Multivariate modeling to estimate the composition of carcass tissues of Santa Inês sheep

The purpose of this study was to establish a multivariate model using two complementary multivariate statistical techniques: Factor Analysis and Stepwise Multiple Regression, to predict tissue composition through carcass characteristics of Santa Inês sheep. The data was obtained from 82 Santa Inês sheep under confinement. The predictor variables were carcass characteristics related to weight, yield, morphometric measures and meat cuts. The use of latent variables from factor analysis in multiple regression models eliminates the problem of multicollinearity of the explanatory variables, improving the accuracy of interpretation of results by proposing a better fit of the mathematical model. However, the coefficient of determination (R²) values were moderate for muscle proportion and total fat, and low for bone proportion, indicating that more appropriate independent variables should be used to better predict the proportion of tissues in Santa Inês sheep.

Keywords:
multivariate analysis; carcass dissection; factor scores; morphometric measures

Authorship

Marilene dos Santos Maciel ^** Author for correspondence. E-mail: marilenemaciel123@hotmail.com

Departamento de Zootecnia, Universidade Federal Rural de Pernambuco, Rua Dom Manuel de Medeiros, s/n, Dois Irmãos, 51171-900, Recife, Pernambuco, Brazil. Universidade Federal Rural de PernambucoBrazilRecife, Pernambuco, BrazilDepartamento de Zootecnia, Universidade Federal Rural de Pernambuco, Rua Dom Manuel de Medeiros, s/n, Dois Irmãos, 51171-900, Recife, Pernambuco, Brazil.

https://orcid.org/0000-0003-4234-9764

Janaína Kelli Gomes Arandas

Francisco Fernando Ramos de Carvalho

George Rodrigo Beltrão da Cruz

Departamento de Ciência Animal, Centro de Ciências Humanas, Sociais e Agrárias, Universidade Federal da Paraíba, Campus Universitário III, Bananeiras, Paraíba, Brazil. Universidade Federal da ParaíbaBrazilBananeiras, Paraíba, BrazilDepartamento de Ciência Animal, Centro de Ciências Humanas, Sociais e Agrárias, Universidade Federal da Paraíba, Campus Universitário III, Bananeiras, Paraíba, Brazil.

Roberto Germano Costa

Departamento de Zootecnia, Universidade Federal da Paraíba, Areia, Paraíba, Brazil. Universidade Federal da ParaíbaBrazilAreia, Paraíba, BrazilDepartamento de Zootecnia, Universidade Federal da Paraíba, Areia, Paraíba, Brazil.

Neila Lidiany Ribeiro

Universidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil. Universidade Federal de Campina GrandeBrazilCampina Grande, Paraíba, BrazilUniversidade Federal de Campina Grande, Campina Grande, Paraíba, Brazil.

Maria Norma Ribeiro

* Author for correspondence. E-mail: marilenemaciel123@hotmail.com

SCIMAGO INSTITUTIONS RANKINGS

Tables

Tables (8)

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Table 1
Main information of the experiments.

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Table 2
Descriptive statistics of dependent variables.

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Table 3
Descriptive statistics of independent variables.

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Table 4
Pearson’s correlation (r) between tissue composition and carcass variables.

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Table 5
Prediction equations for tissue composition according to stepwise multiple regression analysis of the original variables.

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Table 6
Sampling adequacy by Barlett’s test of sphericity and the KMO (Kaiser-Meyer-Olkin) test.

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Table 7
Results of factor analysis applied to the independent variables.

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Table 8
Prediction equations for tissue composition according to stepwise multiple regression analysis of the latent variables.

Table 1 Main information of the experiments.

Characteristics	Experiment 1	Experiment 2
Number of animals	42.0	40.0
Initial age, days	180.0	120.0
Initial weight, kg	21.6 ± 2.2	21.3 ± 2.2
Slaughter weight, kg	28.9 ± 2.6	34.2 ± 3.4
Cold carcass weight, kg	14.1 ± 1.3	15.6 ± 1.8

Table 2 Descriptive statistics of dependent variables.

Variables	µ±sd	Variance	Min.	Max.
Muscle proportion (%)	68.14 ±3.88	15.04	58.87	77.64
Bone proportion (%)	18.87±2.26	5.09	15.28	27.81
Total fat proportion (%)	9.36±2.85	8.14	4.10	17.03

µ±sd = mean ± standard deviation.

