The linear structural relation for several groups of data

Abstract

SUMMARY When observations on two variables are sampled from two or more distinct populations, the linear structural relation between the two variables can be estimated consistently. The maximum likelihood estimators of the parameters in the model are found; they have different forms in different parts of the sample space. A procedure for testing hypotheses about the parameter usually of principal interest, the slope of the relation, is derived; it is complicated by the unusual nature of the parameter estimators. The theory is applied to an example in which the relationship between head length and breadth measurements is studied.