A faster simulation approach to sample size determination for random effect models

Sample size determination is fundamentally important to the successful execution of research but is often inadequately addressed at the design stage, perhaps because it can be a formidable task (particularly in the realm of multilevel analysis). Whilst some analytical formulae exist for multilevel sample size calculations, almost all of these are for specific scenarios and they typically assume a balanced sampling design which is often not the case in practice. Simulation-based methods on the other hand provide a generic approach to sample size determination without the need for analytical formulae or the assumption of balance. There is very little software available to effect sample size determination for unbalanced cross-classified sampling designs. Adequately representing the structure of multilevel data in specific crossed situations is also challenging. This research shows that extending the sampling scheme for unbalanced cross-classified designs by incorporating a model for migration (into a geographical area) gives increases in power as the number of units sampled for the first cross-classification increases, provided that data is not missing for incomers. A drawback of simulation-based estimation methods is that computation times can be very lengthy because of the large number of simulations needed to produce a single estimate. This problem is exacerbated for sample size determination by simulation since the process necessitates producing many estimates in a series of steps. Models and sampling designs with increasing complexity can thus result in impracticable computation times. Results of this research show that the algorithmic techniques proposed for multilevel sample size determination can yield substantial reductions in computation time. These speed improvements are achieved without compromising on the accuracy of the sample size estimates and sometimes provide improved accuracy. The methods are broadly applicable and suggest a potentially valuable way of saving computing and financial resources.