Assessing Spatial Dependence in Count Data: Winsorized and Spatial Filter Specification Alternatives to the Auto‐Poisson Model

The auto-Poisson probability model furnishes an obvious tool for modeling counts of geographically distributed rare events. Unfortunately, its original specification can accommodate only negative spatial autocorrelation, which itself is a rare event. More recent alternative reformulations, namely, the Winsorized and spatial filter specifications, circumvent this drawback. A comparison of their performances presented in this article reveals some of their relative advantages and disadvantages.

[1]  Noel A. C. Cressie,et al.  Statistics for Spatial Data: Cressie/Statistics , 1993 .

[2]  Daniel A. Griffith,et al.  A spatial filtering specification for the auto-Poisson model , 2002 .

[3]  Joseph G. Pigeon,et al.  A cautionary note about assessing the fit of logistic regression models , 1999 .

[4]  D. Clayton,et al.  Empirical Bayes estimates of age-standardized relative risks for use in disease mapping. , 1987, Biometrics.

[5]  Stephen P. Hubbell,et al.  Local neighborhood effects on long-term survival of individual trees in a neotropical forest , 2001, Ecological Research.

[6]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[7]  Giles M. Foody,et al.  Fuzzy mapping of tropical land cover along an environmental gradient from remotely sensed data with an artificial neural network , 1999, J. Geogr. Syst..

[8]  Hulin Wu,et al.  Markov chain Monte Carlo for autologistic regression models with application to the distribution of plant species , 1998 .

[9]  Vic Barnett,et al.  Outliers in Statistical Data , 1980 .

[10]  D. Griffith.  Eigenfunction properties and approximations of selected incidence matrices employed in spatial analyses , 2000 .

[11]  Jonathan M. Graham,et al.  AUTOLOGISTIC MODEL OF SPATIAL PATTERN OF PHYTOPHTHORA EPIDEMIC IN BELL PEPPER: EFFECTS OF SOIL VARIABLES ONDISEASE PRESENCE , 1994 .

[12]  Brian D. Ripley,et al.  Spatial Statistics: Ripley/Spatial Statistics , 2005 .

[13]  Daniel A. Griffith,et al.  A Spatial Filtering Specification for the Autologistic Model , 2004 .

[14]  Daniel A. Griffith,et al.  A linear regression solution to the spatial autocorrelation problem , 2000, J. Geogr. Syst..

[15]  Youngjo Lee,et al.  Modelling and analysing correlated non-normal data , 2001 .

[16]  T. Eo.  Partialling out the spatial component of ecological variation: questions and propositions in the linear modelling framework , 1998 .

[17]  Jun Zhu,et al.  Markov chain Monte Carlo for a Spatial-Temporal Autologistic Regression Model , 2008 .

[18]  Noel A Cressie,et al.  Modeling Poisson variables with positive spatial dependence , 1997 .

[19]  Pierre Legendre,et al.  All-scale spatial analysis of ecological data by means of principal coordinates of neighbour matrices , 2002 .

[20]  A. Hill.  THE DISTRIBUTION OF DRUMLINS IN COUNTY DOWN, IRELAND* , 1973 .

[21]  Peter J. Diggle,et al.  Statistical analysis of spatial point patterns , 1983 .