Table 1 Model evaluation metrics for eight logistic regression models (LR1-LR8), a multi-model ensemble, a random forest model (RF), and an artificial neural network model (ANN) for predicting the development of tar spot (tar spot) on corn between 2018 and 2022 (n = 182).

Model	Accuracy (%)	Kappa^a	Type I error (%)^b	Type II error (%)^c	Precision (%)^d	Recall (%)^e
LR1	85.2	0.55	10.3	33.3	61.5	66.7
LR2	85.2	0.55	10.3	33.3	61.5	66.7
LR3	86.3	0.55	7.5	38.9	66.7	61.1
LR4	86.3	0.56	8.2	36.1	65.7	63.9
LR5	84.1	0.53	12.3	30.6	58.1	69.4
LR6	86.8	0.59	8.9	30.6	65.8	69.4
LR7	83.52	0.52	13.0	30.6	56.8	69.4
LR8	83.52	0.49	11.0	38.9	57.9	61.1
Multi-model ensemble^f	87.4	0.61	8.2	30.6	67.6	69.4
RF^g	90.1	0.64	2.1	41.7	87.5	58.3
ANN^h	85.7	0.54	8.2	38.9	64.7	61.1

^aCohen’s kappa coefficient compares the observed model accuracy with the expected accuracy. As proposed by Landis and Koch⁴⁷, kappa values of 0.00–0.20 as slight agreement, 0.21–0.40 as fair agreement, 0.41–0.60 as moderate agreement, 0.61–0.80 as substantial agreement, and 0.81–1.00 as almost perfect agreement.
^bType I error rate is the percentage of false positives predicted by the model.
^cType II error is the percentage of false negatives predicted by the model.
^dPrecision is defined as the ratios of true positives to all predicted positives.
^eRecall is the true positive rate, which is defined as the ratio of true positives to all observed positives.
^fMultimodel ensemble was created by ensembling risk probabilities from LR4 and LR6.
^gRandom Forest model was developed using 500 trees.
^hArtificial neural network model was developed using nine hidden layers. Risk probability threshold of 35% was used to evaluate the presence of tar spot development.

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