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Aniko
Aniko
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For simplicity, I will ignore the variables other than ZSC and ZSC, and will call them $X$ and $Y$ (their names are too similar for me). You obtained two logisticregression models: $$\text{logit} P(CRI=1) = 5 + 0.7 X - 0.06 Y$$$$CRI = 5 + 0.7 X - 0.06 Y$$ and $$\text{logit} P(CRI=1) = 5 + 0.72 X - 0.1 Y + 0.15 X Y $$$$CRI = 5 + 0.72 X - 0.1 Y + 0.15 X Y $$ The meaning of the coefficient of $Y$ in the first model is the following: if $Y$ is increased by one unit, then regardless of the value of $X$, the log-odds of the outcome areis changed by $-0.06$.

Its meaning in the second model is: if $Y$ is increased by one unit and $X=0$, then the log-odds of the outcome areis changed by $-0.1$. But, if say $X=1$, then the effect of one unit of change in $Y$ is $-0.1+0.15=0.05$, and if $X=-1$ then the effect is $-0.25$.

The moral is that the meaning of the "main effect" term changes when you add interaction, so there should be no surprise if its significance changes, especially if the interaction is non-negligible. In a certain sense, when you fitted the first model, you averaged over all the possible values of $X$ in $-0.1 Y + 0.15 X Y$. Also, the first model is clearly wrong (because it assumes no interaction when there is one), so any inference from it is wrong as well.

Perhaps rewriting the right side as $= 5 + 0.72 X + (0.15 X - 0.1) Y$ would help. The effect of $Y$ could be positive or negative depending on whether $0.15X < 0.1$ or not. You have to put these values into the context of the actual problem. What does $X=0$ mean? what does $Y=0$ mean? etc.

For simplicity, I will ignore the variables other than ZSC and ZSC, and will call them $X$ and $Y$ (their names are too similar for me). You obtained two logistic models: $$\text{logit} P(CRI=1) = 5 + 0.7 X - 0.06 Y$$ and $$\text{logit} P(CRI=1) = 5 + 0.72 X - 0.1 Y + 0.15 X Y $$ The meaning of the coefficient of $Y$ in the first model is the following: if $Y$ is increased by one unit, then regardless of the value of $X$, the log-odds of the outcome are changed by $-0.06$.

Its meaning in the second model is: if $Y$ is increased by one unit and $X=0$, then the log-odds of the outcome are changed by $-0.1$. But, if say $X=1$, then the effect of one unit of change in $Y$ is $-0.1+0.15=0.05$, and if $X=-1$ then the effect is $-0.25$.

The moral is that the meaning of the "main effect" term changes when you add interaction, so there should be no surprise if its significance changes, especially if the interaction is non-negligible. In a certain sense, when you fitted the first model, you averaged over all the possible values of $X$ in $-0.1 Y + 0.15 X Y$. Also, the first model is clearly wrong (because it assumes no interaction when there is one), so any inference from it is wrong as well.

Perhaps rewriting the right side as $= 5 + 0.72 X + (0.15 X - 0.1) Y$ would help. The effect of $Y$ could be positive or negative depending on whether $0.15X < 0.1$ or not. You have to put these values into the context of the actual problem. What does $X=0$ mean? what does $Y=0$ mean? etc.

For simplicity, I will ignore the variables other than ZSC and ZSC, and will call them $X$ and $Y$ (their names are too similar for me). You obtained two regression models: $$CRI = 5 + 0.7 X - 0.06 Y$$ and $$CRI = 5 + 0.72 X - 0.1 Y + 0.15 X Y $$ The meaning of the coefficient of $Y$ in the first model is the following: if $Y$ is increased by one unit, then regardless of the value of $X$, the outcome is changed by $-0.06$.

Its meaning in the second model is: if $Y$ is increased by one unit and $X=0$, then the outcome is changed by $-0.1$. But, if say $X=1$, then the effect of one unit of change in $Y$ is $-0.1+0.15=0.05$, and if $X=-1$ then the effect is $-0.25$.

The moral is that the meaning of the "main effect" term changes when you add interaction, so there should be no surprise if its significance changes, especially if the interaction is non-negligible. In a certain sense, when you fitted the first model, you averaged over all the possible values of $X$ in $-0.1 Y + 0.15 X Y$. Also, the first model is clearly wrong (because it assumes no interaction when there is one), so any inference from it is wrong as well.

Perhaps rewriting the right side as $= 5 + 0.72 X + (0.15 X - 0.1) Y$ would help. The effect of $Y$ could be positive or negative depending on whether $0.15X < 0.1$ or not. You have to put these values into the context of the actual problem. What does $X=0$ mean? what does $Y=0$ mean? etc.

Source Link
Aniko
Aniko
  • 11.1k
  • 34
  • 35

For simplicity, I will ignore the variables other than ZSC and ZSC, and will call them $X$ and $Y$ (their names are too similar for me). You obtained two logistic models: $$\text{logit} P(CRI=1) = 5 + 0.7 X - 0.06 Y$$ and $$\text{logit} P(CRI=1) = 5 + 0.72 X - 0.1 Y + 0.15 X Y $$ The meaning of the coefficient of $Y$ in the first model is the following: if $Y$ is increased by one unit, then regardless of the value of $X$, the log-odds of the outcome are changed by $-0.06$.

Its meaning in the second model is: if $Y$ is increased by one unit and $X=0$, then the log-odds of the outcome are changed by $-0.1$. But, if say $X=1$, then the effect of one unit of change in $Y$ is $-0.1+0.15=0.05$, and if $X=-1$ then the effect is $-0.25$.

The moral is that the meaning of the "main effect" term changes when you add interaction, so there should be no surprise if its significance changes, especially if the interaction is non-negligible. In a certain sense, when you fitted the first model, you averaged over all the possible values of $X$ in $-0.1 Y + 0.15 X Y$. Also, the first model is clearly wrong (because it assumes no interaction when there is one), so any inference from it is wrong as well.

Perhaps rewriting the right side as $= 5 + 0.72 X + (0.15 X - 0.1) Y$ would help. The effect of $Y$ could be positive or negative depending on whether $0.15X < 0.1$ or not. You have to put these values into the context of the actual problem. What does $X=0$ mean? what does $Y=0$ mean? etc.