Modelling the population fluctuation of winter moth and mottled umber moth in central and northern Germany

Forest Ecosystems

Table 3 Model statistics of the stepwise selection process, calculated from predictions employing the full models including fixed and random effects, as well as predictions using fixed effects only (right part of the table). For comparison, the optimal cutpoints that were derived for the full models were also employed for the fixed effects predictions

	Model	Cutpoint	Predictions based on fixed and random effects				Predictions based on fixed effects only
	Model	Cutpoint	Sensitivity	Specificity	Accuracy	Auc	Sensitivity	Specificity	Accuracy	AUC
4.4	π_ij = h(β_{0 ecoregion} + f_ecoregion(j) + b_i)	0.439	0.568	0.973	0.906	0.930	0.316	0.954	0.848	0.831
4.5	π_ij = h(β_{0 ecoregion} + f_ecoregion(j) + β₁pesticide_ij + b_i)	0.422	0.604	0.967	0.906	0.930	0.316	0.957	0.850	0.836
4.6	π_ij = h(β_{0 ecoregion} + f_ecoregion(j) + β₁pesticide_ij + f₁(prec_pupa_ij) + b_i)	0.427	0.596	0.966	0.904	0.915	0.467	0.927	0.850	0.850
4.7	π_ij = h(β_{0 ecoregion} + f_ecoregion(j) + β₁pesticide_ij + f₁(prec_pupa_ij) + f₂(tmin_imago_ij) + b_i)	0.433	0.586	0.966	0.903	0.924	0.446	0.945	0.862	0.860