quantile regression

A study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical techniqueAbstract While the physiological conditions of most animals are reflected in their body fluids, in dairy cows physiological conditions are reflected in milk combinations. When negative energy balance occur, production that caused body fat store destruction, goes in two major metabolic ways in liver and breast tissues. In breast tissues, free fatty acids increase fat to protein ratio and in liver, free fatty acid change metabolism leading to increase of ketone bodies. Lactation persistency in dairy cows is one of inheritable economic trait and important characteristic of the lactation curve. The change of this trait is under control of different factors such as animal genetics structure. The amount of cow production at the peak of milk production depends on the calving physical condition, genetics, the absence of infectious and metabolic diseases, and postpartum diet. Fat to protein ratio in early lactation is associated with performance during lactation. Fat to protein ratio is also correlated with some diseases such as retained placenta, displacement of abomasum, metritis, endometritis, mastitis and culling. Fat to protein ratio (FPR) in test day milk records is a good indicator for body fat metabolism and the level of negative energy balance, and that it could be used as a selection criterion to improve metabolic stability. Quantile regression has not been widely used for modeling of biologic characteristics of livestock and this research aimed to evaluate the shape of fat percentage, protein percentage and FPR in test day milk records of Iranian dairy cows using a polynomial quantile regression model. The data used in this study were provided by the Animal Breeding Centre, Iran. Initial data set were edited by Excel and Foxpro software. The traits under consideration were fat percentage, protein percentage and fat to protein ratio (calculated based on the magnitude of the first two traits). All cows had value for all traits. Final data comprised a total of 784,532 test day records collected from 93,259 first-parity dairy cows (progeny of 2741 sires and 79843 dams) distributed in 660 herds over the country and calved between 2003 and 2013. In the data, test day fat percentage and protein percentage had a minimum of 1 and 1.5 and a maximum of 7 and 7, respectively. By SPSS software, some statistical characteristics of the traits were calculated, and by SAS software a quadratic polynomial quantile regression model (in the range of quantiles 5 to 95) was fitted to the data. Based upon the fitted model, linear and quadratic regression coefficients were estimated for the effect of day of lactation on each trait in different quantiles. In the model, traits and day of lactation were response and independent variables, respectively. Quadratic effect of day of lactation is considered due to nonlinear variation of the traits over the course of the lactation curve. Mean fat percentage, protein percentage and fat to protein ratio over the lactation course were found to be 3.35%, 3.08% and 1.1, respectively. As expected, for each trait a nonlinear change was observed over the lactation period. The highest content fat to protein ratio occurs in the early period of lactation and the lowest was observed in the sixth and seventh months of lactation. In terms of absolute values, minimum (953.564) and maximum (1797.661) linear regression coefficient of days in milk were obtained in quantiles 5 and 95, respectively. The same trend was also observed for quadratic regression coefficient of days in milk. Linear and quadratic regression coefficients of fat and protein percentages ranged over different quantiles so that minimum and maximum absolute values were observed in quantiles 5 and 95, respectively. Quantile regression model is an appropriated statistical technique for evaluate the effects of an independent factor which differently affects the shape of a response variable. In this research, the effect of days in milk on three traits (fat and protein percentage, as well as fat to protein ratio) was modeled by quantile regression. The findings of the present research indicate that the curve shape of fat percentage, protein percentage and fat to protein ratio are different for the quantiles suggesting that these differences are needed to be taken into account in nutrition management and cattle breeding scheme.Keywords: Dairy cow, Modeling, Quantile regression, Ratio of milk compositionA study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical techniqueA study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical techniqueA study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical techniqueA study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical techniqueA study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical techniqueA study on the curve of far percentage, protein percentage and fat to protein ratio in test day milk records of Iranian dairy cows using quantile regression statistical technique

