Suppose I have a task. I recruited 100 people to do the task, each performed the task 5 times and I scored them. In total, I have 500 scores.

I have an independent variable (well, let's say how much money I paid for each time one person do the task - it doesn't matter) so I want to perform a linear regression to see if the score achieved have some relations with the salary.

So, my dataframe has 500 data points. I am afraid that, due to the fact 500 data points are created by only 100 persons, it might lead to some problems relate to colinearity, and performing a linear regression on 500 scores might be not a good idea.

My question is:

1) Do I have to worry about the issue? 2) If so, what should I do to check the dependent of the score on the salary?

Thank you very much?

(If you can give example in R, it's perfect. Otherwise there is no problem)


1 Answer 1


I wouldn't expect collinearity to be a problem. (To be honest, it sounds a little like you are misunderstanding what collinearity is.)

I'd rather worry about modeling the dependence between the different trials completed by each separate individual. You have a design, which is typically modeled using s or s (nomenclature differs somewhat for the same models between disciplines). There are many good textbooks and online resources out there on repeated measures.

In R, people typically use the lme4 or the nlme packages. Look at those, too.

  • $\begingroup$ Thanks a lot for your comment. In fact, I did not check the colinearity, I just wonder if the fact that the task is repeated by one person can lead to some problems. $\endgroup$ Jun 14, 2017 at 8:32
  • $\begingroup$ For repeated measure design, I wonder too. A person here repeats the task but in the same condition, so I suppose there is no between variable? $\endgroup$ Jun 14, 2017 at 8:33
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    $\begingroup$ Yes, judging from your explanation, there is simply a repeated factor, i.e., the participant. So you should model the fact that observations from one participant will be much more highly correlated than observations from multiple participants. See here. $\endgroup$ Jun 14, 2017 at 9:12

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