  Current implementations of multiresolution methods are limited in terms of
possible types of responses and approaches to inference. We provide a
multiresolution approach for spatial analysis of non-Gaussian responses using
latent Gaussian models and Bayesian inference via integrated nested Laplace
approximation (INLA). The approach builds on `LatticeKrig', but uses a
reparameterization of the model parameters that is intuitive and interpretable
so that modeling and prior selection can be guided by expert knowledge about
the different spatial scales at which dependence acts. The priors can be used
to make inference robust and integration over model parameters allows for more
accurate posterior estimates of uncertainty. The extended LatticeKrig (ELK)
model is compared to a standard implementation of LatticeKrig (LK), and a
standard Mat\'ern model, and we find modest improvement in spatial
oversmoothing and prediction for the ELK model for counts of secondary
education completion for women in Kenya collected in the 2014 Kenya demographic
health survey. Through a simulation study with Gaussian responses and a
realistic mix of short and long scale dependencies, we demonstrate that the
differences between the three approaches for prediction increases with distance
to nearest observation.
