Regression Analysis of Time as Independent Variable in Experiment we conducted an experiment on a sample of 30 persons. For every person, we observed the outcome variable every 15 minutes, so for each person 10 times.
IV: Time (in Minutes)
DV: Interval Scale [1;9]
n = 30 people, 10 observations each
What‘s the ideal method of analysis for this? Can I simply run a simple linear regression model on the 300 IV->DV pairs, ignoring the person? Or, is it important linking observations to persons? How would you analyse this?
Thanks!!

*

*Tried a simple Linear Regression Model

*Researched Cross-Sectional Time Series Analysis and Panel Data Analysis, but unsure about their fit

 A: Running a simple linear regression model on the 300 pairs is a viable option. However, as you suspected, it would presume that there is no difference between the individuals. So the next possibility would be to fit a new model for each of the 30 people, giving you 30 different models. This, however, would ignore the fact, that those 30 datasets (of size 10) all come from the same experiment, always with human beings, which would suggest that they should be similar.
That's why you might want to consider random effect models, which, intuitively, fit a new model for each individual but at the same time make sure that they are similar, borrowing information from each other.
There are good implementations available, e.g. in R.
In your situation, the standard first step would be to use a random intercept and a random slope.
Other models, which also combine the individual time series in a smart way instead of considering them either equal or independent, thus benefitting from correlations, would be e.g. VAR, state space models, or fully-fledged Bayesian models, but those are somehow more involved.
