Random Coefficient Models

Abstract

Quantitative social research relies heavily on data that originate either from surveys with sampling designs that depart from simple random sampling, or from observational studies with no formal sampling design. Simple random sampling is often not feasible, or its use would yield data with less information about certain features of interest, and it is often economically prohibitive. For example, in studies of school effectiveness it may be difficult to secure the cooperation of a school or a classroom. Therefore it would be rather wasteful to collect data from a small number of students in such a classroom. Data from a larger proportion, or from all the students, could be collected at a small additional expense, thus reducing the number of classrooms required for a sample to contain sufficient information for the intended purposes. Similarly, in household surveys, having contacted a selected individual, it would make sense to collect data from the rest of the members of the household at the same time. When this is done, we usually end up with data for which the standard assumptions of independence (such as in ordinary regression) are inappropriate.