I had a question regarding changes in parameter estimates between single and multilevel models. Based on LR tests, a 3-level model was appropriate for my data. I compared four experimental conditions (level-2 in this case) using dummy coding. After observing a large discrepancy between the parameter estimates and basic descriptive statistics, I ran a single level model to confirm I coded correctly, which I did, and a two level model for diagnostic purposes. I observed marked parameter changes each time a level was added. Iíve found the same effect with several continuous metrics I was examining as well.
The number of cases within each level-2 cluster varies considerably. I am not sure if that would affect anything.
I was hoping someone could help me diagnose this issue.
Adding levels in multilevel analysis can very well change parameter estimates; that is to be expected. Your test says that the 1-level and 2-level models are wrong so their results should be ignored. The multilevel literature discusses these changes in estimates.
Varying number of cases within level 2 clusters should not be a major factor in what you are seeing.