Use of regularized quantile regression to predict the genetic merit of pigs for asymmetric carcass traits

The objective of this work was to evaluate the use of regularized quantile regression (RQR) to predict the genetic merit of pigs for asymmetric carcass traits, compared with the Bayesian lasso (Blasso) method. The genetic data of the traits carcass yield, bacon thickness, and backfat thickness from a F₂ population composed of 345 individuals, generated by crossing animals from the Piau breed with those of a commercial breed, were used. RQR was evaluated considering different quantiles (τ = 0.05 to 0.95). The RQR model used to estimate the genetic merit showed accuracies higher than or equal to those obtained by Blasso, for all studies traits. There was an increase of 6.7 and 20.0% in accuracy when the quantiles 0.15 and 0.45 were considered in the evaluation of carcass yield and bacon thickness, respectively. The obtained results are indicative that the regularized quantile regression presents higher accuracy than the Bayesian lasso method for the prediction of the genetic merit of pigs for asymmetric carcass variables.

Index terms:
Sus scrofa; Blasso; shrinkage

Authorship

Patricia Mendes dos Santos

Universidade Federal de Viçosa, Departamento de Estatística, Avenida P.H. Rolfs, s/no, CEP 36570-000 Viçosa, MG, Brazil. E-mail: patymendesdossantos@hotmail.com, campanaac@gmail.com, moysesnascim@ufv.br, camila.azevedo@ufv.brUniversidade Federal de ViçosaBrazilViçosa, MG, BrazilUniversidade Federal de Viçosa, Departamento de Estatística, Avenida P.H. Rolfs, s/no, CEP 36570-000 Viçosa, MG, Brazil. E-mail: patymendesdossantos@hotmail.com, campanaac@gmail.com, moysesnascim@ufv.br, camila.azevedo@ufv.br

Ana Carolina Campana Nascimento

Moysés Nascimento

Fabyano Fonseca e Silva

Universidade Federal de Viçosa, Departamento de Zootecnia, Avenida P.H. Rolfs, s/no, CEP 36570-000 Viçosa, MG, Brazil. E-mail: fabyanofonseca@ufv.br,sfacioni@ufv.br, plopes@ufv.brUniversidade Federal de ViçosaBrazilViçosa, MG, BrazilUniversidade Federal de Viçosa, Departamento de Zootecnia, Avenida P.H. Rolfs, s/no, CEP 36570-000 Viçosa, MG, Brazil. E-mail: fabyanofonseca@ufv.br,sfacioni@ufv.br, plopes@ufv.br

Camila Ferreira Azevedo

Rodrigo Reis Mota

Université de Liège, Gembloux Agro-Bio Tech, Passage des Déportés 2, B5030 Gembloux, Belgium. E-mail: rreismota@hotmail.comUniversité de LiègeBelgiumGembloux, BelgiumUniversité de Liège, Gembloux Agro-Bio Tech, Passage des Déportés 2, B5030 Gembloux, Belgium. E-mail: rreismota@hotmail.com

Simone Eliza Facioni Guimarães

Paulo Sávio Lopes

SCIMAGO INSTITUTIONS RANKINGS

Figures | Tables | Formulas

Figures (1)
Tables (3)
Formulas (7)

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Figure 1.
Manhattan plots of the estimated single nucleotide polymorphism (SNP) effects, obtained by the following Bayesian lasso and regularized quantile regression values: and for the variable carcass yield, respectively (A and B); and for bacon thickness, respectively (C and D); and and for backfat thickness immediately after the last rib in the dorsal-lumbar line, respectively (E and F).

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Table 1.
Test statistics and p-values associated with the D’Agostino-Pearson test.

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Table 2.
Accuracies obtained by the Bayesian lasso (Blasso) and the regularized quantile regression (RQR) methods for the traits under study.

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Table 3.
Estimates of Spearman’s correlation coefficient (r_s) between the genomic estimated breeding values of the animals and Cohen’s kappa coefficient (k) for the traits under study, both obtained by the Bayesian lasso (Blasso) and the regularized quantile regression (RQR) methods.

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Figure 1. Manhattan plots of the estimated single nucleotide polymorphism (SNP) effects, obtained by the following Bayesian lasso and regularized quantile regression values: and for the variable carcass yield, respectively (A and B); and for bacon thickness, respectively (C and D); and and for backfat thickness immediately after the last rib in the dorsal-lumbar line, respectively (E and F).

