Estimation of Linear Compartmental Model Parameters Using Marginal Likelihood

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Abstract
Linear compartmental models are an important tool in describing behavior of complex biological systems. Applications of such models range from pharmacokinetics and tracer experiments to a description of egg production in fruit-flies and poultry. Parameters of these models have commonly been estimated by iterative nonlinear curve fitting techniques based on least squares. These methods are appropriate when the sample size is large and the variance in the observations is constant. They can be adapted to provide efficient estimates by double iteration when the variance is a function of the response. If the sample size is small, such methods are not always satisfactory; problems of convergence may occur and the standard errors commonly given with such estimates may be grossly misleading. The marginal likelihood approach adopted in this paper provides exact inferences for the model parameters when the coefficient of variation in the response is constant. The practical advantages of the procedure include comprehensive information about the reliability of the estimates and their ranges of error and absence of convergence problems.

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