Growth curve for height at withers of Mangalarga Marchador horses with heterocedasticity

ABSTRACT This work aimed to evaluate the fit of models Brody, Gompertz, Logistic and Von Bertalanffy to height at the withers of Mangalarga Marchador horses, weighed by the inverse of variance, in order to select the best model and predict growth and maturity of this breed pf animals. We used data of 230 equines from 06 to 176 months of age who were divided by sex and 16 age classes. The models were compared according to the quality assessors: coefficient of determination (R2); residual standard deviation (RSD) and Akaike information criteria (AIC). The estimation of the parameters from models was performed by the weighted least squares method in Software R. All models evaluated were suitable to describe the growth curve in both sexes. In view of the evaluators used, the logistic model was the most suitable to describe the growth curves in withers height in both sexes for the race Mangalarga Marchador. A strong growth at first age was also observed. The males reached a greater adult height, but females did so sooner, because they presented higher estimates for the maturity index.

摘要 本研究旨在以方差倒数为权重，评估Brody、Gompertz、Logistic及Von Bertalanffy四种生长模型对曼加尔加马查多马（Mangalarga Marchador）鬐甲高数据的拟合效果，以期筛选最优模型并预测该品种马匹的生长与成熟规律。
本研究共纳入230匹年龄介于6至176月龄的马匹，按性别与16个年龄组进行分组。采用决定系数（coefficient of determination, R²）、残差标准偏差（residual standard deviation, RSD）以及赤池信息准则（Akaike information criterion, AIC）作为模型质量评价指标。借助R软件中的加权最小二乘法完成模型参数估计。
所有参评模型均能有效描述两个性别的生长曲线。就本次采用的评价指标而言，Logistic模型是适配曼加尔加马查多马两个性别鬐甲高生长曲线的最优模型。研究同时观察到该品种马匹在幼年阶段呈现较强的生长速率；公马的成年体高更高，但母马的成熟更早，这是由于其成熟指数的估计值更高。