Table 3 Descriptive statistics of independent variables.

Variables	Abbreviations	µ±sd	Variance	Min.	Max.
Weight (kg)
Live weight at slaughter	LWS	31.58±4.00	15.97	22.70	42.00
Empty body weight	EBW	25.73±3.33	11.06	18.27	34.70
Hot carcass weight	HCW	15.17±1.80	3.25	11.20	20.20
Cold carcass weight	CCW	14.87±1.73	2.98	11.09	20.00
Yield (%)
Biological yield	BY	59.15±3.68	13.51	48.12	73.88
Hot carcass yield	HCY	48.18±3.07	9.45	38.64	60.26
Cold carcass yield	CCY	47.27±3.29	10.82	37.08	59.60
Leg yield	LEGY	30.08±3.75	14.05	19.37	41.27
Loin yield	LOIY	12.93±2.17	4.70	7.63	20.12
Rib yield	RIBY	29.99±3.89	15.16	19.74	38.53
Neck yield	NECY	6.92±1.19	1.41	4.18	9.98
Shoulder yield	SHOY	18.81±2.44	5.93	10.90	23.78
Morphometric measures (cm)
Carcass external length	CEL	56.39±3.03	9.15	48.00	65.00
Carcass internal length	CIL	60.66±4.59	21.04	51.00	71.00
Leg length	LL	34.57±2.85	8.12	28.00	39.00
Croup width	CW	17.99±3.47	12.07	12.20	26.00
Thorax width	TW	17.21±4.08	16.61	11.20	24.50
Croup perimeter	CP	57.09±5.47	29.93	49.00	91.00
Leg perimeter	LP	37.31±3.09	9.53	28.00	43.00
Thorax perimeter	TP	67.96±3.77	14.22	58.00	85.50
Carcass compactness index	CCI	0.25±0.02	0.00	0.20	0.29
Cuts (kg)
Leg	LEG	2.22±0.30	0.09	1.41	3.02
Loin	LOI	0.96±0.18	0.03	0.64	1.46
Rib	RIB	2.22±0.30	0.09	1.51	3.14
Neck	NEC	0.76±0.26	0.07	0.38	1.27
Shoulder	SHO	1.39±0.17	0.03	0.99	1.83

Table 4 Pearson’s correlation (r) between tissue composition and carcass variables.

Variables	Abbreviations	Muscle (%)	Bone (%)	Fat (%)
Weight (kg)
Live weight at slaughter	LWS	-0.412*	-0.362*	0.501*
Empty body weight	EBW	-0.428*	-0.364*	0.525*
Hot carcass weight	HCW	-0.255*	-0.361*	0.412*
Cold carcass weight	CCW	-0.215^NS	-0.327*	0.367*
Yield (%)
Biological yield	BY	0.418*	0.069 ^NS	-0.331*
Hot carcass yield	HCY	0.356*	0.048 ^NS	-0.246*
Cold carcass yield	CCY	0.407*	0.113 ^NS	-0.319*
Leg yield	LEGY	-0.096 ^NS	0.094 ^NS	0.033 ^NS
Loin yield	LOIY	-0.525*	-0.142 ^NS	0.494*
Rib yield	RIBY	0.222*	0.155 ^NS	-0.206 ^NS
Neck yield	NECY	0.371*	-0.091 ^NS	-0.235^NS
Shoulder yield	SHOY	0.307*	0.093 ^NS	-0.282*
Morphometric measures (cm)
Carcass external length	CEL	-0.411*	-0.002 ^NS	0.353*
Carcass internal length	CIL	-0.590*	-0.186 ^NS	0.567*
Leg length	LL	-0.588*	-0.079 ^NS	0.486*
Croup width	CW	-0.688*	-0.313*	0.618*
Thorax width	TW	-0.661*	-0.348*	0.605*
Croup perimeter	CP	-0.204 ^NS	-0.199 ^NS	0.205 ^NS
Leg perimeter	LP	0.490*	0.039 ^NS	-0.435*
Thorax perimeter	TP	-0.180 ^NS	-0.271*	0.270*
Carcass compactness index	CCI	0.258*	-0.273*	-0.039 ^NS
Cuts (kg)
Leg	LEG	-0.239*	-0.201 ^NS	0.324*
Loin	LOI	-0.570*	-0.324*	0.643*
Rib	RIB	0.061 ^NS	-0.144 ^NS	0.097 ^NS
Neck	NEC	-0.672*	-0.446*	0.746*
Shoulder	SHO	0.161 ^NS	-0.212 ^NS	0.023 ^NS

^NSp > 0.05; *p < 0.05.

