Some design problems with multilevel data
by
Toby Lewis
Centre for Statistics, University of East Anglia, Norwich

Goldstein(1995), in his book 'Multilevel Statistical Models', said: "When designing a study where the multilevel nested structure of a population is to be modelled, the allocation of level 1 units among level 2 units and the allocation of these among level 3 units etc., will clearly affect the precision of the resulting estimates of both the fixed and random parameters.... At the present time there appears to be little empirical or theoretical work on issues of optimum design for multilevel models." The amount of work on sample design published up to now remains quite limited; an account will be given of this work.

Some current work on an industrial modelling problem with design aspects will also be described; this is the engine mapping process in the automotive industry, the process of modelling engine behaviour as a function of adjustable engine parameters. In this work we have assumed a 2-level repeated measures model, with a second-order polynomial having random coefficients, for the response.

Date received: April 12, 2002