Multilevel model of school data

Hi, I have a model I am working with to estimate 6 grade test scores from a sample of students who were in a school district from K-6. I am using both Stata and MLWIN to compare results. The ICC from the random intercept model is around .15, so there is school level variance to explain. I have school size, school free/reduced rate, school mobility and student teacher ratio as school level variables. When I add these my school level variance goes away and the residual plot of the school residuals shows no difference in school means. Very nice. Now when I add student level variables, such as school choice decision (neighborhood school/magnet school), gender, stayed in same school all 7 years, students free reduced status and ethnicity, the coefficients on my Level 2 variables are all insignificant now, my level 2 variance is still low, and I get significant coefficients on the level 1 variables. Should I just drop the level 2 variables now since they are really composites of the level one variables, for the most part? Cross level interactions don't seem to help. What is a good explanation of why the coefficients are changing on the level 2 variables (other than lack of independence between levels!?) Thanks so much
Hey there. Can you clarify by what you are calling level 1 and level 2 variables? Is level 1 school level and level 2 student level?
[QUOTE=Colin;80324]Hey there. Can you clarify by what you are calling level 1 and level 2 variables? Is level 1 school level and level 2 student level?[/QUOTE]

Hi Colin, I should have clarified. Level 1 is student level, level 2 is school level. Some of my school level variables are aggregates of student level, such as the school free reduced lunch rate, school size. I use the student FRED status as well as a level 1 variable. Other school level variables are curriculum type, student teacher ratio and mobility rate. These have some relationship to student level variables in that low student teacher ratios are at schools with high need students. When I run the model without student level variables I explain almost all the between school variance. When I add student level variables I still explain the between variance but all the school level variables are now insignficant, the coefficients really change. I thought the model would keep interactions between levels out unless I explicilty modeled them, but that may be a big misunderstanding on my part.



Phineas Packard
Hi Larry,

Yes you can drop the lvl2 variables but of course you should still keep the random intercepts so that your SEs are correct. I should note however, that there is a difference between vanilla lvl2, culture, and context variables and the lv2 effects are calculated differently for each. It looks like you have some context effects and thus you will need to judge the significance of your lv2 variables slightly differently (note that the formula changes depending on whether you are using group or grand mean centering). On a personal note it seem that your model should at least include school average achievement to account for the effect of the big-fish-little-pond effect on yr6 achievement.

This gives a good tutorial:
Harker, R., & Tymms, P. (2004). The effects of student composition on school outcomes. School effectiveness and school improvement, 15(2), 177–199.