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

Forest Ecosystems

Table 4 Various zero-inflated Poisson regression models validated during model selection

	Model	AIC	Mixture parameter
g ₁(λ _i) = β ₀₁	9.1	7584.1	g ₂(ω _i) = β ₀₂; ω _i = 0.52
g ₁(λ _i) = β ₀₁ + f ₁₁(DWT _i)	9.2	7262.3	g ₂(ω _i) = β ₀₂; ω _i = 0.51
g ₁(λ _i) = β ₀₁ + f ₁₁(DWT _i) + f ₂₁(CTH _i)	9.3	7217.5	g ₂(ω _i) = β ₀₂; ω _i = 0.50
g ₁(λ _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) = 28.81	9.4	5708.3	g ₂(ω _i) = β ₀₂; ω _i = 0.20
g ₁(λ _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	9.5	5092.2	g ₂(ω _i) = β ₀₂; ω _i = 0.12
g ₁(λ _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	9.6	5051.3	g ₂(ω _i) = β ₀₂ + f ₁₂(DWT _i)

Model complexity increases from model 9.1 to 9.6. 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.