Contextually Specific Effects and other Generalizations of the Hierarchical Linear Model for Comparative Analysis

Abstract

Contextually specific differences among members of a context pose substantive and methodological problems in multilevel analysis. An important example is ethnic identity in comparative studies involving different societies. Ethnic (and religious) group membership in many societies is a basis not only for differentiation among members but also for the identification and maintenance of deeply rooted integrative ties. So important is ethnicity that the existence of different groups within societies sometimes delays or prohibits the taking of censuses. Moreover, even when ethnic information is available in national statistical data sources, researchers are sometimes prohibited from reporting the results of analyses that contain ethnic detail. Despite these constraints, information on ethnicity is often available for pluralistic societies. Where it is available, ethnicity poses a challenging analytic problem for comparative analysis. If researchers wish to compare different societies, how is ethnicity to be allowed for within a framework of quantitative comparative analysis? Using the notion of contextual specificity, we present an answer to this question within the multilevel analysis paradigm. Ethnicity is taken into account, but ethnic differences as such are not modeled across contexts. This strategy is effected through a generalization of the hierarchical linear model for multilevel analysis, using the method of restricted maximum likelihood in combination with empirical Bayes. The methodology proposed here is applicable to dimensions other than ethnicity. We illustrate the approach with an empirical example concerning the dependence of fertility on socioeconomic origins of women in 36 Third World countries, using data from the World Fertility Survey.

Key Words:

• Empirical Bayes estimation of fixed and random effects
• Mixed linear model
• Multilevel and contextual analysis
• Repeated measures for longitudinal data
• Restricted maximum likelihood estimation of variance and co-variance components