. Author manuscript; available in PMC: 2017 Jun 5.

Published in final edited form as: J Dairy Sci. 2015 Sep 18;98(11):8133–8151. doi: 10.3168/jds.2014-9143

Table 4.

Prediction R-squared (R²_VAL), square root of the mean-squared prediction error (RMSE) in testing data sets by trait and model, and pair-wise comparisons of prediction accuracies of the models for 4 milk FA¹

Trait² and model	R²_VAL				RMSE	Pair-wise comparisons
Trait² and model	Mean	Minimum	Maximum	SD	RMSE	PLS	MPLS	Bayes RR	Bayes A	Bayes B
C10:0
PLS	0.44	0.33	0.57	0.07	0.49	—	100	100	100	100
MPLS	0.56	0.44	0.68	0.07	0.43	^***	—	80	100	100
Bayes RR	0.59	0.50	0.68	0.06	0.41	^***	^***	—	100	96
Bayes A	0.66	0.58	0.75	0.05	0.38	^***	^***	^***	—	64
Bayes B	0.67	0.55	0.75	0.06	0.38	^***	^***	^***	NS	—
C14:1 cis-9
PLS	0.30	0.20	0.41	0.06	0.28	—	88	100	100	100
MPLS	0.33	0.18	0.44	0.06	0.27	^***	—	48	100	100
Bayes RR	0.33	0.25	0.42	0.05	0.27	^***	NS	—	96	100
Bayes A	0.38	0.28	0.48	0.06	0.26	^***	^***	^***	—	96
Bayes B	0.48	0.37	0.65	0.06	0.24	^***	^***	^***	^***	—
C16:0
PLS	0.41	0.25	0.60	0.08	2.82	—	100	100	100	100
MPLS	0.51	0.34	0.70	0.08	2.55	^***	—	84	100	96
Bayes RR	0.54	0.40	0.70	0.07	2.45	^***	^***	—	84	92
Bayes A	0.58	0.46	0.72	0.07	2.33	^***	^***	^***	—	72
Bayes B	0.60	0.42	0.74	0.08	2.30	^***	^***	^***	NS	—
C18:0
PLS	0.26	0.09	0.38	0.08	1.65	—	80	92	100	100
MPLS	0.30	0.16	0.43	0.08	1.61	^***	—	64	100	100
Bayes RR	0.31	0.17	0.42	0.07	1.57	^***	NS	—	96	96
Bayes A	0.45	0.24	0.59	0.08	1.40	^***	^***	^***	—	76
Bayes B	0.49	0.30	0.65	0.11	1.35	^***	^***	^***	^***	—

PLS = partial least squares regression; MPLS = modified partial least squares regression, Bayes RR = Bayes ridge regression; R²_VAL = coefficient of determination calculated as the square of the correlation between observed and predicted values; Mean, Minimum, Maximum = mean, minimum, and maximum of the R² of 25 replicates; RMSE = mean of the root mean square errors of 25 replicates; the values above the diagonal indicate the percentage of replicates where the model in the column had a higher prediction R²_VAL than the model in the row; the asterisks below the diagonal indicate P-values from paired t-tests comparing the R²_VAL of the model in the column and the model in the row:

^***

Significant differences at the 0.001 level; NS indicates no significant difference at the 0.05 level.

C10:0 = decanoic (capric) acid; C14:1 cis-9 = 9-tetradecenoic (myristoleic) acid; C16:0 = hexadecanoic (palmitic) acid; C18:0 = octadecanoic (stearic) acid; each FA is expressed as a percentage of the total FA by weight.