Estimating Variance Components in Unbalanced Designs

However, once one comes to unbalanced designs, things suddenly get more complicated, and often recourse has to be made to quite sophisticated software to get reasonable results.

The purpose of this report is to derive some unbiased estimators of the vari­ance components for a two-way table or a three-way table, with one observation per cell as is usual in generalizability theory, but where some of the observa­ tions are missing. It will be assumed throughout that missing observations are missing completely at random. Furthermore, it wiU be asswued that the data are collected to produce a complete design, so that it is reasonable to expect that the missing values are incidental and that their number is not exorbitantly high. In the simulation studies therefore, the highest percentage of empty cells will be set to 16%.

In the next section a rather detailed derivation will be given for a two-way table. The subsequent section will give the results for a three-way table. In Section 4, some examples will be given which compare the present estimators with the REML estimators provided by BMDP3V.