(EDEP 768) Week 4: Follow up on Discussion of Random Slopes 1

(EDEP 768) Week 4: Follow up on Discussion of Random Slopes 1

Week 4: Follow up
Discussion of Random Slopes

(References use of corresponding level-2 data set: Wk4EDEP768data.sav)

I wanted to follow up a little bit on our discussion of random slopes the other day. When we want to investigate whether the lowSES-achievement slope varies randomly, we need to define a random component to the model (). So we will now have the following:

.

We can save the slope estimates of the level-1 model:

,

And then use them as the outcome in the level-2 model:

.

We can then add a set of predictors to explain this variability. We might want first to see what the variability in slopes looks like. In order to do this, I saved the level-1 estimates of the variability in lowSES-math achievement slopes (eblowses). Here are the estimates (to the right) for the first 10 schools:
You can see they vary considerably even in the first 10 schools. Notably, some are positive, indicating that low SES students actually score a bit higher in math than their higher SES peers. Six of the 10, however, are negative ranging from about -7 to -14 points. / / -6.842
1.936
3.032
4.440
-11.621
-12.028
3.647
0.280
-14.554
-7.812

Now we add the four predictors to the model. I am showing this as a multiple regression model to show you that the level-2 model is similar to a regression model using the slope as the dependent variable. There are 154 schools in the model.

Below are the estimates for the multiple regression model (Table 1; Wk4EDEP768data.sav). You can see that school context (which is actually student composition) and the school quality composite are significant in explaining variability in the lowses-achievement slopes.
Table 1

You can compare the results of the model above to the slope model (Table 2; last week’s data set Wk3EDEP768data.sav) in the handout below:

Table 2

You can see that the estimates are a little different in each model, but they make the same point that school context and the school quality composite are statistically significant (p < .05).

The level-2 regression model seems to account for about 37% of the variability in the slopes (Table 3).

Table 3

Of course, it is more efficient to run this as a “mixed” model (with both the intercept and slope estimated simultaneously) like in the handout. But running it as a multiple regression model does illustrate how we build a level-2 model to explain the variability in slopes at that level.