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Forest Ecosystems

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.
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