Random regression models using Legendre orthogonal polynomials to evaluate the milk production of Alpine goats

Silva, F.G.; Torres, R.A.; Brito, Luiz F.; Euclydes, Ricardo Frederico; Melo, Ana Lúcia Puerro de; Souza, N. O.; Ribeiro, Jéssica; Rodrigues, Marcelo Teixeira

doi:10.4238/2013.december.11.1

Cited by 12 publications

(18 citation statements)

References 20 publications

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“…However, in more technologically advanced systems, it is recommended to invest in resources to determine all possible lactations, obtaining responses of greater economic return. The results obtained by Silva et al (2013b), claiming that less technological systems can obtain good selection responses if milk controls are practiced with maximum intervals of 21 days, may also help convince producers, given that weekly controls, as was the case in the herds under study, can be viewed as a great barrier by producers, due to the global trend in increases in skilled labor.…”

Section: Resultsmentioning

confidence: 98%

“…It is unnecessary to represent the results graphically, because the lowest correlation values found between lactation days for each one of the first four calving orders were 95.8, 95.3, 99.7, and 98.1, respectively. Figure 2 shows that the first lactation exhibited the lowest percentage of variation explained by the regression model over time, even though the model was chosen from the 980 models tested by Silva et al (2013b); this is probably because in the first lactation there were goats with different ages at first calving, and because this covariate with linear and quadratic effects was not sufficient to correct the variations caused when the female calved too early, which in this case could be a result of many productive-and reproductive-precocity genes being involved. For the age at the second, third, and fourth calvings, however, we expected to find a lower divergence of milk yield in the beginning of lactation due to the age at calving, because all of the animals were sufficiently developed to undergo their reproductive and productive phases.…”

Section: Resultsmentioning

confidence: 99%

“…The models adopted in the TDMY evaluations contained combinations of adjustment for the polynomials of the fixed, genetic random, and permanent environmental curves of the orders of four, two, and seven, in addition to the number of classes of residual variances equal to five, following the best model found by Silva et al (2013b) for the same herd. The singletrait random regression animal model used in each of the four lactations is generally described as follows:…”

Section: Methodsmentioning

confidence: 99%

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Genetic evaluation of milk yield in Alpine goats for the first four lactations using random regression models

et al. 2014

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ABSTRACT. Random regression models have been used in evaluating test-day milk yield, providing accurate estimates of genetic values in animals. However, herd evaluation with only information from the first lactation may not be the best option from an economic perspective. Other factors should be taken into account, particularly other lactations. Our objective in this study was to analyze the genetic divergence between the first four lactations of Alpine goats. The RENPED software was used to perform descriptive statistics, check for errors in pedigree, recode the data, and for Pearson's and Spearman's correlations. The WOMBAT software was used to estimate the variance components and predict the breeding values. The CALC software was adopted to calculate the percentage of coincidence between the ranking of the animals and the animals kept in common at each lactation evaluation. The results show that selection using only the first lactation in small herds with a low degree of technology can be employed as a palliative measure, in view of the difficulty in evaluating all lactations. However, the selection of breeding goats and the production of catalogues should not be based only on the first lactation, because the results demonstrate inversions in the classification of the best breeders when other lactations are analyzed.

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Section: Resultsmentioning

confidence: 98%

Section: Resultsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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Genetic evaluation of milk yield in Alpine goats for the first four lactations using random regression models

et al. 2014

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“…The Legendre orthogonal polynomials were introduced by French mathematician Adrien‐Marie Legendre in 1782 (Refaat, ). They have been frequently applied in technical fields (see, for example, Silva et al , ) as well as social sciences, including mortality modeling (see, for example, Renshaw et al , ; Sithole et al , ). Defining an n th‐order Legendre polynomial as φ n ( z ), on its interval of orthogonality [−1,1], we have the following property:

{falsefalse}_{\int}^{- 1} φ_{j} (z) φ_{k} (z) d z = ({, \begin{matrix} 0, & if j \neq k \\ 1, & if j = k \end{matrix})

Legendre polynomials also satisfy the following three‐term recursive relationship:

(n + 1) φ_{n + 1} (z) = (2 n + 1) z φ_{n} (z) - n φ_{n - 1} (z), for n = 1, 2, 3, \dots

Thus the first seven Legendre orthogonal polynomials are as follows:

\begin{matrix} φ_{0} (z) & = 1 \\ φ_{1} (z) & = z \\ φ_{2} (z) & = \frac{1}{2} (3 z^{2} - 1) \\ φ_{3} (z) & = \frac{1}{2} (5 z^{3} - 3 z) \\ φ_{4} (z) & = \frac{1}{8} (35 z^{4} - 30 z^{2} + 3) \\ φ_{5} (z) & = \frac{1}{8} (63 z^{5} -<...> \end{matrix}

