Choice of statistical analysis: compare change in two "groups" over two time points

[Sara Hansen]

I have two continuous variables: performance and expected performance, at two time points: baseline and after 1 year. Furthermore, I have some potential confounders I would like to adjust for: weight, smoking and gender.

I would like to test the following hypothesis: The decrease in performance from baseline to after 1 year is not significantly different than the decrease in expected performance from baseline to after 1 year.

Does anybody have an idea of which type of test would be the best choice for this?


Example of data (however, I could reformat it to long format instead / make other reformats depending on type of test):

id	base. score	exp. base score	FU score	exp. FU score
1	28	30	36	37
2	27	33	40	44
3	32	29	41	35

[Carlo Lazzaro]

Sara:
do you have two dependent variables that you want to test in the same regression or your plan is to regress them separately in two different regressions?

[Sara Hansen]

Sara:
do you have two dependent variables that you want to test in the same regression or your plan is to regress them separately in two different regressions?

Initially I was thinking testing both dependent variables in the same, but perhaps testing in two separate could also work.
I'm just not sure how to be able to answer the question whether or not there is a significantly difference in the participant's change performance from baseline to 1 year vs the expected change in performance...

[Carlo Lazzaro]

Sara:
-xtreg,fe-might be an option.

[David Mangen]

Initially I was thinking testing both dependent variables in the same, but perhaps testing in two separate could also work.
I'm just not sure how to be able to answer the question whether or not there is a significantly difference in the participant's change performance from baseline to 1 year vs the expected change in performance...

I would consider setting up a structural equation model. The three confounding variables become the endogenous measures; they influence both measures at baseline. Baseline measures influence their respective follow up measures. For one test of the model the two effect coefficients of baseline on follow up are constrained to be equal. In the second test the two coefficients are estimated uniquely for each equation. If the goodness of fit has significantly improved then the change models are significantly different.

You might find it necessary to add other effects to the overall model to get a good overall fit, but that is a different matter.