Model Assisted Statistics and Applications 10 (2015) 109–115 109 DOI 10.3233/MAS-140318 IOS Press Study of growth pattern of cattle under different error structures Surendra Singh, A.K. Paul ∗ , Ranjit Kumar Paul, L.M. Bhar, Ashok Kumar and Wasi Alam Indian Agricultural Statistics Research Institute, New Delhi, India Abstract. Logistic and Gompertz growth models are fitted in growth data for Friesian × Sahiwal (F × S) and Friesian × Sahiwal × Haryana (F × S × H) breed at Agra station, Gompertz model gives better fit than Logistic model. The Generalized Least Squares (GLS) estimates are found to be more precise than Ordinary Least Squares (OLS) estimates for both Logistic as well as Gompertz model under heteroscedastic error condition for both breeds. Growth is found better for F × S × H breed, therefore, triple cross may have increased maturing rate while asymptotic weight (mature weight) is found better for F × S breed. Breed type significantly affects weight at maturity. Keywords: Growth, gompertz model, logistic model, asymptotic weight, heteroscedastic error 1. Introduction It is important to study the growth of animal because characteristics like meat, milk, wool etc. depend on growth. Nonlinear models are used to predict rates and change in the shape of the organism. They can be applied to determine the food requirements so as to get a desired growth. The estimated parameters of growth function can evaluate various growth characteristics of animal like rate of maturing, rate of gain, mature size and related characters. However the series of weight and age data points are analytically unwieldy and difficult to interpret. One method of condensing the information contained in such a data series in a few biological interpretable parameters is the use of nonlinear models. A number of such nonlinear models are available in the literatures. The growth pattern of cows has been studied under homoscedastic error structure in the literatures. However comparison of such models is needed to find a most appropriate model. Such comparison of nonlinear models for weight and age data in cattle has been done under homoscedastic error structure [2,3,6]. However, generally growth data do not follow homoscedastic error structure. Errors of growth model generally have heteroscedastic error structure. Kolluru [7] studied only logistic model under heteroscedastic error condition for cattle growth. Therefore, there is a need to study other models also under heteroscedastic error structure. In this back-drop, the present study has been taken up to describe growth pattern of F × S and F × S × H breed using nonlinear models like, Logistic and Gompertz models. Section 2 describes the methodology in details; followed by results and discussions in Section 3. 2. Materials and methods Data used in the study were collected from history sheets of cattle right from birth to 36 months of age from military dairy farms at Agra, India for F × S breed and for F × S × H breed. Logistic and Gompertz models are fitted to study the performance of these breeds. The functional form of the models is as follows. * Corresponding author: A.K. Paul, Indian Agricultural Statistics Research Institute, New Delhi-12, India. E-mail: pal@iasri.res.in. ISSN 1574-1699/15/$35.00 c  2015 – IOS Press and the authors. All rights reserved