Multilevel Regression on Two Time Points

[Daniel Loke]

Hi there!

I'm currently conducting an analysis of data from two measurements, where we are attempting to pinpoint stable and time-varying predictors for a neurological phenomenon (continuous outcome). All included patients were measured once (T1), and once again six months later (T2). We have an abundance of predictors based on previous research, some of which are correlated with each other. The plan was to conduct a multilevel regression with time points (Level 1) nested within subjects (Level 2). Due to a high degree of stability in most of the included constructs, I thought that an investigation of between-subject and within-subject covariance would be interesting, to figure out 1) stable between-subject predictors of this phenomon, and 2) correlated changes within-subjects to investigate temporal assocations. Data has adjusted to a long format (two rows per subject). Does the following procedure violate any statistical assumptions I am not aware of?

1. Generate individual mean variables (aggregate at level 2) for outcome variable and all predictor variables.
2. Generate individual mean-centered scores for all time points(centered level 1), as a deviation from the average score
3. Evaluate correlations between aggregate level 2 variables for both outcome and predictor, and run a factor analysis on all signifcant associations (p < .025 due to long format)
4. Evaluate correlations between centered level 1-variables for both outcome and predictor, and run a factor analysis on all signifcant associations (p < .025 due to long format)
5. Perform a linear multilevel regression (mixed-command) first inputting factors from level 2-FA (explains only variance at level 2 in the outcome)
6. Add factors from centered level 1-FA to the multilevel regression (explains only variance at level 1 in the outcome).

While I am aware of the shortcomings of using only two time points, this approach does make sense to me as a way of evaluating stable between-subject associations and within-subject covariation with predictors. However, I am having difficulties in identifying studies which has employed a similar method. Am I misunderstanding something basic?

[Clyde Schechter]

Well, I'm not sure what the factor analyses accomplish. If you are creating orthogonal factors then I suppose you are working your way around the colinearity among the various predictors. BUT you do that at the price of going from predictors that are things you can measure, to "factors" that are just artificial linear combinations of those measures and may not correspond to anything that exists in the real world. And when somebody sees your work and asks you what those factors "mean," you will probably find yourself at a loss for words. So my inclination would be to omit steps 3 and 4 and just use the original predictors. There are worse, far, far worse things in life than correlation among predictors (unless it is extreme, in which case you need a gargantuan data set to overcome it.)

Be that as it may, I also don't grasp step 5. If you are looking only the variance at level 2, and have no level 1 predictors, it would be simpler to just do a "flat" regression of mean outcome against means of predictors. Having the illusion of multilevel structure when all of the actual data is at one level will not be informative, and I wouldn't be surprised if it just made the estimation fail to converge anyway. It seems to me that step 6 is the "pay dirt" of your process and my inclination would be to skip step 5 and go directly to the real multi-level model.

That said, unless I have overlooked some details, you can probably save yourself a little effort by installing -xthybrid-, by Francisco Perales and Reinhard Schunck, available from both SSC and the Stata Journal. It will automate steps 1, 2, and 6 all in a single line command. It also gives a very nicely organized output display demarcating the within- and between- patient effects.