The Problem of Missing Data on Spatial Surfaces

Abstract

Although the problem of missing data arises in most branches of the discipline, it has received little systematic treatment in the geographical literature. In an effort to overcome this deficiency, this paper reviews a number of methods for approaching the problem. Of the three classes of solutions—ad hoc, cartographic interpolation, and statistical—the statistical approaches appear to be preferable. In this review a modified version of the Orchard and Woodbury missing-information principle receives the greatest emphasis because it combines classical statistical theory with trend surface and spatial autoregressive models. Although the best solution of all is to return to the experimental situation in order to collect supplementary data, this is often impractical or impossible. The analyst should then consider the estimation techniques presented here. The methods used to address the missing data problem thus become an important stage in the overall process of experimental design, sampling, and hypothesis testing.

Key Words:

• missing data
• cartographic interpolation
• trend surface model
• spatial filter
• kriging
• Orchard and Woodbury missing-information principle