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I was told that if I have a regression model $Y=b_0 + b_1X + b_2Z + b_3(X *Z)$, coefficients $b_1$ and $b_2$ have conditional effects. What does this mean exactly? How do I know when I have main effects or conditional effects?

Ferdi
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Sara
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  • The $XZ$ term is called an interaction. Your question appears to be answered at https://stats.stackexchange.com/questions/4901/what-are-best-practices-in-identifying-interaction-effects. Is that the thrust of your question, or are you trying to ask something different? – whuber Dec 14 '17 at 19:31
  • I do know what an interaction is. My confused concerns that as far as I understood, the coefficients b1 and b2 were the main effects for variables X and Z, respectively. I was recently told that these coefficients do not represent these variables' main effects but their condiitonal effects. I am quite confused about what this means exactly, because I thought that e.g. b1 is the change in Y for every unit change in X, when all other variables are held constant (controlled for). – Sara Dec 15 '17 at 15:04
  • Thus, I do not understand why this would be called a conditional effect, since it represents a change in Y, WHILE the other predictors are held constant - wouldn't this make it a MAIN effects and not a CONDITIONAL effects? – Sara Dec 15 '17 at 15:04
  • That indeed is how many people would describe it. Have you posed your question to the person who told you this? All I can imagine is that they might have wished to emphasize the fact that all coefficient estimates in any multiple regression model are conditional on the inclusion of all other variables. On that account, though, even in the model $E[Y]=b_0+b_1X+b_2Z$ one would have to characterize $b_1$ and $b_2$ as "conditional." – whuber Dec 15 '17 at 21:17

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