Aggregation and Measurement Error

The measurement process often involves an aggregating operation that has not been systematically studied by sociologists. Sometimes one aggregates "similar" behavioral acts of the same individual, whereas on other occasions "similar" individuals are aggregated. But similar with respect to what? If the aggregated units are similar with respect to underlying causes or assumed effects, then the rationale for aggregation is relatively clearcut, though complications will usually be encountered. But if aggregation has been based on administrative convenience or geographic proximity, it may be exceedingly difficult to make meaningful microversus macro-level comparisons. The so-called problem of "ecological correlations" is merely a special case of this difficulty, which is a fundamental one for sociological research and theory. The causal approach to measurement error may be utilized to conceptualize the problem, but ultimate resolutions will require much better data than are presently available. The future of macro-level sociological research obviously depends on our ability to improve our measurements and to conceptualize more adequately the causal and other types of linkages between aggregate or global theoretical variables and operational indicators. The causal approach to measurement error has been applied to relatively simple kinds of models suggested by social-psychological theories, as for example models in which all indicators are taken as effects of unmeasured variables, or in which cause and effect indicators have been combined.' In a sense to be discussed below, these models are analogous to macro-level aggregation models. But on the latter level we seem to lack theories of the measurement process of the kinds that have been developed by psychologists. The literature on aggregation within econometrics has recently been surveyed by Hannan (1970), but insofar as I am aware has not been applied to any concrete sociological research. A nonsystematic examination of macro-level sociological research, plus conversations with colleagues and graduate students working in this area, leaves me with the impression that macro-level measurement is for the most part opportunistic and atheoretical. Lacking the necessary resources to collect their own data, investigators have often searched for available indicators without adequately spelling out the assumed connections with the variables they are intended to measure. It is perhaps significant that there is a current interest in "social indicators," with the presumption being made that we already know what we want to measure. The prior question, of course, is "Indicators of what?" As Duncan (1969) has noted, it is often necessary to proceed by developing actual measures, whereas it may only later become possible to study their mathematical properties and empirical behavior. It would indeed be unwise to become immobilized by too many "conceptual clarifications" in the absence of empirical measures and data. On the other hand, I would be equally disturbed by the opposite tendency of relying exclusively on operational indices and their intercorrelations, without an accompanying theory of data or auxiliary theory of the measurement process. What are some of the most common reasons for aggregating or summing a series of observations? First, we should note that many variables on both the micro and macro levels do not involve an explicit aggregating operation. * I would like to thank Peter Blau, Alvin Jacobson, Michael Hannan, Gerhard Lenski, and Powhatan Wooldridge for their helpful comments on an earlier version of this paper. ' For illustrations of causal approaches where indicators are taken as effects of unmeasured variables see Althauser and Heberlein (1970); Althauser et al. (1971); Blalock (1970); Costner (1969); Heise (1969); Siegel and Hodge (1968). For discussions of models in which at least some indicators are taken as causes of unmeasured variables see Blalock (1971); Costner (1970); and Land (1970).