Interaction term and partial least square regression I am investigating the association of air pollution with birth weight. Given that there is collinearity between air pollutants, I chose to use PLS regression. 
To my understanding, we could use partial least square (PLS) regression to account for the collinearity between different predictors. Therefore, it is not necessary to add any interaction term in the PLS model, do I understand correctly?
And would it be at risk of overfitting if I add interaction term? 
 A: Let me give a quite rough and intuitive answer. Please feel free to edit it.
Collinearity between predictors $X_1$ and $X_2$ means $X_1$ is linearly correlated to $X_2$, that is, $X_1 \approx a + b X_2$ (very rough, not rigorous). Note that the response $Y$ is not considered when we talk about collinearity. Suppose the regression model is $Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$. When collinearity exists between $X_1$ and $X_2$, the model "reduces" to $$Y\approx\beta_0 + \beta_1 (aX_2 +b) + \beta_2 X_2 + \epsilon$$ $$= \gamma_0 + \gamma_1 X_2 + \epsilon.$$
Interaction terms are included to the model when the effects of $X_1$ and $X_2$ on the response $Y$ are not additive (note $Y$ is considered here). What does it mean by "effects are not additive"? Intuitively speaking, the contribution of $X_1$ to $Y$ is not "independent" of $X_2$, and is "manipulated" by $X_2$. A typical situation is that the coefficient of $X_1$, $\beta_1$, is linearly correlated to $X_2$, ie, $\beta_1 = aX_2 +b$. Suppose the regression model is $Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$. When $\beta_1$ is linearly depended on $X_2$, the original model becomes $$Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$$ $$= \beta_0 + (aX_2 +b)X_1 + \beta_2 X_2 + \epsilon$$ $$= \beta_0 + b X_1 + \beta_2 X_2 + a X_1 X_2 + \epsilon$$ $$= \gamma_0 + \gamma_1 X_1+ \gamma_2 X_2 + \gamma_3 X_1 X_2 + \epsilon.$$
As you can see, collinearity and interaction affect the original model in different ways.
If we denote $X_3=X_1 X_2$, the above regression model with interaction is just a new model with one new $X_3$ variable added. Will introduction of $X_3=X_1 X_2$ cause overfitting? It depends. On the one hand, if there is really interaction, then you may underfit if you don't include the interaction term in the model. On the other hand, you may overfit it if you add an interaction term but there is actually no interaction. In addtion, no matter the new term added is $X_3=X_1 X_2$ or any other $X_4$, as long as you introduce more variables to the model, the risk of overfitting arises.
The interpretation of the model is affected by the interaction term. When explaining $Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \epsilon$, you may say "with $X_2$ fixed, as $X_1$ increases by 1 unit, Y increases by $\beta_1$ units". However, when explaining $Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_1 X_2 + \epsilon$, you should say "with $X_2$ fixed, as $X_1$ increases by 1 unit, Y increases by $\beta_1+\beta_3 X_2$ units". Here you can see the unit contribution of $X_1$ to $Y$ is a function of $X_2$, which means "interaction".
