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Table 2 Various Poisson regression models validated during model selection

From: A spatially-explicit count data regression for modeling the density of forest cockchafer (Melolontha hippocastani) larvae in the Hessian Ried (Germany)

  Model AIC Dispersion parameter
g(λ i ) = β 0 7.1 12263.0 11.71***
g(λ i ) = β 0 + f 1(DWT i ) 7.2 10881.7 9.64***
g(λ i ) = β 0 + f 1(DWT i ) + f 2(CTH i ) 7.3 10692.3 9.31***
g(λ i ) = β 0 + f 1(DWT i ) + f 2(CTH i ) + f 3(east i , north i ), edf for f 3(east i , north i ) = 28.753 7.4 6193.4 4.34***
g(λ i ) = β 0 + f 1(DWT i ) + f 2(CTH i ) + f 3(east i , north i ), edf for f 3(east i , north i ) = 121.619 7.5 5394.4 2.75***
g(λ i ) = β 0 + f 1(DWT i ) + f 2(CTH i ) + f 3(east i , north i ), edf for f 3(east i , north i ) = 198.121 7.6 5128.1 2.31***
g(λ i ) = β 0 + f 1(DWT i ) + f 2(CTH i ) + f 3(east i , north i ), edf for f 3(east i , north i ) = 321.446 7.7 4745.3 1.90***
  1. Complexity increases from model 7.1 to 7.7. ***denotes significant deviance (level of significance 0.001) from equidispersion (ϕ = 1) by applying a regression based test with the alternative hypothesis of a quasi-Poisson model (Cameron and Trivedi [1990]) implemented in the R library AER (Kleiber and Zeileis [2008]). The flexibility of the spatial model component increases with increasing estimated degrees of freedom (edf) of the 2-dimensional smoothing function f 3.
  2. with DWT i : simulated distance to water table in October 2007 at plot i (m); CTH i : modeled clay thickness at plot i (%); (east i , north i ): Gauß-Krüger east and north coordinates of plot i defined in relation to the 3rd meridian.