Okay, now will someone explain hierarchical linear modeling to me?? That's the thing I have to understand for my job this week. Right now I'm at the "okay they've got these bits of data, they do magic magic magic annnnnnd PROFIT!" stage.
Probably too late, lisah, but I would suggest a book called "Multilevel Analysis for Applied Research: It's Just Regression!"
Very friendly for people who need to understand the concepts without bothering with all of the math.
In the meantime, a regular regression uses an intercept and a slope to show how x can be used to predict y.
y= b0x +b1x +e
The only new thing in hierarchical modeling is that we now use a new regression equation to predict the intercept (b0) and slope (b1). So instead of asking how well x predicts y, we are asking how well we can predict how well x predicts y for a certain group. We want to see if z predicts the strength of association between x and y.
So, for instance, in the work I am doing this afternoon, at the first level I am predicting weekly changes in depression in women by the amount of stress they experienced the previous week. Some women's depression appears to be highly responsive to changes in stress, and other women's depression is not. Then at level 2, I will try to explain differences in the strength of that association between stress and depression. It has been hypothesized, for instance, that women with better support networks or with non-ruminative coping strategies will show less response (predictability) in their depression from variation in stress. We'll see.
In business, a more common example would be learning at level one whether a certain kind of advertising or sale pricing is associated with more purchases, and at level 2 whether you can predict what kinds of customers are going to be more highly influenced by a certain kind of advertising or sale. For instance, I've been told that large retailers have learned that some kinds of ads mostly attract bargain seeking "bottom feeders" who increase sales of the advertised low-margin product but do not help overall revenues because they only buy the thing on sale, while other kinds of ads attract the sort of people who can be up-sold to a more expensive version of the target product or who buy the advertised product but also buy five unrelated things once you get them in the store.
This is where the "magic magic magic annnnnnd PROFIT!" stage comes in.