Questions on the change of variance

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KK123456
Posts: 4
Joined: Tue Feb 28, 2017 11:21 am

Questions on the change of variance

Post by KK123456 »

Dear everyone:
I have a question on the drop of variance at the higher level. I am modeling 2 two-level random slope model. I found that when I just added some independent variables into the null model, and all slopes are fixed, but the variance at level-2 (school) still drops. I was a lit bit confuse about this drop. I can understand the drop of the variance at the individual level, but how does the drop at level-2 occur?

Thanks everyone!
ChrisCharlton
Posts: 1224
Joined: Mon Oct 19, 2009 10:34 am

Re: Questions on the change of variance

Post by ChrisCharlton »

Could you please provide screenshots of simple examples where this occurs to further illustration the details of this?
KK123456
Posts: 4
Joined: Tue Feb 28, 2017 11:21 am

Re: Questions on the change of variance

Post by KK123456 »

Thanks for your reply.
Here is the example:
For the null model, the random part shows that σu0^2=0.076; σe0^2=0.248
when I added several independent variables into the null model and keeps the coefficients fixed (NOT randomly varies cross schools), the random part shows that σu0^2=0.075; σe0^2=0.228
As you can see both σu0^2 and σe0^2 dropped. My question is now I have not added level-2 variables, why the σu0^2 (level-2 variance) dropped?

Thanks
ChrisCharlton
Posts: 1224
Joined: Mon Oct 19, 2009 10:34 am

Re: Questions on the change of variance

Post by ChrisCharlton »

I asked George about this and he said the following:
This is because most level 1 variables vary in their mean value across level 2 units. Thus adding level 1 variables typically explains away variation between level 2 units as well as well as between level 1 units.
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