Contextually Specific Effects and Other Generalizations of the Hierarchical Linear Model for Comparative Analysis
Wong, George Y., Mason, William M., Journal of the American Statistical Association
This article extends the hierarchical--or multilevel--linear model in ways that enhance its usefulness for quantitative comparative analysis based on relatively large numbers of contexts (e.g., countries, states, cities). The substantive focus is on comparative analysis of cohort human fertility during the 1970s in countries that were among the poorest during the 1970s and earlier. We address the important policy question of whether official government family planning programs in such countries had an impact on cohort fertility during the 1970s. To provide a better answer to this question than has heretofore been possible using cross-national information, it is necessary not only to model key aspects of cumulative fertility from a perspective in which policy considerations are one component, but also to develop further the analytic tools for quantitative comparative analysis.
In this article we extend the model of Mason, Wong, and Entwisle (1983) for comparative analysis to allow for contextually specific variables and for restrictions on coefficients and micro error variances. In its full generality, our extension has not previously been formulated. The notion of contextual specificity is central to the persistent debate in the social sciences over whether comparative analysis is possible between even two countries, much less among many countries. The argument against comparative analysis is that it cannot take account of factors that are truly noncomparable. If this argument were valid, the social sciences would be unable to draw conclusions beyond the bounds of a single context (e.g., a single society).
Ethnic group membership is potentially important for comparative analysis, yet it is not generally comparable across societies. Many phenomena--including fertility--are known or thought to vary in part as a function of ethnicity. The contextual specificity of ethnicity might, therefore, preclude comparative analysis of fertility. Thus the question, can ethnicity be incorporated formally into comparative analyses based on large numbers of countries? We propose treating ethnicity as contextually specific, which would permit the meaning of the ethnic dimension to vary between countries. Our approach is to incorporate the notion of contextually specific variables into a general linear hierarchical model. Contextual specificity can be used with other variables besides ethnicity and in situations in which noncomparability is not the primary issue. Our other extensions of the hierarchical linear model (restrictions on coefficients and micro error variances) are primarily for obtaining greater efficiency in estimation and do not involve fundamental alteration of the multilevel model.
We turn next to a treatment of contextually specific variables that is motivated entirely by the need to incorporate ethnicity into quantitative comparative analysis. We then present a substantive model of fertility that allows ethnicity to have different meanings in different societies and also addresses the policy question of whether government-sponsored family planning programs had an impact on cumulative fertility during their early years (primarily the 1970s). This is followed by presentation of the statistical model, presentation of findings, and further discussion.
2. ETHNICITY AND QUANTITATIVE COMPARATIVE ANALYSIS
Apart from small and relatively isolated population groupings, most, perhaps all, contemporary societies display ethnic or religious diversity (Yinger 1985). The importance of ethnic group identity (and religious group identity, which is sometimes fused with ethnicity) for societal functioning has varied historically, and varies now, within and between societies. Ethnicity and religion cannot, therefore, be ignored in comparative analysis. But how is the existence of ethnic or religious identification to be comprehended? Should such bases of identification define groups that become units of analysis in their own right, and if so, what are the implications of this view for formal models of comparative analysis? …