CORRECTING MEASURES OF RELATIONSHIP BETWEEN AGGREGATE-LEVEL VARIABLESFOR BOTH UNRELIABILITY AND CORRELATED ERRORS - AN EMPIRICAL EXAMPLE

Many social scientists conducting macro-level analyses use aggregate-l evel variables (weighted sums of the characteristics of the individual s within the macro-level units: e.g., means, percents, or rates) to de scribe macro-level units (e.g., schools, cities, or states). Researche rs have long known that aggregate-level variables are likely to be mor e reliable than individual-level variables. More recently, they have r ecognized the possibility of estimating the reliability of aggregate-l evel variables using information on the variability of these variables and variability of the individual-level characteristics (on which the y are based). These reliability estimates can be used to correct measu res of association at the aggregate-level for unreliability. When corr ecting measures of relationship, however, researchers will often need to consider the correlated errors generated when the same set of indiv iduals responds to the same questions used to create the aggregate-lev el variables (the problem of joint sampling). This paper shows how to estimate these correlated measurement errors and use them, and aggrega te-level reliability coefficients, to correct measures of relationship at the aggregate-level. These techniques are applied to data from the Senate National Election Studies to illustrate the impact of these co rrections. (C) 1998 Academic Press.