# What does multiplicativity and additivity mean in the context of regression?

I frequently read that multiplicativity and additivity applies to this and that in various forms of regression. However, in the textbooks I've read, no authors seems to declare what that actually means. This is perhaps a shortcoming of many textbooks on regression, since they all explain how to interpret individual parameter estimates/coefficients, but few (if any) explain how and whether parameter estimates can be added to each other.

Grateful for any advice on how multiplicativity and additivity applies to regression, and whether there are difference in linear, logistic and Cox regression or perhaps interpreted in the same way?

Typical textbook (Mastering Public Health: A Postgraduate Guide to Examinations and Revalidation, Second Edition, Edition 2) stating that the above:

• Can you give some examples of what you have read? (quotes, with references, please) ... it's difficult to discuss what you might have read in the abstract. – Glen_b Feb 14 '16 at 9:04
• I don't have any particular text in mind, since it's something I've came a cross many times. But I did a quick search on Google and found the above textbook, from which I took a screenshot (second column). – Adam Robinsson Feb 14 '16 at 9:08
• Thanks; I, at least, wouldn't have guessed that was quite the sort of thing you meant. – Glen_b Feb 14 '16 at 9:12

What they mean here is that the interpretation of the parameter estimates varies in terms of how one unit change in an independent variable is related to the dependent variable.

In ordinary least squares regression, each one unit change in the IV is associated with the same change in the DV - that change is expressed by the parameter estimate. So, if you have one IV and the parameter estimates are $b_0 = 30$ and $b_1 = 3.5$ then the predicted $Y$ goes from $30$ to $33.5$ to $37$ as $X_1$ goes from $0$ to $1$ to $2$.

In multiplicative regression models, on the other hand, it would be a multiple. That is, at $X_1 = 1$ it would be $3.5$ times the value for $X_1 = 0$ and for $X_1 = 2$ it would be $3.5$ times the value for $X_1$.