Table 5 Prediction equations for tissue composition according to stepwise multiple regression analysis of the original variables.

Dependent variable	Number	Equation	Cp	R²	MSE	P Value
Muscle proportion (%)	1	Y = 91.961 - 0.768 × CW	27.290	0.474	2.831	<.0001
	2	Y = 68.314 - 0.798 × CW + 57.885 × CCI	9.595	0.574	2.563	<.0001
	3	Y = 69.817 - 0.653 × CW + 57.293 × CCI - 4.227 × LOI	7.392	0.596	2.514	<.0001
	4	Y = 68.151 - 0.493 × CW + 39.931 × CCI - 9.014 × LOI + 6.582 × SHO	1.438	0.636	2.401	<.0001
Bone proportion (%)	1	Y = 21.853 - 3.940 × NEC	16.141	0.199	2.032	<.0001
	2	Y = 29.708 - 31.432 × CCI - 4.076 × NEC	8.044	0.287	1.930	<.0001
	3	Y = 21.476 + 0.264 × LL - 29.227 × CCI - 5.984 × NEC	2.676	0.351	1.853	<.0001
	4	Y = 25.638 + 0.331 × LL - 0.117 × TP - 23.331 × CCI - 5.927 × NEC	1.411	0.379	1.824	<.0001
	5	Y = 25.682 + 0.374 × LL + 0.087 × CP - 0.189 × TP - 28.207 × CCI - 6.420 × NEC	0.639	0.403	1.801	<.0001
	6	Y = 21.476 + 0.110 × CCY + 0.404 × LL + 0.093 × CP - 0.208 × TP - 33.589 × CCI - 6.094 × NEC	0.512	0.422	1.785	<.0001
Total fat proportion (%)	1	Y = 3.052 + 8.331 × NEC	2.420	0.556	3.660	<.0001
Total fat proportion (%)	2	Y = 5.718 + 8.137 × NEC - 0.364 × NECY	0.429	0.579	3.518	<.0001

Mallows’ Cp (Cp); Coefficient of determination (R²); Mean square error (MSE); Croup width (CW); Carcass compactness index (CCI); Loin (LOI); Shoulder (SHO); Neck (NEC); Leg length (LL); Thorax perimeter (TP); Croup perimeter (CP); Cold carcass yield (CCY); Neck yield (NECY).

Table 6 Sampling adequacy by Barlett’s test of sphericity and the KMO (Kaiser-Meyer-Olkin) test.

Bartlett’s sphericity test	DF	325
	Chi-Square	4761.91
	Pr > Chi Sq	<.0001
KMO test (Kaiser-Meyer-Olkin)	---	0.702

Table 7 Results of factor analysis applied to the independent variables.

Variables	Factor 1	Factor 2	Factor 3	Factor 4	Factor 5	Factor 6	C
LWS	0.762	0.122	-0.404	0.349	0.315	-0.035	0.980
EBW	0.773	0.131	-0.353	0.342	0.348	-0.032	0.978
HCW	0.783	0.078	0.074	0.466	0.368	-0.017	0.978
CCW	0.779	0.011	0.112	0.469	0.376	-0.052	0.984
BY	-0.102	-0.135	0.904	0.153	-0.033	0.033	0.871
HCY	-0.046	-0.112	0.956	0.159	0.056	0.035	0.959
CCY	-0.085	-0.215	0.939	0.130	0.045	-0.022	0.955
CEL	0.712	0.319	-0.051	0.002	0.089	-0.185	0.653
CIL	0.600	0.550	-0.184	0.080	0.361	-0.049	0.835
LL	0.617	0.598	-0.171	-0.010	0.087	-0.051	0.778
CW	0.523	0.473	-0.355	0.121	0.450	0.074	0.846
TW	0.454	0.409	-0.396	0.094	0.526	0.092	0.824
CP	0.179	-0.071	0.015	0.167	0.859	0.063	0.807
LP	-0.123	-0.774	0.091	0.116	0.171	-0.061	0.670
TP	0.329	0.137	0.162	-0.042	0.699	-0.133	0.661
CCI	0.419	-0.546	0.202	0.573	0.230	-0.047	0.898
LEG	0.302	0.220	0.113	0.431	0.156	0.770	0.956
LOI	0.235	0.697	-0.034	0.462	0.248	0.340	0.932
RIB	0.076	0.212	0.389	0.760	-0.062	0.069	0.789
NEC	0.309	0.706	-0.268	0.244	0.347	0.089	0.855
SHO	-0.163	0.028	0.109	0.863	0.131	0.178	0.833
LEGY	-0.357	0.229	-0.005	0.000	-0.153	0.872	0.963
LOIY	-0.251	0.789	-0.147	0.188	0.040	0.413	0.916
RIBY	-0.570	0.210	0.280	0.342	-0.387	0.091	0.723
NECY	-0.802	-0.015	-0.005	0.199	0.012	-0.194	0.720
SHOY	-0.791	0.016	-0.010	0.382	-0.186	0.182	0.840
Eigenvalues	9.802	4.437	4.105	1.702	1.119	1.039	---
Variance (%)	37.70	17.06	15.79	6.54	4.30	4.00	85.40

