In the general linear model we assume that different factors have an additive effect on the measured numerical target. For example, in the model we can see that being a male adds, on average, 20 kg to the subjects' weigh and being from France reduce, on average, your weight by 4.5 kg. So the factors (like gender, country, education) have an additive effect on the numerical target (or dependent variable).

I think that in many cases it is more natural to assume that effect is not additive but multiplicative. Are there models that adopt this assumption. Of course one can take a logarithm of the target and then apply the additive model to the "new" target and then, by taking exponent of the sum of the additive effects we get a product of effects (so, a multiplicative model). But, in this approach we have two problems:

  1. Sometimes target is zero. So, we are cannot take a logarithm of it.
  2. By working with the logarithm of the target we do not minimize the square deviation from the original target.

I found related questions but they are not answered yet:

  1. How to model a multiplicative effect from this hypothesis?
  2. How to model a multiplicative effect of a parameter

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