How valid can data fusion be?

Data fusion techniques typically aim to achieve a complete data file from different sources which do not contain the same units. Traditionally, this is done on the basis of variables common to all files. It is well known that those approaches establish conditional independence of the specific variables given the common variables, although they may be conditionally dependent in reality. We discuss the objectives of data fusion in the light of their feasibility and distinguish four levels of validity that a fusion technique may achieve. For a rather general situation, we derive the feasible set of correlation matrices for the variables not jointly observed and suggest a new quality index for data fusion. Finally, we present a suitable and effcient multiple imputation procedure to make use of auxiliary information and to overcome the conditional independence assumption.