## Level 2 variance increases with inclusion of Level 1 predictors

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PetrouEUR
Posts: 4
Joined: Mon Nov 27, 2017 3:14 pm

### Level 2 variance increases with inclusion of Level 1 predictors

Dear Mlwin users,

Have you ever had the following issue?

The variance (estimate) of Level 2 increases when new Level 1 predictors are added in a regression equation (all as predictors of a Level 1 outcome).
I usually have this when all predictors in the equation are at Level 1.

I'm quite puzzled by this because I have read that this is mathematically impossible. This has as a result than when I calculate the Rsquare of the new model, this is a negative percentage. To calculate the Rsquare per model I use the following formula:
(Level 2 variance of null model – Level 2 variance of subsequent model) / Level 2 variance null model.

Best,
Paris
billb
Posts: 132
Joined: Fri May 21, 2010 1:21 pm

### Re: Level 2 variance increases with inclusion of Level 1 predictors

Hi Paris,
This is a quite common phenomenon and easy to explain. Imagine for example growth curves between individuals measured yearly for 10 years. In a model without age we would have lots of variation within an individual as their heights at age 4 say will be very different from their heights at age 13 and in fact this will dominate the between individual variation. Now add age (a level 1 variable in) and we explain lots of the within individual variation and suddenly the between individual variation (level 2) appears.
Hope this helps,
Bill.
namphan1998
Posts: 3
Joined: Mon Dec 11, 2017 3:02 am

### Re: Level 2 variance increases with inclusion of Level 1 predictors

Thank you so much Billb!!

This is what im looking for!!

Keep up the good work!