A maximum likelihood estimation method for random coefficient regression models

doi:10.1093/biomet/73.3.645

Biometrika 1986 73(3):645-656; doi:10.1093/biomet/73.3.645
© 1986 by Biometrika Trust

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A maximum likelihood estimation method for random coefficient regression models

A. MALLET

Département de biomathématiques INSERM, 75634 PariS 13, France

A method for estimating the distribution of the parameters ofa random coefficient regression model is proposed. This distribution,accounting for interindividual variability, is assumed to liein a wide class of probability distributions rather than ina given parametric class. Estimation is based on observationsfrom a sample of individuals and likelihood is the estimationcriterion. Experimental designs may be different among individuals,allowing the method to apply to routinely collected data. Theproblem has strong connections with the theory of optimum designof experiments. Conditions are given under which the problemhas a unique solution, which then corresponds to a discretedistribution. A simple pharmacokinetic model involving two parametersis used as an example; these parameters have a bimodal distributionas statistical specification. Moreover, only one observationis available per individual; thus the method applies even whenthe model is not identifiable.

Key Words: Constrained optimization • D-optimality • Interindividual variability • Maximum likelihood • Mixing distribution • Probability measure estimation • Random regression model

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