Fast generalized spatial multilevel blockNNGP modeling

Typical geostatistical models only consider the case where we observe one response at each location. However, the situation with multiple replicates at spatial locations is seldom discussed. Moreover, the generalized spatial Gaussian process models encounter computational difficulties when the size of the spatial domain becomes massive. Thus, fast generalized spatial multilevel models that use block nearest neighbor Gaussian process to scale to large datasets are introduced. The proposed method uses integrated nested Laplace approximation (INLA) to avoid long sequential updates of the Markov chain Monte Carlo (MCMC) methods. A simulation study is performed under different response distributions to show the model parameter estimation capacity, computational efficiency, and prediction performance. Finally, the proposed models are fitted to the data of Beijing housing transactions to predict the sales price of houses at unobserved locations. The studies demonstrate that the proposed models have advantages in fitting and prediction, making the interpretation better substantiated.