Contextual Analysis through the Multilevel Linear Model

Abstract

A general linear multilevel model and its estimation are described and illustrated empirically. The specification of a multilevel linear model within the covariance component framework was rendered. This model is appropriate for a wide range of applications in contextual analysis because it allows for macro as well as micro errors. Then an estimation procedure the restricted maximum likelihood/Bayes (REML/Bayes) was proposed and described for this multilevel model. Finally an extended empirical example was presented with the primary purpose of illustrating the use of the statistical methodology in conjunction with a meaningful substantive problem not to carry out a critical test of the underlying substantive theory and not to demonstrate the general superiority of the proposed estimation procedure. The example suggests that the REML/Bayes estimation procedure may be appropriate inasmuch as the results extracted with REML/Bayes are more consistent with theoretical anticipations than those extracted with ordinary least squares or estimated generalized least squares. The methodology presented by no means exhausts the subject of multilevel estimation. There is a need for estimation procedures to handle discrete micro response variables systems of micro-structural equations and other generalizations. Work is currently proceeding on some of these extensions of the multilevel linear model as the goal of sound estimation procedures for generalized multilevel models is worthwhile and by no means esoteric. It may be hard for researchers to find contextual effects unless they use efficient and appropriate estimation techniques.