low unexplained variance on third level, but third level variable with high explanatory power

[marjolijndewilde]

Dear all,

I have a three-level linear model. The null model proves to have very low unexplained variance at the third level (VPC's of lower than 10%). However, If I introduce one particular third level variabel (categorical variable), it proves to be highly significant and to have the highest z-scores of all other explaining variables.
Is this possible?

Some details:
- almost 6000 measurements on the lowest level (client cases), almost 600 (social workers) on the second and 90 (municipalities) on the third level.
- sampling is d-efficient (experimental) on the lowest level and stratified random sampling on the second and the third
- unexplained variances in the null model at the three levels: 1=1; 2=1.91; 3=0.27
- unexplained variances after adding all explaining variables: 1=0.94; 2=1.35; 3=0.09
- z-score of the particular variable on the third level = -4.3. there is a 20 procentpoint change in the explained variable, depending on the value of this independent variable
- I am studying the likelihood that a social assistance client will lose this social assistance if she refuses a job offer. The variable with the highest z-scores is a variable on the lowest (client) level = the number of times she refuses a job offer. The variable I am confused about because of the low unexplained variance at the third level and the high explaining power of this third level variable, is the political party of the president of the social assistance organisation (social assistance in Belgium is managed by politically appointed administrators).

I would love to know if you see some methodological explanations for this finding.
Marjolijn (University of Antwerp)

[billb]

Hi Marjolin,
Don't see any problem here - your variables appears to explain 2 thirds of the level 3 variation and the Z score is only 4.3 which although very significant you do have 6000 data points and so it is possible to have much bigger Z scores.
Best wishes,
Bill.