When part of the nesting information in a two-way nested model is miss
ing, there has been no way to use all of the data in the analysis of v
ariance components. Discarding the data with missing nesting informati
on loses useful information, and in some circumstances, this approach
cannot separate variance components from one another. To make use of t
he data with missing nesting information, computable sums of squares f
or the data with missing nesting information can be linearly combined
with sums of squares for the data with complete nesting information. P
respecified weights are needed for the combination. Different estimate
s are obtained by using different weights. Because all of these estima
tors are unbiased, variances and covariances of these estimators are d
erived and used to compare these estimators. In addition, a simulation
study is conducted to provide evidence for the reliability of the var
iances and covariances formulas. Finally, as an application, the propo
sed methods are applied to the analysis of a proficiency testing progr
am.