The Consequence of Ignoring a Level of Nesting in Multilevel Analysis
By M. Moerbeek
This paper studies the consequence of ignoring the top or intermediate level in a three level model. Both empirical and analytical studies are carried out to examine the bias, variance (SE), power of the data analysis.
Results are very clean, which are summarized in the following:
1. bias (balanced design):
|
Top Level ignored |
Mediate level ignored |
|
|
Fixed effect estimates |
unchanged |
Unchanged |
|
Random effect estimates |
overestimated |
overestimated |
2. Bias (unbalanced design):
|
Top Level ignored |
Mediate level ignored |
|
|
Fixed effect estimates |
overestimated |
underestimated |
|
Random effect estimates |
Overestimated |
overestimated |
3. Variance (SE) of the fixed slope:
|
Level of variation |
Top Level ignored |
Mediate level ignored |
|
person |
unchanged |
underestimated |
|
Class |
overestimated |
--- |
|
school |
--- |
unchanged |
4. Power and type I error rate when testing the fixed slope:
|
Level of variation |
Top Level ignored |
Mediate level ignored |
|
person |
unchanged |
Higher Type I error rate |
|
Class |
Lower power |
--- |
|
school |
--- |
unchanged |