The aim was to estimate the inbreeding coefficient and its impact on important economic traits in Yazd native fowls breeding station by quantile regression. Therefore, 57400 data collected from 2001 to 2017 (15 generations) was used. Traits included body weight at hatch (BW1), the 8th (BW8) and 12th week (BW12), age and weight at sex maturity (ASM, WSM), the egg number (12 weeks of production) (EN), average egg weight (28th, 30th, 32th weeks of production) and the first egg weight (EW1). Data was edited by Foxpro and estimation of inbreeding coefficient was computed by CFC. The regression coefficient of inbreeding was fitted on generation by linear regression of Rsoftware. Impact of inbreeding on traits was investigated by quantile regression. The fixed effects in the models were sex, hatch number, generation and inbreeding depression was considered as covariate. Pedigree analysis showed that 79percent of population were inbred and average of individual inbreeding coefficient was %3. The slope trend of individual inbreeding was increased by 0.5 percent on generation. Exploring different trait quantile distributions, it was revealed that inbreeding depression had different impacts over range of its distribution in a way that a much pronounced effect was observed in extremes (25%, 75%).Quantile regression was not converged for BW1, ASM and EW1 and they were estimated by linear regression as 0.001, 0.053 and 0.063,respectively. According to quantile regression, the impact of inbreeding depression was not equal on different parts of traits' distribution, which give us a better insight of the effect of inbreeding.

The aim of the present study was to estimate the impact of somatic cell count on daily milk yield of Iranian dairy cows using quantile regression statistical technique. A total of 784,532 test day records belonging to 93,259 first-parity cows distributed in 660 herds and calved during 2003-2013 were used. The studied trait was test day milk yield and the model was defined as a quantile regression. All of the estimated regression coefficients were negative, which indicated a decrease in the amount of daily milk production when milk somatic cell counts increased, so that, in the spite of lactation stage, on the basis of absolute value, the lowest and highest regression coefficients observed at ninety-fifth percentile and fifth, respectively. Considering lactation stage in the seventh stage of fifth percentile, the highest decrease was 238 g milk reduction per day, for increase of 100 thousand somatic cells per ml/L of milk, and in the 95th percentile of the fourth stage, the lowest decrease was 64 grams milk reduction per day, for increase 100 thousand somatic cells per ml/L of milk. The results revealed that in high quantiles of daily milk yield, the impact of SCC on milk production decreases indicating that high-producing cows are less influenced in terms of loss of milk production as SCC increases. The difference in the amount of somatic cell count on the amount of milk production in cows with different production potential should be considered in the genetic evaluation of herds.

The main aim of the present research was the genetic analysis of the first lactation milk yield trait and evaluation of the impact of selection for milk on the phenotype of age at first calving in Iranian dairy cows using quantile regression. Lactation milk records of 327190 first parity cows (progeny of 5260 sires and 235172 dams) in 637 herds (in 15 provinces) and calved between 2007 and 2015 were utilized. Genetic analysis was carried out with the use of an animal model. In the model, fixed effects of the province, herd, year and month of calving, covariates of lactation length, age at first calving, percentage of Holstein gene, as well as the random effect of the cow were included. The model was fitted on the data using the DMU package. Regression of age at first calving on predicted breeding value was fitted through a quantile regression model. The findings revealed that the heritability of lactation milk yield was equal to 0.276. Annual genetic gain in grade and Holstein purebred were found to be 17.352 (R2=0.913) and 23.398 (R2=0.962) Kg, respectively (P<0.0001). All estimated regression coefficients were negative in different percentiles of age at first calving and ranged between -0.0009 and -0.0344 (month per Kg) which indicates that the influence of genetic potential of cows for milk yield on different parts of calving age distribution is not the same.

Inbreeding, which has been defined as the mating between relative animals, leads to increase homozygous genotypes and decrease heterozygous genotypes in a population. As a result, the progenies of such mating are inbred (Wakchaure and Genguly 2015). Reduction of the traits associated with physiological efficiency and reproductive potential are the most important impacts of inbreeding in the farm animals (Filho et al. 2015, Fleming et al. 2018). Traits in livestock have different heritabilities suggesting that they are not influenced by inbreeding in a similar pattern and that although animals’ fitness is generally deteriorated; the magnitude of inbreeding depends on the type of the trait (Roff 1998; Derose and Roff, 1999, Wright et al. 2008, Mikkelsen et al. 2010). Until now, all studies regarding effects of inbreeding on productive and reproductive traits of dairy cows have been focused on using the statistical models in which inbreeding coefficient was included as covariable (Behmaram et al. 2017) or as the classified variable (Amirzadeh 2012). As inbreeding coefficient is defined as a covariable in the model, only a regression coefficient is estimated describing average changes of the trait per increasing / decreasing inbreeding coefficient. As a matter of fact, inbreeding may unequally influence the shape of distribution of the trait. Based on this assumption, this research aimed to estimate inbreeding effects on some productive and reproductive traits of Iranian dairy cows using Quantile regression statistical method.     

