# Plausible Reasoning and Spatial-Statistical Theory

Donegan, Connor (2024). Plausible Reasoning and Spatial-Statistical Theory: A Critique of Recent Writings on 'Spatial Confounding'. *Geographical Analysis*. DOI:10.1111/gean.12408 (open access)

This project has a dual motivation.

The first motivation is explicit in the paper - I am interested in the historical development of spatial-statistical theory. What kinds of theoretical concepts have researchers used to justify and understand their use of various techniques for the analysis of spatial data? By “theoretical” I mean systems of concepts and principles that are not reducible to sets of operations, mathematical equations, or empirical results. This topic has become particularly important recently since established methods for spatial data analysis have been challenged by influential statistical and biostatistical researchers.

The second motivation for this project is methodological but in a slightly different sense—in my dissertation, this research topic serves as a case study in plausible reasoning. I use the term plausible reasoning to refer to a perspective on logic and epistemology which was developed by George Pólya. Pólya’s work on patterns of plausible inference drew from probability theory and classical logic to provide a fairly systematic treatment of non-demonstrative logic or probable inference. Although his work is not well known among social science researchers, he was a major source of inspiration for the philosopher of science Imre Lakatos (who is extremely influential across social science paradigms). As a case study in the application of plausible reasoning, this paper makes deliberate use of analogy as an analytical device that can (1) spur creative theorization and (2) help to reveal conceptual inconsistencies that may be latent in current ways of thinking.

** Abstract **

Statistical research on correlation with spatial data dates at least to Student's (W. S. Gosset's) 1914 paper on “the elimination of spurious correlation due to position in time and space.” Since 1968, much of this work has been organized around the concept of spatial autocorrelation (SA). A growing statistical literature is now organized around the concept of “spatial confounding” (SC) but is estranged from, and often at odds with, the SA literature and its history. The SC literature is producing new, sometimes flawed, statistical techniques such as Restricted Spatial Regression (RSR). This article brings the SC literature into conversation with the SA literature and provides a theoretically grounded review of the history of research on correlation with spatial data, explaining some of its implications for the the SC literature. The article builds upon principles of plausible inference to synthesize a guiding theoretical thread that runs throughout the SA literature. This leads to a concise theoretical critique of RSR and a clarification of the logic behind standard spatial-statistical models.