Abstract #8

# 8
Estimation of parameter values in nutrition models.
L. Moraes*1, 1The Ohio State University, Columbus, OH.

The use of modeling techniques in animal nutrition relies on the construction of mathematical models determined by a set of parameters. In practice, parameter true values are unknown. Estimators must be obtained with data from designed experiments, observational studies, meta-analysis or another appropriate data generating mechanism. For virtually any type of model, parameter estimates have to be optimal in some sense. For example, linear regression least squares estimates are the minimizers of the squared differences between observations and predictions. In this setting, if model errors are assumed to independent, identically and normally distributed, least squares estimators coincide with maximum likelihood estimators. Maximum likelihood is the standard estimation method for more complex models used in animal nutrition. It seeks parameter values that maximize the likelihood function: a function constructed with the probability density of the observations but as a function of parameters while fixing the data. Nonlinear models are regularly used in the development of mechanistic models as these allow the relationship between variables to be specified by a function that is nonlinear with respect to the parameters. The flexibility of specifying nonlinear functional forms comes with a cost: the function to be optimized is often complex and an analytical solution to the problem is many times not available. Further, several of the mechanistic models used in animal nutrition rely on the use of differential equations that require numerical integration. Parameter estimation in these cases is usually approached by algorithmic optimization of either a likelihood function or a nonlinear least squares cost function. Recently, Bayesian methods have been proposed as estimation approaches for nutrition models as they naturally describe multilevel structures and incorporate prior information in the analysis. This lesson will cover parameter estimation in a variety of models frequently used in animal nutrition as well as demonstration exercises. During a hands-on exercise, workshop participants will estimate parameters in different models using the freely available software R.

Key Words: least squares, likelihood, Bayesian