Table 1. Test statistics and p-values associated with the D’Agostino-Pearson test.

Variable⁽¹⁾	Asymmetry	Kurtosis	Omnibus test⁽²⁾
CY	-15.82***	12.10***	396.75***
BT	3.48***	1.18^ns	14.29***
LRBF	2.58***	2.35**	12.19***

⁽¹⁾
CY, carcass yield; BT, bacon thickness; and LRBF, backfat thickness immediately after the last rib in the dorsal-lumbar line. ⁽²⁾Normality test. *, **, and ***Significant at 10, 5, and 1% probability, respectively. ^nsNonsignificant.

Table 2. Accuracies obtained by the Bayesian lasso (Blasso) and the regularized quantile regression (RQR) methods for the traits under study.

Trait⁽¹⁾	Model
Trait⁽¹⁾	RQR⁽²⁾	RQR⁽³⁾	Blasso
CY	0.48 (2.5)	0.10 (43.22)	0.45 (43.22)
BT	0.54 (14.5)	0.26 (22.44)	0.45 (22.44)
LRBF	0.39 (11.5)	0.01 (31.37)	0.39 (31.37)

⁽¹⁾
CY, carcass yield; BT, bacon thickness; and LRBF, backfat thickness immediately after the last rib in the dorsal-lumbar line. ⁽²⁾Model with shrinkage parameter value from the grid of values. ⁽³⁾Model with shrinkage parameter value from Blasso. Values between parentheses were used as shrinkage parameters in the fit of the models.

Table 3. Estimates of Spearman’s correlation coefficient (r_s) between the genomic estimated breeding values of the animals and Cohen’s kappa coefficient (k) for the traits under study, both obtained by the Bayesian lasso (Blasso) and the regularized quantile regression (RQR) methods.

Trait⁽¹⁾	r_s	k⁽²⁾
CY	0.57***	0.38
BT	0.35***	0.34
LRBF	0.69***	0.54

⁽¹⁾
CY, carcass yield; BT, bacon thickness; and LRBF, backfat thickness immediately after the last rib in the dorsal-lumbar line. ⁽²⁾Refers to the agreement among 10% of the individuals that presented the highest genomic breeding values predicted by RQR and Blasso. ***Significant at 1% probability.

y_{i} = μ + \sum_{j = 1}^{237} x_{ij} g_{j} + e_{i}

min {\sum_{i = 1}^{n} ρ_{τ} (y_{i} - μ - \sum_{j = 1}^{p} x_{ij} g_{j}) + λ \sum_{j = 1}^{p} | g_{j} |}

ρ_{τ} (y_{i} - μ - \sum_{j = 1}^{p} x_{ij} g_{j}) = {\begin{matrix} τ (y_{i} - μ - \sum_{j = 1}^{p} x_{ij} g_{j}), {if y}_{i} - μ - \sum_{j = 1}^{p} x_{ij} g_{j} > 0 \\ (1- τ) (y_{i} - μ - \sum_{j = 1}^{p} x_{ij} g_{j}), \end{matrix}

{GEBV}_{i} (τ) = {\overset{⌢}{y}}_{i} (τ) = \sum_{j = 1}^{p} x_{ij} {\overset{⌢}{g}}_{j} (τ)

{GEBV}_{i} = {\overset{⌢}{y}}_{i} = \sum_{j = 1}^{p} x_{ij} {\overset{⌢}{g}}_{j}

r_{y, \overset{⌢}{g}} = r_{y, \overset{⌢}{y}} / \sqrt{h^{2}}

r y, \overset{⌢}{g} = cov (y, \overset{⌢}{y}) / \sqrt{var (y) var (\overset{⌢}{y});}

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Use of regularized quantile regression to predict the genetic merit of pigs for asymmetric carcass traits

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[TFN1] ⁽¹⁾
CY, carcass yield; BT, bacon thickness; and LRBF, backfat thickness immediately after the last rib in the dorsal-lumbar line. ⁽²⁾Normality test. *, **, and ***Significant at 10, 5, and 1% probability, respectively. ^nsNonsignificant.