Better Autologistic Regression

Abstract

Autologistic regression is an important probability model for dichotomous random variables observed along with covariate information. It has been used in various fields for analyzing binary data possessing spatial or network structure. The model can be viewed as an extension of the autologistic model (also known as the Ising model, quadratic exponential binary distribution, or Boltzmann machine) to include covariates. It can also be viewed as an extension of logistic regression to handle responses that are not independent. Not all authors use exactly the same form of the autologistic regression model. Variations of the model differ in two respects. First, the variable coding-the two numbers used to represent the two possible states of the variables-might differ. Common coding choices are (zero, one) and (minus one, plus one). Second, the model might appear in either of two algebraic forms: a standard form, or a recently proposed centered form. Little attention has been paid to the effect of these differences, and the literature shows ambiguity about their importance. It is shown here that changes to either coding or centering in fact produce distinct, non-nested probability models. Theoretical results, numerical studies, and analysis of an ecological data set all show that the differences among the models can be large and practically significant. Understanding the nature of the differences and making appropriate modeling choices can lead to significantly improved autologistic regression analyses. The results strongly suggest that the standard model with plus/minus coding, which we call the symmetric autologistic model, is the most natural choice among the autologistic variants.

Spatially Explicit Modeling of Community Occupancy using Markov Random Field Models with Imperfect Observation: Mesocarnivores in Apostle Islands National Lakeshore

“…However theoretical studies with this model by Wolters (2017) suggested better performance of a symmetrical coding rather than centering the model when associations (e.g. competition, spatial autocorrelations) were expected.…”

“…Models with a centering term mostly used in ecology enabled modeling of the "large scale" response due to environmental predictors (centered auto-logistic models Hughes et al (2011)) which tried to detect auto-correlation in the residuals of a large scale response due to environmental drivers. However theoretical studies with this model by Wolters (2017) suggested better performance of a symmetrically coded model compare to a centered model when associations (e.g. competition, spatial autocorrelations) were expected.…”

“…Models with a centering term that modeled the "large scale" response due to environmental predictors (centered autologistic model Hughes et al 2011) which tried to detect auto-correlation in the residuals of large scale response due to environment were used in ecology. However theoretical studies on this model by Wolters (2017) suggested better performance of a symmetrical coding rather than centering the model when associations (e.g. competition, spatial autocorrelations) were expected strong and because centered models will predicted non-linear relationships between strength of association and log odds of two species being coexist/co-absent while symmetrical coding did not have this problem.…”

Weather persistence on sub-seasonal to seasonal timescales: a methodological review

“…The link to drought occurrence at the previous time step is implicitly taken into account with previous precipitation or soil moisture anomalies. If previous system values are explicitly included as covariates to the model, one speaks of autologistic regression (Wolters, 2017).…”

Weather persistence on sub-seasonal to seasonal timescales: a methodological review

“…The link to drought occurrence at the previous time step is implicitly taken into account with previous precipitation or soil moisture anomalies. If previous system values are explicitly included as covariates to the model, one speaks of auto-logistic regression (Wolters, 2017).…”