I would like to fit the data with a linear model for each participant that would look like this:

$$ Y=B_0 + B_1X_1 + (B_2 + B_3X_1)X_2$$

where $B_i$ are the regression coefficients and $X_i$ the regressors.

Depending on participant's particularities, $B_2$ could be positive or negative. But my hypothesis is that $B_3$ should be of the opposite sign than $B_2$ for each participant.

Doing that, by hypothesis $B_3$ and $B_2$ should be correlated. So, two questions:

1. Isn't that an issue for the fitting?

2. If not, which kind of test should I run to test my hypothesis?

  • $\begingroup$ What do you mean by "fit a linear model for each participant"? Regression estimates the coefficients for groups of subjects (participants). $\endgroup$
    – Peter Flom
    Mar 23, 2017 at 10:53
  • $\begingroup$ I mean that I would collect about 500 trials for each participant and fit the data for each participant individually in order to find regression estimates for each subject $\endgroup$ Mar 23, 2017 at 11:10
  • $\begingroup$ Why not collect all data, add a categorical variable participant and fit a single model? $\endgroup$
    – DeltaIV
    Mar 23, 2017 at 11:27
  • $\begingroup$ Because actually, the hypothesis that I want to test is the opposite sign between B2 and B3 for each participant (independently of the sign of B2, that could differ between participants) $\endgroup$ Mar 23, 2017 at 14:13


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