. Further research is recommended to utilize data with more complex predictor variables.