Communality (C); Live weight at slaughter (LWS); Empty body weight (EBW); Hot carcass weight (HCW); Cold carcass weight (CCW); Biological yield (BY); Hot carcass yield (HCY); Cold carcass yield (CCY); Carcass external length (CEL); Carcass internal length (CIL); Leg length (LL); Croup width (CW); Thorax width (TW); Croup perimeter (CP); Leg perimeter (LP); Thorax perimeter (TP); Carcass Compactness Index (CCI); Leg (LEG); Loin (LOI); Rib (RIB); Neck (NEC); Shoulder (SHO); Leg yield (LEGY); Loin yield (LOIY); Rib yield (RIBY); Neck yield (NECY); Shoulder yield (SHOY).

Table 8 Prediction equations for tissue composition according to stepwise multiple regression analysis of the latent variables.

Dependent variable	Number	Equation	C(p)	R²	MSE	P Value
Muscle proportion, %	1	Y = 68.142 - 2.328 × Factor3	48.630	0.360	9.745	<.0001
	2	Y = 68.142 - 1.200 × Factor1 - 2.328 × Factor3	31.978	0.456	8.394	<.0001
	3	Y = 68.142 - 1.200 × Factor1 + 1.138 × Factor2 - 2.328 × Factor3	17.213	0.542	7.159	<.0001
	4	Y = 68.142 - 1.200 × Factor1 + 1.138 × Factor2 - 2.328 × Factor3 - 0.795 × Factor5	11.027	0.584	6.589	<.0001
	5	Y = 68.142 - 1.200 × Factor1 + 1.138 × Factor2 - 2.328 × Factor3 - 0.795 × Factor5 - 0.581 × Factor6	8.651	0.607	6.317	<.0001
	6	Y = 68.142 - 1.200 × Factor1 + 1.138 × Factor2 - 2.328 × Factor3 + 0.531 × Factor4 - 0.795 × Factor5 - 0.581 × Factor6	7.000	0.625	6.099	<.0001
Bone proportion, %	1	Y = 18.870 - 0.746 × Factor5	8.629	0.109	4.590	0.0027
Bone proportion, %	2	Y = 18.870 - 0.673 × Factor4 - 0.746 × Factor5	2.181	0.198	4.186	0.0002
Total fat proportion, %	1	Y = 9.359 + 1.518 × Factor3	32.048	0.283	5.907	<.0001
	2	Y = 9.359 + 0.880 × Factor1 + 1.518 × Factor3	19.703	0.378	5.189	<.0001
	3	Y = 9.359 + 0.880 × Factor1 + 1.518 × Factor3 + 0.709 × Factor5	12.392	0.440	4.735	<.0001
	4	Y = 9.359 + 0.880 × Factor1 - 0.677 × Factor2 + 1.518 × Factor3 + 0.709 × Factor5	5.899	0.496	4.315	<.0001

Mallows’ Cp (Cp); Coefficient of determination (R²); Mean square error (MSE); Croup width (CW); Carcass compactness index (CCI); Loin (LOI); Shoulder (SHO); Neck (NEC); Leg length (LL); Thorax perimeter (TP); Croup perimeter (CP); Cold carcass yield (CCY); Neck yield (NECY).

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Multivariate modeling to estimate the composition of carcass tissues of Santa Inês sheep

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[1] * Author for correspondence. E-mail: marilenemaciel123@hotmail.com