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Effects of Residual Smoothing on the Posterior of the Fixed Effects in Disease‐Mapping Models
Author(s) -
Reich Brian J.,
Hodges James S.,
Zadnik Vesna
Publication year - 2006
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2006.00617.x
Subject(s) - random effects model , covariate , fixed effects model , collinearity , statistics , mathematics , autoregressive model , econometrics , smoothing , measure (data warehouse) , variance (accounting) , variance inflation factor , residual , linear regression , panel data , computer science , medicine , multicollinearity , data mining , economics , algorithm , meta analysis , accounting
Summary Disease‐mapping models for areal data often have fixed effects to measure the effect of spatially varying covariates and random effects with a conditionally autoregressive (CAR) prior to account for spatial clustering. In such spatial regressions, the objective may be to estimate the fixed effects while accounting for the spatial correlation. But adding the CAR random effects can cause large changes in the posterior mean and variance of fixed effects compared to the nonspatial regression model. This article explores the impact of adding spatial random effects on fixed effect estimates and posterior variance. Diagnostics are proposed to measure posterior variance inflation from collinearity between the fixed effect covariates and the CAR random effects and to measure each region's influence on the change in the fixed effect's estimates by adding the CAR random effects. A new model that alleviates the collinearity between the fixed effect covariates and the CAR random effects is developed and extensions of these methods to point‐referenced data models are discussed.

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