Non-linear mixed effect models for estimation of growth parameters in Goats

Abstract

Modelling growth of an animal is a complex process, because it requires describing longitudinal measurements with few parameters with biological interpretation. With longitudinal data, the variance of observations may increase with time (age), and repeated measurements of an individual over time are correlated. The non-independence of data violates a key assumption underlying many statistical procedures and has been ignored in most traditional non-linear fixed effect models. A solution to this problem is the use of non-linear mixed effect models (NLMM). A NLMM makes it possible to account for random covariates before testing for fixed effects and control autocorrelation in repeated measures. In this study, growth data of Goat has been used. Attempt has been made to develop the Von-bertalanffy mixed model. Logistic, Gompertz and Von-bertalanffy fixed and mixed models have also been explored for these data. Comparison of the models i.e. between fixed and mixed type of the same model and among different fixed and mixed models has been attempted. The goodness of fit statistics like i.e. Mean Square Error (MSE) and Root Mean Square Error (RMSE) of the fitted models has been computed. The parameters of the best fitted models along with their corresponding standard error are estimated. The performance of mixed effect models was found to be better than the fixed effect model. Specifically, under the category of mixed effect model, the Logistic model out performed over the other types that were considered in the study