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Table 3 Various negative binomial 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 Explained deviance (%) Dispersion parameter
g 1(μ i ) = β 01 8.1 5335.4 0 g 2(1/ϕ) = β 02;
ϕ = 0.255
g 1(μ i ) = β 01 + f 11(DWT i ) 8.2 5207.1 12 g 2(1/ϕ) = β 02;
ϕ = 0.308
g 1(μ i ) = β 01 + f 11(DWT i ) + f 21(CTH i ) 8.3 5171.9 15.7 g 2(1/ϕ) = β 02;
ϕ = 0.323
g 1(μ i ) = β 01 + f 11(DWT i ) + f 21(CTH i ) + f 31(east i , north i ), edf for f 31(east i , north i ) = 25.96 8.4 4343.8 63.4 g 2(1/ϕ) = β 02;
ϕ = 1.051
g 1(μ i ) = β 01 + f 11(DWT i ) + f 21(CTH i ) + f 31(east i , north i ), edf for f 31(east i , north i ) = 117.35 8.5 4161.3 75.1 g 2(1/ϕ) = β 02;
ϕ = 1.664
g 1(μ i ) = β 01 + f 11(DWT i ) + f 21(CTH i ) + f 31(east i , north i ), edf for f 31(east i , north i ) = 117.35 8.6 4154.5 75.4 g 2(1/ϕ ι ) =
β 02 + f 12(DWT i )
  1. Complexity increases from model 8.1 to 8.6. 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.