Impacts of spatial imputation on location-allocation problem solutions

Abstract

Georeferenced data often contain missing values, and such missing values can considerably affect spatial modeling. A spatial location model can also suffer from this issue when there are missing values in its geographic distribution of weights. Although general imputation approaches have been developed, one distinguishing fact here is that spatial imputation generally performs better for georeferenced data because it can reflect a fundamental property of those data, that is, spatial autocorrelation or spatial dependency. This paper explores how spatial imputation exploiting spatial autocorrelation can contribute to estimating missing values in a weights surface for location modeling and subsequently improve solutions for spatial optimization, specifically p-median problems using a spatially imputed weights surface. This paper examines two spatial imputation methods, ordinary co-kriging and Moran eigenvector spatial filtering. Their results are compared with conventional linear regression, essentially Expectation-Maximization algorithm results for independent observations of Gaussian random variable cases. Simulation experiments show that spatial imputation produces better results for georeferenced data than simply ignoring any missing values and non-spatial imputation, and appropriately imputed values can enhance spatial optimization solutions, regardless of the number of medians, p.