Interpreting Models with Multiple Interaction Terms: Gender, Weight, and Height

[FallenApple]

If there are two interaction terms in a single model, does that mess up the interpretation of it? For example, Gender*Weight and Gender*Height.

Say the model is Y~Weight+Height +Gender +Gender*Weight+Gender*Height.

Would I simply interpret it as usual? That is, "The difference in mean response for a one unit increase in weight differs between the genders by the value of the interaction coefficient between weight and gender for a subpopulation of people with Height=some fixed value"?I've heard that having multiple interactions isn't good because it might complicate the interpetability. I'm not sure how though which is why I'm asking.

Also, isn't the power higher in a model with two interaction if there are in fact two interactions vs having a separate model for each interaction term?

 

[andrewkirk]

My understanding is that, if the fitted coefficients are B1 to B5 from left to right (ignoring the constant term B0) the interpretation is as follows:

sensitivity of Y to Weight is (B1 + B4 * Gender), so the sensitivity varies by Gender
sensitivity of Y to Height is (B2 + B5 * Gender), so the sensitivity varies by Gender
sensitivity of Y to Gender is (B3 + B4 * Weight + B5 * Height), so the sensitivity varies by Weight and Height

The interaction terms tell us the sensitivities of the sensitivities.

 

[FallenApple]

My understanding is that, if the fitted coefficients are B1 to B5 from left to right (ignoring the constant term B0) the interpretation is as follows:

sensitivity of Y to Weight is (B1 + B4 * Gender), so the sensitivity varies by Gender
sensitivity of Y to Height is (B2 + B5 * Gender), so the sensitivity varies by Gender
sensitivity of Y to Gender is (B3 + B4 * Weight + B5 * Height), so the sensitivity varies by Weight and Height

The interaction terms tell us the sensitivities of the sensitivities.

Got it. Now to interpret say effect of weight across gender, would I have to fix the height? From a mathematical point of view, I could just fix it and it would drop out. But it could be a confounder so I'm not sure.

if height is x=a

then

B3 + B4 * Weight + B5 * a

Then a unit difference in weight gives rise to B4. So holding weight fixed, the difference in mean response for unit increase in weight is B4. Then height seemingly does matter.