« Relational database dimensions (Excel) | Main | Very large sample sizes = statistical significance »

Longitudinal data (change scores)

Baseline-adjustment is generally preferred to change scores, because it is less parameterized - allowing the data more freedom to fit itself. In calculation terms it is the difference between models like these:

wt2 = 1*wt1 + error

wt2 = 0.973*wt1 + error

Interestingly, you can use change on the left side and get "identical" results - i.e. treatment effects will be identical but the wt1 coefficient will change its estimate/units.

wt2-wt1 = 0.973*wt1 + error

That makes sense because you are modeling two equations like these:

y = ax + b

y-x = ax + b (alternatively y = (a+1)x + b , a linear transformation)


On to a more complicated question...

Study design: Randomized trial of weight loss
Question: How to model weight loss maintenance from time 4 to time 5

Warning: I went out on a limb to answer this question

The specific question was whether to adjust for time 4 ("baseline") when modeling change from 4 to 5 and adjusting for change from 1 to 4. (Background: This is about maintenance and weight loss from baseline to 4 may predict performance from 4 to 5. Do the successful people remain successful or do the people who lost have greater regain potential? Are there two effects here, and will the results be influenced by whether completeness of data is related to early performance?)

In other words, choose between these 2 models:

wt(5-4) = wt(4-1) + error

wt(5-4) = wt(4-1) + wt4 + error

The latter is algebraically equivalent to wt5 = wt4 + wt1 + error and gives identical results.
The former is NOT equivalent to wt5 = wt1 + error, but it's close. Therefore I prefer the model with wt4 because I don't want wt4 to drop out of the equation. This is my intuition rather than something I know to be correct.