The data set was provided by Animal Breeding Centre, Iran. Foxpro (version 2.6) and UEStudio (version 09) software were utilized for editing initial data. Final data consisted of 580,802 records belonging to 580,802 first-parity cows distributed in 1,185 herds (over 20 provinces of the country) and calved between years 1991 and 2015. The traits under consideration were lactation milk yield (TMILK), 305d, 2X milk yield (MILK3052X), average daily milk yield (ADM), lactation length (LL), and age at the first calving (AFC). The average of the traits in the final data set was 9,447 Kg, 7,792 Kg, 30 Kg, 315 d and 25.6 m, respectively. Holstein gene percentage (HGP) of the cows in the pedigree file was set to be in the range of 50 to 100 and AFC of the cows was set to be between 18 and 48 months. Inbreeding coefficient (IC) of individual animals was calculated by CFC software (Sargolzaei et al. 2006). Fitting a series of the Quantile regression models was conducted with the use of SAS (version 9.4) software. Quantile regression, which was introduced by Koenker and Bassett (1978), extends the regression model to conditional quantiles of the response variable, such as the 90th percentile. Quantile regression is particularly useful when the rate of change in the conditional Quantile, expressed by the regression coefficients, depends on the Quantile (Chen 2005). In all the models used in this research, fixed effects of province, year and month of calving, as well as linear co-variables of HGP, IC and AFC (except of the model for AFC as the trait) were included. For TMILK, lactation length was also included as linear co-variable. Moreover, in addition to the quantile models and for the sake of estimating usual regression coefficient, general linear model (GLM) was also fitted for each trait in which a single regression coefficient of the trait on IC was defined. Ordinary least-squares regression can be used to estimate conditional percentiles by making a distributional assumption such as normality for the error term in the model. The main advantage of Quantile regression over ordinary least-squares regression is its flexibility for modeling data with heterogeneous conditional distributions (Chen 2005).      

Based upon the analysis of main pedigree file, the total number of animals was 1,941,871 (16,169 sires and 895,376 dams) among which the number of base and non-base animals were 246,388 (3,936 sires and 120,287 dams) and 1,695483 (12,233 sires and 775,089 dams), respectively.Total number of inbred animals in the pedigree was 1,211,343. Average IC for total as well as inbred animals was found to be 0.9149% (minimum 0% and maximum 47.02%) and 1.4651% (minimum 0.00038% and maximum 47.02%), respectively. For the cows with records for all five traits, IC ranged from 0 to 38.45% with the average of 1.13% (SD=1.63%). Estimate of annual change of IC was found to be 0.017 (SE=0.005), which was statistically significant (P<0.01) indicating that there is a positive increase of inbreeding in Iranian dairy cows’ population over the time. Within each trait, different Quantiles were unequally influenced as animal’s IC increased. Vast majority of the estimated regression coefficients in different Quantiles were statistically significant (P<0.05). Based upon fitting Quantile regression model and the average estimated regression coefficients, it was found that TMILK, MILK3052X, ADM, LL, and AFC changed -5.5 (Kg), -2.6 (Kg), -18 (g), 0.35 (d) and 0.30 (d), respectively as the IC of the animal increased by 1%. Estimated simple regression coefficients based on fitting GLM models were found to be -9.83 Kg (SE=1.332 Kg), -6.9 Kg (SE=0.169 Kg), -32 gram (SE=4.2 gram), 0.2087 d (SE=0.08234 d) and 0.0158 m (SE=0.0024 m), respectively and all were statistically significant (P<0.05).     

This research indicated that different Quantiles of some productive and reproductive traits of Iranian dairy cows are not equally affected by inbreeding phenomenon suggesting that Quantile regression models are needed to be utilized in the future research for evaluating the impacts of inbreeding on the other traits, which are of great economic importance.