  In the analysis of observational data in social sciences and businesses, it
is difficult to obtain a "(quasi) single-source dataset" in which the variables
of interest are simultaneously observed. Instead, multiple-source datasets are
typically acquired for different individuals or units. Various methods have
been proposed to investigate the relationship between the variables in each
dataset, e.g., matching and latent variable modeling. It is necessary to
utilize these datasets as a single-source dataset with missing variables.
Existing methods assume that the datasets to be integrated are acquired from
the same population or that the sampling depends on covariates. This assumption
is referred to as missing at random (MAR) in terms of missingness. However, as
will been shown in application studies, it is likely that this assumption does
not hold in actual data analysis and the results obtained may be biased. We
propose a data fusion method that does not assume that datasets are homogenous.
We use a Gaussian process latent variable model for non-MAR missing data. This
model assumes that the variables of concern and the probability of being
missing depend on latent variables. A simulation study and real-world data
analysis show that the proposed method with a missing-data mechanism and the
latent Gaussian process yields valid estimates, whereas an existing method
provides severely biased estimates. This is the first study in which non-random
assignment to datasets is considered and resolved under resonable assumptions
in data fusion problem.
