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

Forest Ecosystems

Table 3 Various negative binomial regression models validated during model selection

	Model	AIC	Explained deviance (%)	Dispersion parameter
g ₁(μ _i) = β ₀₁	8.1	5335.4	0	g ₂(1/ϕ) = β ₀₂;
g ₁(μ _i) = β ₀₁	8.1	5335.4	0	ϕ = 0.255
g ₁(μ _i) = β ₀₁ + f ₁₁(DWT _i)	8.2	5207.1	12	g ₂(1/ϕ) = β ₀₂;
g ₁(μ _i) = β ₀₁ + f ₁₁(DWT _i)	8.2	5207.1	12	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;
g ₁(μ _i) = β ₀₁ + f ₁₁(DWT _i) + f ₂₁(CTH _i)	8.3	5171.9	15.7	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;
	8.4	4343.8	63.4	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;
	8.5	4161.3	75.1	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) =
	8.6	4154.5	75.4	β ₀₂ + f ₁₂(DWT _i)

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.
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 3^rd meridian.