Determination of Sample Size and Comparison of Estimation Methods in Multilevel Models

Abstract

The main purpose of this study was to examine the impact of sample size on multilevel model estimates and their standard errors under different methods of estimations. Three different studies were designed to achieve the objectives of the study. In study 1, two level binary logistic random intercept and random slope regression model was used. The performance of two estimation methods was observed under varying conditions of the design factors i.e the number of groups, group sizes and intraclass correlation (ICC). Maximum Likelihood (ML) with adaptive quadrature and Penalized Quasi-likelihood (PQL) methods of estimation were used in study 1. Similarly, three categories and five categories two level ordinal logistic random intercept and random slope regression models were used in study 2. The performance of ML and PQL methods of estimation was observed under varying conditions of the design factors i.e., the number of groups, group sizes, ICC and distribution of category responses. Moreover, a two level random intercept and random slope linear regression model was used in study 3. The performance of Restricted Maximum Likelihood Method (REML) and Bootstrap by means of Minimum Norm Quadratic Unbiased Estimators (MINQUE) was observed under varying conditions of the design factors. In all the three studies relative parameter bias and 95% confidence interval coverage rates were used to assess accuracy and precision of estimates and their standard errors. Further, empirical power rates were also computed in study 1 and study 2.