Table 4.

AIC scores of the linear mixed effects models with predictions from each metric as an independent variable from the routine and cross-validated analyses.

Heuristic assumptions	Akaike information criterion		Akaike information criterion – cross-validated
	Metric	Value, t-statistic, and probability	Metric	Value, t-statistic, and probability
No heuristic	Mx-S	3053.56, 33.31, 8.75 × 10−15	Pr-S	3127.75, 30.79, 0.001
	No alternates		Mx-S	3131.42, 30.67, 8.83 × 10−5
Free heuristic – impervious	Pr-S	2993.57, 35.38, 0.093†	Pr-S	3123.17, 30.92, 0.005
	Mx-S	2994.51, 35.31, 0.058†	Mx-S	3125.74, 30.84, 0.002
Free heuristic – vulnerable	Pr-S	2988.82, 35.6, 1.0*	Pr-S	3112.75, 31.27, 1.0*
	Mx-S	2992.66, 35.36, 0.147†	No alternates
Obligatory heuristic – impervious	Mx-S	3247.29, 1.90, 7.48 × 10−57	Mx-T	3246.15, 2.19, 1.08 × 10−29
	All other metrics had probability > 0.05 in comparison to Mx-S		All other metrics had probability > 0.05 in comparison to Mx-T
Obligatory heuristic – vulnerable	Mx-T	3118.53, 25.01, 6.82 × 10−29	Pr-S	3207.31, 9.79, 2.93 × 10−21
	Pr-I	3123.34, 31.13, 6.16 × 10−30	Mx-S	3207.42, 10.56, 2.77 × 10−21
			Pr-I	3208.15, 24.39, 1.92 × 10−21

For each model, three values are listed: the AIC, the t-statistic for the mixed-effects model, and the probability that the model would minimize information loss relative to the best-fitting model (i.e., lowest AIC score) within the routine or cross-validated analysis.

*Indicates the model with the best fit across all heuristic assumptions.

^†Indicates that the model has a greater than 5% probability of minimizing the information loss, relative to the best model. This probability was computed using Eq. 3. Alternates were listed under each heuristic assumption if their AIC values were within 6 points of the lowest AIC value found under that assumption. (This difference corresponds to at least a 5% probability of minimizing the information loss.)