Table 2.

Comparison of predictive performance of linear mixed effects model, BPNN model and linear mixed effects neural network model

Models			RMSE	MAPE	MAE	R 2
Linear mixed-effects model	lm1	Training set	0.547	1.364	0.400	0.700
		Validation set	0.557	1.389	0.408	0.680
		Test set	0.558	1.645	0.412	0.688
	lm11	Training set	0.547	1.368	0.400	0.700
		Validation set	0.555	1.386	0.407	0.681
		Test set	0.557	1.647	0.411	0.689
	lm2	Training set	0.548	1.374	0.403	0.699
		Validation set	0.584	1.370	0.430	0.647
		Test set	0.562	1.678	0.416	0.684
	lm22	Training set	0.554	1.388	0.407	0.693
		Validation set	0.557	1.397	0.410	0.679
		Test set	0.559	1.624	0.411	0.687
	lm3	Training set	0.548	1.374	0.403	0.699
		Validation set	0.557	1.393	0.409	0.679
		Test set	0.562	1.676	0.417	0.684
	lm33	Training set	0.554	1.388	0.408	0.693
		Validation set	0.557	1.398	0.411	0.679
		Test set	0.559	1.622	0.411	0.687
BPNN model	BPNN1	Training set	0.505	1.215	0.376	0.745
		Validation set	0.588	1.338	0.429	0.644
		Test set	0.626	1.658	0.446	0.608
	BPNN2	Training set	0.515	1.218	0.381	0.734
		Validation set	0.573	1.313	0.421	0.660
		Test set	0.600	1.649	0.433	0.639
	BPNN3	Training set	0.527	1.240	0.388	0.722
		Validation set	0.573	1.291	0.417	0.661
		Test set	0.593	1.651	0.422	0.648
Mixed-effects neural network model	lm22-BPNN1	Training set	0.447	1.322	0.322	0.800
		Validation set	0.552	1.444	0.380	0.682
		Test set	0.542	1.565	0.393	0.706
	lm22-BPNN2	Training set	0.456	1.306	0.325	0.792
		Validation set	0.527	1.390	0.369	0.708
		Test set	0.551	1.574	0.401	0.696
	lm22-BPNN3	Training set	0.471	1.287	0.331	0.778
		Validation set	0.527	1.347	0.361	0.709
		Test set	0.565	1.628	0.411	0.680
	lm11-BPNN1	Training set	0.447	1.323	0.322	0.800
		Validation set	0.552	1.444	0.380	0.682
		Test set	0.511	1.412	0.359	0.738
	lm11-BPNN2	Training set	0.456	1.306	0.325	0.792
		Validation set	0.527	1.389	0.369	0.708
		Test set	0.518	1.411	0.361	0.731
	lm11-BPNN3	Training set	0.471	1.291	0.330	0.778
		Validation set	0.525	1.351	0.359	0.711
		Test set	0.526	1.455	0.365	0.723