Varying intercept regression model

Abstract

Varying intercept model is a regression model that is applied to nested data, which consists of several groups and each group contains several individual observations. Several characteristics are often found in nested data, namely, the variance between groups and individual observations from the same group are correlated. By considering errors in two different levels, the individual and group levels, the varying intercept model is more suitable than the linear regression model in nested data because varying intercept model accommodates those characteristics. In this thesis, we discussed the varying intercept model both with and without a predictor variable. The varying intercept model consists of several parameters that must be estimated, namely, regression coefficients and variance components. There is also a random effect, which is a group effect and also a random variable. The regression coefficients are estimated using Generalized Least Squares (GLS) and Maximum Likelihood (ML) via the Expectation-Maximization (EM) algorithm. The random effect in varying intercept model is predicted using Best Linear Unbiased Prediction (BLUP). On the other side, the variance components in varying intercept model are estimated using Maximum Likelihood via Expectation-Maximization (EM) Algorithm. In this thesis, we used a simulation to analyze the effect of the standard deviation of the error components in the varying intercept model and the effect of the number of individual observations in each group toward the standard deviation of the error components. The simulation results show that if the standard deviation of the error component in the individual level is greater than the standard deviation of the error component in the group level, then the classifications of individual observations into several groups should be ignored. On the other hand, if the standard deviation of the error component in the individual level is not greater than the standard deviation of the error component in the group level, then the classifications of individual observations into several groups should not be ignored. The simulation results also show that the number of individual observations in each group is not associated with the standard deviation of the error components.