  Data-fusion involves the integration of multiple related datasets. The
statistical file-matching problem is a canonical data-fusion problem in
multivariate analysis, where the objective is to characterise the joint
distribution of a set of variables when only strict subsets of marginal
distributions have been observed. Estimation of the covariance matrix of the
full set of variables is challenging given the missing-data pattern. Factor
analysis models use lower-dimensional latent variables in the data-generating
process, and this introduces low-rank components in the complete-data matrix
and the population covariance matrix. The low-rank structure of the factor
analysis model can be exploited to estimate the full covariance matrix from
incomplete data via low-rank matrix completion. We prove the identifiability of
the factor analysis model in the statistical file-matching problem under
conditions on the number of factors and the number of shared variables over the
observed marginal subsets. Additionally, we provide an EM algorithm for
parameter estimation. On several real datasets, the factor model gives smaller
reconstruction errors in file-matching problems than the common approaches for
low-rank matrix completion.
