On assuming additivity and linearity — redux

20 Oct, 2013 at 17:07 | Posted in Statistics & Econometrics | 1 Comment

In an article posted here a couple of weeks ago — What are the key assumptions of linear regression models? — yours truly tried to argue that since econometrics doesn’t content itself with only making “optimal predictions,” but also aspires to explain things in terms of causes and effects, econometricians need loads of assumptions — and that most important of these are additivity and linearity.

Let me take the opportunity to cite one of my favourite introductory statistics textbooks on one further reason these assumptions are made — and why they ought to be much more argued for on both epistemological and ontological grounds when used (emphasis added):

In a hypothesis test … the sample comes from an unknown population. If the population is really unknown, it would suggest that we do not know the standard deviation, and therefore, we cannot calculate the standard error. gravetterTo solve this dilemma, we have made an assumption. Specifically, we assume that the standard deviation for the unknown population (after treatment) is the same as it was for the population before treatment.

Actually this assumption is the consequence of a more general assumption that is part of many statistical procedure. The general assumption states that the effect of the treatment is to add a constant amount to … every score in the population … You should also note that this assumption is a theoretical ideal. In actual experiments, a treatment generally does not show a perfect and consistent additive effect.

1 Comment

  1. More generally, one has estimates such as P(A|B:C), for a context C, and wishes to estimate P(A|B:C’) for some other context, such as ‘in the future’. This is difficult unless ‘the future is like the past’ (i.e., no interventions) or P(A|B) is regarded as largely context-independent, and in this sense causal. This doesn’t seem to be a problem, unless you just take it for granted. For example, in 2005-2008 many assumed stability without looking at the factors on which that stability depended.

    Additivity and linearity seem to be a special case.

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