A rule for inferring individual-level relationships from aggregate data
G Firebaugh - American sociological review, 1978 - JSTOR
American sociological review, 1978•JSTOR
Under certain conditions aggregate-level data provide unbiased estimates of individual-
level relationships. Here I present these conditions in the form of a single theoretical
decision rule: bias is absent when, and only when, the group mean of the independent
variable (X) has no effect on Y, with X controlled. This paper introduces this rule,
demonstrates it for the general n-variable case, compares it with prior discussions of cross-
level inference, and illustrates it with the 1930 census data used by Robinson (1950). The …
level relationships. Here I present these conditions in the form of a single theoretical
decision rule: bias is absent when, and only when, the group mean of the independent
variable (X) has no effect on Y, with X controlled. This paper introduces this rule,
demonstrates it for the general n-variable case, compares it with prior discussions of cross-
level inference, and illustrates it with the 1930 census data used by Robinson (1950). The …
Under certain conditions aggregate-level data provide unbiased estimates of individual-level relationships. Here I present these conditions in the form of a single theoretical decision rule: bias is absent when, and only when, the group mean of the independent variable (X) has no effect on Y, with X controlled. This paper introduces this rule, demonstrates it for the general n-variable case, compares it with prior discussions of cross-level inference, and illustrates it with the 1930 census data used by Robinson (1950). The final section discusses the implications of this rule for the converse type of cross-level inference: the use of individual-level data to estimate aggregate-level relationships.
JSTOR