…”

Section: Methodsmentioning

confidence: 99%

“…The Legendre orthogonal polynomials were introduced by French mathematician Adrien-Marie Legendre in 1782 (Refaat, 2009). They have been frequently applied in technical fields (see, for example, Silva et al, 2013) as well as social sciences, including mortality modeling (see, for example, Renshaw et al, 1996;Sithole et al, 2000). Defining an nth-order Legendre polynomial as ' n .´/, on its interval of orthogonality OE 1; 1, we have the following property:…”

Section: Legendre Orthogonal Polynomialsmentioning

confidence: 99%

A Flexible Functional Form Approach To Mortality Modeling: Do We Need Additional Cohort Dummies?

Han

O’Hare

Vahid

2016

Journal of Forecasting

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The increasing amount of attention paid to longevity risk and funding for old age has created the need for precise mortality models and accurate future mortality forecasts. Orthogonal polynomials have been widely used in technical fields and there have also been applications in mortality modeling. In this paper we adopt a flexible functional form approach using two‐dimensional Legendre orthogonal polynomials to fit and forecast mortality rates. Unlike some of the existing mortality models in the literature, the model we propose does not impose any restrictions on the age, time or cohort structure of the data and thus allows for different model designs for different countries' mortality experience. We conduct an empirical study using male mortality data from a range of developed countries and explore the possibility of using age–time effects to capture cohort effects in the underlying mortality data. It is found that, for some countries, cohort dummies still need to be incorporated into the model. Moreover, when comparing the proposed model with well‐known mortality models in the literature, we find that our model provides comparable fitting but with a much smaller number of parameters. Based on 5‐year‐ahead mortality forecasts, it can be concluded that the proposed model improves the overall accuracy of the future mortality projection. Copyright © 2016 John Wiley & Sons, Ltd.

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Genetic analysis of litter size and number of kids born alive across parities in Spanish goat breeds using a random regression model

Ziadi

Muñoz-Mejías

Rodríguez

et al. 2021

Italian Journal of Animal Science

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Genetic parameters of litter size (LS) and number of kids born alive (NBA) were estimated across parities in Florida and Payoya goat breeds using a threshold random regression model (RRM). We analysed the reproductive records for the Florida and Payoya breeds separately, and a total of 130.849 and 67.478 reproductive records from the first to the seventh parities from Florida and Payoya, respectively, were included in the analysis. Random regressions on Legendre polynomials of standardised parity were included for permanent environmental and additive genetic effects. We based our estimation of all the covariance components on Bayesian inference under categorical distribution and considered heterogeneous residual variances in the model. The estimates of heritabilities ranged from null to 0.37 for LS and from 0.02 to 0.20 for NBA, while the repeatability estimates were between 0.008-0.60 and 0.03-0.44 for LS and NBA, respectively. Phenotypic correlations within-trait along parities ranged widely from À0.31 to 0.97, while the genetic correlations within-trait through parities showed a wider range and magnitude of values, from À0.98 to 0.99 for LS and from À0.72 to 0.99 for NBA. The estimates of genetic correlations between LS and NBA in the different parities were positive in the first two parities and negative in the later ones. Due to the noticeable changes in variance and the incomplete genetic correlations, the use of a random regression model to analyse LS and NBA is recommended in goat breeds. HIGHLIGHTSA bivariate threshold random regression model has been used for the first time to estimate genetic parameters of litter size and number of kids born alive across parities in Spanish goat breeds. The evolution of genetic parameters along parities is different between Florida and Payoya that have different production systems, being more intensive in the case of the Florida breed. Estimates of variance were not constant across parities for both traits and breeds. Genetic correlations within-trait across parities were different from unity. Thus, LS and NBA should be treated as different traits in successive parities. Given that the estimates of variance and covariances are not constant across parities for both traits and breeds, the use of RRM is highly recommended.

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Random regression models using Legendre orthogonal polynomials to evaluate the milk production of Alpine goats

Cited by 12 publications

References 20 publications

Genetic evaluation of milk yield in Alpine goats for the first four lactations using random regression models

Genetic evaluation of milk yield in Alpine goats for the first four lactations using random regression models

A Flexible Functional Form Approach To Mortality Modeling: Do We Need Additional Cohort Dummies?

Genetic analysis of litter size and number of kids born alive across parities in Spanish goat breeds using a random regression model

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