# Testing hypothesis on one wave of panel data

Hi all,

I have data on several individuals and their workplace, collected over a number of years (say, five). The companies participating in this study are the same in each wave, but the people change. Before the last wave, an intervention was carried out which makes me hypothesise that one of the person-level variables, say x_1, should now be more strongly correlated with the outcome variable y.

Given these premises, my approach would by to run a three-level model with people nested in companies nested in years and add a ‘random’ slope of the form (1 + x1 | year). The idea is, even if the variance is small and the fit compared to (1 | year) does not improve, if it is possible to recover the posterior distribution of these deviation w_1 to w_5 from \beta_1 (the global average for the variable of interest x_1) I should be able to carry out statistical tests of difference from the mean / median of the coefficient for last wave compared to previous waves, or to use simulations to see if the last wave’s posterior is different from the earlier ones.

Does this make sense and would it work? Are there any other approaches that you would recommend?

Thank you,

k.

I guess since the people are changing, if there is some sorta noticeable different in the coefficients, it’s not clear if the intervention worked or if the people just changed enough to make the coefficient different.

Since you have an idea for all the bits and pieces that are moving around, the thing to do would be generate simulated data and see if you can recover the parameters you want.

I’d guess http://www.stat.columbia.edu/~gelman/arm/ is the book for this. My pretty uninformed impression is that studies where the people get shuffled are much much less informative than ones where you track individuals.

Hi Ben,

Thank you for your reply. It is true that longitudinal data would serve me better. In this case the longitudinal element is the level-2 units, which stay the same, though of course by aggregating one cannot know if it was the people changed. I can control for the other variables and detect the marginal effect of x_1 by year. A simulation sounds like a good idea.