  Anonymizing the GPS locations of observations can bias a spatial model's
parameter estimates and attenuate spatial predictions when improperly accounted
for, and is relevant in applications from public health to paleoseismology. In
this work, we demonstrate that a newly introduced method for geostatistical
modeling in the presence of anonymized point locations can be extended to
account for more general kinds of positional uncertainty due to location
anonymization, including both jittering (a form of random perturbations of GPS
coordinates) and geomasking (reporting only the name of the area containing the
true GPS coordinates). We further provide a numerical integration scheme that
flexibly accounts for the positional uncertainty as well as spatial and
covariate information.
  We apply the method to women's secondary education completion data in the
2018 Nigeria demographic and health survey (NDHS) containing jittered point
locations, and the 2016 Nigeria multiple indicator cluster survey (NMICS)
containing geomasked locations. We show that accounting for the positional
uncertainty in the surveys can improve predictions in terms of their continuous
rank probability score.
