Abstract
The objective of this study was to evaluate the use of probit and logit link functions for the genetic evaluation of early pregnancy using simulated data. The following simulation/analysis structures were constructed: logit/logit, logit/probit, probit/logit, and probit/probit. The percentages of precocious females were 5, 10, 15, 20, 25 and 30% and were adjusted based on a change in the mean of the latent variable. The parametric heritability (h²) was 0.40. Simulation and genetic evaluation were implemented in the R software. Heritability estimates (ĥ²) were compared with h² using the mean squared error. Pearson correlations between predicted and true breeding values and the percentage of coincidence between true and predicted ranking, considering the 10% of bulls with the highest breeding values (TOP10) were calculated. The mean ĥ² values were under- and overestimated for all percentages of precocious females when logit/probit and probit/logit models used. In addition, the mean squared errors of these models were high when compared with those obtained with the probit/probit and logit/logit models. Considering ĥ², probit/probit and logit/logit were also superior to logit/probit and probit/logit, providing values close to the parametric heritability. Logit/probit and probit/logit presented low Pearson correlations, whereas the correlations obtained with probit/probit and logit/logit ranged from moderate to high. With respect to the TOP10 bulls, logit/probit and probit/logit presented much lower percentages than probit/probit and logit/logit. The genetic parameter estimates and predictions of breeding values of the animals obtained with the logit/logit and probit/probit models were similar. In contrast, the results obtained with probit/logit and logit/probit were not satisfactory. There is need to compare the estimation and prediction ability of logit and probit link functions.
Highlights
One of the factors that determine the economic viability of sustainable beef cattle enterprises is the reproductive performance of the herd
According to McCullagh & Nelder (1989), these models can be defined based on the specification of three components: i) a random component represented by independent random variables that belong to the same distribution, which is part of an exponential family such as binomial and Poisson; ii) a systematic component, called linear predictor, in which explanatory variables enter in the form of the linear sum of their effects; iii) a link function that combines the random and systematic components, i.e., relates the mean to the linear predictor and permits modeling, for example, the probability of a female being precocious
Where ηpx1 is the linear predictor and p is the number of heifers (1500); β3x1 is the vector of fixed effects, β’ = [μ,β1,β2], whose values adopted for the simulation were β1 = 1and β1 = –1, and μ is the overall mean (Table 2); upx1 is the vector of additive genetic values, with u ~Np(0, Aσ2u), where A is the relationship matrix between animals and σ2u is the additive genetic variance of the population; Xpx3 and Xpxp are incidence matrices of effects β and u, respectively
Summary
One of the factors that determine the economic viability of sustainable beef cattle enterprises is the reproductive performance of the herd. The identification and evaluation of reproductive traits that can be measured and present a potential for selection are essential. In this respect, early pregnancy is an measured trait since it comprises only two categories (pregnant and non-pregnant). The evaluation of phenotypic expression does not result in additional costs, since the diagnosis of pregnancy is a routine practice in beef cattle farming. One of the main challenges of using categorical traits in breeding programs is the development of adequate statistical methods for the estimation of parameters and the prediction of breeding values. According to McCullagh & Nelder (1989), these models can be defined based on the specification of three components: i) a random component represented by independent random variables that belong to the same distribution, which is part of an exponential family such as binomial and Poisson; ii) a systematic component, called linear predictor, in which explanatory variables enter in the form of the linear sum of their effects; iii) a link function that combines the random and systematic components, i.e., relates the mean to the linear predictor and permits modeling, for example, the probability of a female being precocious
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