This article examine the asymptotic effect of omitting a random coefficient in a multi-level model. The author gives the analytic expressions for the change in both estimates of the random effect (variance) and the fixed effect. The formulas they derived can be applied when evaluating the results of a multilevel analysis performed by other researchers and when there is no access to the raw data. They also studied the effects of omittion on a T-test asymptotically.
Their study is quite general in the sense that their conclusions not only applies to two-level, but also higher-level models. However, the final expression of the change in estimates is too complicated for readers to draw useful informations.
The study on T-test statistics are quite informative in practice, providing information on when the t-test will be liberal or conservative. However, the limitation is that it is an asymptotic result (meanning that under the ideal condition of infinite sample size). For practioners to apply their results, it is also important to know whether their conclusions are still accurate with moderate sample sizes.