Mean centering predictors on subject level
Posted: 24 Mar 2021, 10:26
Hi!
I have data from where participants could choose how to split 10 points between themselves and a random recipient. Before they had to do this, they had to rate how personally appropriate they think each action is, on a 4-point scale with numerical values -1, -1/3, 1/3, and 1. I use the payoff and the appropriateness rating as predictors in the conditional logit model.
What I discovered is that I get the same results when, instead of taking the raw appropriateness ratings, I take the deviation of a given actions appropriateness rating from the mean appropriateness rating of a given subject, i.e., personal norm rating of action i, subject j – mean personal norm rating over all actions of subject j.
I guess, but am not entirely sure, that this makes sense because I essentially just center the norm ratings on the subject level? And similar to centering a variable in a linear regression, the coefficient (excluding the intercept) does not change.
Following this train of thought, if the model fit gives a positive utility weight for the appropriateness rating, is it valid to say that on average (meaning average over all subjects), the subjects choose actions that have a higher appropriateness rating than the average appropriateness rating over all alternatives for a given subject (i.e., over all subjects, the average deviation (appropriateness rating of chosen action of subject j – mean appropriateness ratings of all actions of subject j) is positive)?
I made some plots that align with this interpretation:
The plots show the available alternatives on the x-axis and each point is a subject that ended up choosing that alternative. On the y-axis is how the appropriateness rating of the chosen alternative for a given subject j deviates from the mean appropriateness rating over all alternatives for that given subject j. The red line is the mean of all deviations over all subjects.
What I could show with the models is that if I exclude subjects who chose the alternative “exit”, the utility weight of the appropriateness rating is positive (significantly) (right plot), but when I include them it is a lot smaller (though still positive), but not significant anymore (left plot). The plots seem to confirm this (i.e., the mean deviation over all subjects (red line) is higher if we exclude subjects who chose the alternative “exit”).
Would appreciate it if you could tell me whether what I wrote makes any sense.
I have data from where participants could choose how to split 10 points between themselves and a random recipient. Before they had to do this, they had to rate how personally appropriate they think each action is, on a 4-point scale with numerical values -1, -1/3, 1/3, and 1. I use the payoff and the appropriateness rating as predictors in the conditional logit model.
What I discovered is that I get the same results when, instead of taking the raw appropriateness ratings, I take the deviation of a given actions appropriateness rating from the mean appropriateness rating of a given subject, i.e., personal norm rating of action i, subject j – mean personal norm rating over all actions of subject j.
I guess, but am not entirely sure, that this makes sense because I essentially just center the norm ratings on the subject level? And similar to centering a variable in a linear regression, the coefficient (excluding the intercept) does not change.
Following this train of thought, if the model fit gives a positive utility weight for the appropriateness rating, is it valid to say that on average (meaning average over all subjects), the subjects choose actions that have a higher appropriateness rating than the average appropriateness rating over all alternatives for a given subject (i.e., over all subjects, the average deviation (appropriateness rating of chosen action of subject j – mean appropriateness ratings of all actions of subject j) is positive)?
I made some plots that align with this interpretation:
- apollo_forum.png (14 KiB) Viewed 6913 times
What I could show with the models is that if I exclude subjects who chose the alternative “exit”, the utility weight of the appropriateness rating is positive (significantly) (right plot), but when I include them it is a lot smaller (though still positive), but not significant anymore (left plot). The plots seem to confirm this (i.e., the mean deviation over all subjects (red line) is higher if we exclude subjects who chose the alternative “exit”).
Would appreciate it if you could tell me whether what I wrote makes any sense.