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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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