# A memory-free spatial additive mixed modeling for big spatial data

## TL;DR

This paper introduces a memory-free, fast spatial additive mixed modeling method capable of handling millions of observations by estimating spatial dependence directly from residuals, significantly improving computational efficiency and scalability.

## Contribution

It develops a novel spatial additive mixed model that estimates spatial structure without prior knowledge, using a pre-compression technique to achieve memory independence and efficiency.

## Key findings

- Accurately estimates spatial effects in large datasets
- Achieves computational complexity independent of sample size
- Demonstrates efficiency and accuracy through simulations

## Abstract

This study develops a spatial additive mixed modeling (AMM) approach estimating spatial and non-spatial effects from large samples, such as millions of observations. Although fast AMM approaches are already well-established, they are restrictive in that they assume an known spatial dependence structure. To overcome this limitation, this study develops a fast AMM with the estimation of spatial structure in residuals and regression coefficients together with non-spatial effects. We rely on a Moran coefficient-based approach to estimate the spatial structure. The proposed approach pre-compresses large matrices whose size grows with respect to the sample size N before the model estimation; thus, the computational complexity for the estimation is independent of the sample size. Furthermore, the pre-compression is done through a block-wise procedure that makes the memory consumption independent of N. Eventually, the spatial AMM is memory-free and fast even for millions of observations. The developed approach is compared to alternatives through Monte Carlo simulation experiments. The result confirms the accuracy and computational efficiency of the developed approach. The developed approaches are implemented in an R package spmoran.

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Source: https://tomesphere.com/paper/1907.11369