Regression with 'stacked' data I've occasionally seen people do something like the following. Let's say we have a survey battery with k questions, for instance an evaluation of red jelly beans, an evaluation of green jelly beans, etc. Then we have another battery of related questions, such as an evaluation of the color red, green, and so forth. The data might look like this:




id
y1
y2 
y3 
x1
x2
x3




1
10
9
5
6
10
5


2 
9
 5
10
0
10
5




The data is then 'stacked', so that for each respondent there are k rows:




id
y
x




1
10
6


1
9
10


1
5
5


2
9
0


2
5
10


2
10
5




Finally, a model such as OLS is fitted, with y as the dependent variable and x as the independent variable. Most likely there are several independent variables, and they may have been constructed in more complicated ways.
I'm trying to understand whether this is a sensible thing to do, and what issues might arise. It feels a bit fishy: observations are not independent (there are k observations for each respondent, and n (the number of respondents) observations for each type of jelly bean). A model with mixed effects would seem reasonable, as suggested in answers to similar questions here and here.
If, however, the analysis was performed as described, what should I be cautious about when interpreting the results?

As there is no time variable, then it's not a stacked panel data, so those techniques don't apply to the letter.
So, it's a cross sectional data, where you know there are groups of answers (color of jelly bean). You could try to run the stacked data model, with the advantage of higher number of observations, but chances are you find high heterogeneity.
It all depends on what's your goal. Do you want to separate your results depending on the color of the bean.
Assuming you want to stay in OLS:
Option 1: You could try three models with $n=2$ as $y_c = f(x_c)$ for each color ($c$), assuming you have more data, it should be ok. Separate conclusions.
Option 2: You could try the stacked data model with $n=6$, but you'll need to add a "color" variable, to control for that feature. This variable should be coded as a factor, which is quite similar to a fixed effects model. Thus, your model will be $y = f(x,c)$.
