Combine longitudinal data to increase power?

Question

I have a set of data of ~13 people. We collect their data every 2 months for 2 years.

I'm interested to see if a variable A in the data affect people's performance as well as their growth rate. So the main goal is to compare the behavior between the participants. I know I have a rather small sample size to do this but it's hard to collect longitudinal data for a bigger group. The time stamp is used to calculate their growth rate over time.

However, since overall performance is also something I want to look into, I wonder if there is any way I can combine the data to increase the power of the analysis? I only have 13 people but each of them has 12 performance data points collected at different time. What would be the best way to utilize this to compensate for the small sample size?

Thank you!

Answer 1

If the correlations of the repeated measurements of each participant are not that strong, you can gain information from using all available data, especially for within participants effects.

In any case, an analysis based on mixed-effects models or marginal models that appropriately accounts for these correlations would be the way to go. You could have a look at my course notes on these models to gain an understanding on how they work.

Answer 2

Thank you Dimitris Rizopoulos for the answer (sorry I don't have enough reputation yet to directly comment to your answer) ! My worry is that using all the available data would introduce a confounding factor (time), as participants' performance increases over time regardless of variable A.

I try using gls, something like g <- gls(varB~varA*varC,correlation =corCompSymm(form=~Date|Subject),data=data)

does it look ok?