The Effect of Sample Size on Random Component in Multilevel Modeling

Abstract

In cluster-correlated data arise when there exists any condition for that individual are grouped among themselves. Data of this kind arise frequently in social science, behavioral, and medical sciences since individuals can be grouped in so many different ways. Multilevel modeling (MLM) is an approach that can be used to handle cluster or grouped data. Analyzing of correlated data is different from the usual way for independent data since we have to consider the correlation structure among individuals within cluster. In random effects models’ correlation structure can be estimated by considering the models parameters are allowed to vary across the cluster. Random effect models have two components, within cluster components, cluster-specific response is described by a regression model with a population-level intercept and slope, other is between-cluster component: variation in cluster-intercepts and slopes is captured. In a multilevel model, cluster level variance component is more affected by no. of cluster as well as cluster size. So, this is important to aware the researcher about no. of cluster and cluster size in estimating the random components of random effect models for correlated continuous and discrete outcome respectively in MLM since it produces bias estimate for few no. of cluster and cluster size. The parameters of random effects models can be estimated by Maximum Likelihood and Restricted Maximum Likelihood (REML) estimation for correlated continuous outcome, on the contrast besides REML, Penalized Quassi Likelihood (PQL) and Adaptive Gaussian Quadrature (AGQ) estimation techniques are applied for correlated discrete outcome. In this thesis, using the simulation procedure we would be compared among these estimation techniques by exploring the influence of no. of cluster and cluster size on estimated random parameters from random effect models of two-level and three levels for continuous and discrete outcome respectively. Relative bias, mean square error and coverage probability would be used for comparison purpose among the estimation techniques.