Predicting body weight of South African Sussex cattle at weaning using multivariate adaptive regression splines and classification and regression tree data mining algorithms

Figures & data

Figure 1. Showing linear body measurements measured during study. SH: Sternum height, WH: Withers height, HG: Heart girth, HH: Hip height, BL: Body length, RL: Rump length, RW: Rump width.

Table 1. Descriptive statistics of body weight and linear body measurements in South African Sussex weaner calve.

Traits	Female (n = 57)	Male (n = 44)
	Mean ± SD	Mean ± SD
BW (kg)	236.23^b ± 39.55	269.27^a ± 37.59
SH (cm)	58.77^b ± 0.43	60.34^a ± 4.32
WH (cm)	104.42^b ± 5.04	111.52^a ± 3.83
HG (cm)	147.61^b ± 8.99	155.93^a ± 14.12
HH (mm)	111.12^b ± 6.56	117.00^a ± 4.20
BL (cm)	117.47^b ± 10.17	123.32^a ± 6.82
RL (cm)	38.84 ± 3.38	40.09 ± 3.49
RW (cm)	31.93 ± 3.94	32.82 ± 4.17

^ab Means in the same row with different superscripts are significantly different. BW: body weight, SH: sternum height, WH: withers height, HG: heart girth, HH: hip height, BL: body length, RL: rump length, RW: rump width, SD: standard deviation.

Table 2. Correlation matrix of measured traits, female below diagonal and male above diagonal.

Traits	BW	SH	WH	HG	HH	BL	RL	RW
BW (kg)		0.24^ns	0.51**	0.51**	0.74**	0.63**	0.33*	0.53**
SH (cm)	0.23^ns		0.23^ns	0.37**	0.12^ns	0.34*	0.21^ns	0.22^ns
WH (cm)	0.60**	0.42**		0.37**	0.67**	0.30*	0.14^ns	0.14^ns
HG (cm)	0.76**	0.39**	0.76**		0.36**	0.34*	0.24^ns	0.26^ns
HH (mm)	0.62**	0.53**	0.80**	0.77**		0.39**	0.05^ns	0.18^ns
BL (cm)	0.44**	0.47**	0.68**	0.55**	0.72**		0.27^ns	0.26^ns
RL (cm)	0.41**	0.47**	0.56**	0.59**	0.61**	0.52**		0.43**
RW (cm)	0.60**	0.47**	0.62**	0.65**	0.72**	0.58**	0.64**

BW: body weight, SH: sternum height, WH: withers height, HG: heart girth, HH: hip height, BL: body length, RL: rump length, RW: rump width, ns: not significant, * significant (p ≤ 0.05) and ** significant (p ≤ 0.01).

Table 3. MARS model.

Variables	Coefficients
Intercept	214.54
h (HG – 141)	2.65
h (HH – 111)	3.30
h (35 – RW)	−2.49

Table 4. CART algorithm outcome based on the cross-validation method.

	Complexity parameter	Number of splits	Relative error	Mean of the error
1	0.51	0	1.00	1.04
2	0.12	1	0.49	0.67
3	0.09	2	0.38	0.61
4	0.05	3	0.29	0.59
5	0.34	4	0.24	0.54
6	0.28	5	0.20	0.50
7	0.03	6	0.17	0.45
8	0.01	7	0.15	0.43
9	0.01	8	0.13	0.40
10	0.01	9	0.12	0.43

Table 5. Goodness of fit criteria for MARS and CART algorithms.

	MARS		CART
Criterions	Training	Test	Training	Test	Decision
Pearson’s correlation coefficient (r)	0.90	0.82	0.94	0.72	Greater is better
Root mean square error (RMSE)	19.01	22.13	15.19	28.13	Smaller is better
Relative root mean square error (RRMSE)	7.62	8.73	6.09	11.09	Smaller is better
Standard deviation ratio (SDR)	0.44	0.60	0.35	0.77	Smaller is better
Coefficient of variation (CV)	7.67	8.78	6.13	11.09	Smaller is better
Mean absolute percentage error (MAPE)	6.53	5.87	5.33	8.59	Smaller is better
Relative approximation error (RAE)	0.01	0.01	0.00	0.01	Smaller is better
Akaike’s information criterion (AIC)	437.93	181.43	397.18	186.83	Smaller is better
Performance index (PI)	4.01	4.80	3.14	6.46	Smaller is better
Mean error (ME)	0.00	3.55	0.00	−1.09	The expected value is zero
Mean absolute deviation (MAD)	15.39	15.12	12.80	21.53	Smaller is better
Coefficient of determination (Rsq)	0.81	0.63	0.88	0.40	Greater is better
Adjusted coefficient of determination (ARsq)	0.80	0.57	0.88	0.40	Greater is better

Figure 2. Model selection for the optimal MARS model.

Figure 3. CART model.

Data availability statement

For data requests, please contact the author T.L.T.