What is more appropriate model - Additive or Multiplicative I have a data set consisting of 3 variables - distance, day, factor.
day : day of the week 
factor : before/after 
My data has weekly seasonality, ie, if I aggregate distances, then weekends are greater than weekdays etc. From Sunday to Saturday, it would be an U shape. 
I am interested in comparing before and after effect of an experiment. For that I am planning to do ANOVA.
My question is whether I should consider an additive model or an multiplicative model? How should I use the data to determine that?
 A: I assume you want to know the effect of the factor on distance, controlling for day of week.  
Multiplicative Interpretation
If you think that the factor changes distances by a proportion i.e. increases/decreases by 25 percent rather than by 25 meters, then you'd probably want to set it up as a count data regression e.g. Poisson regression or one of it's overdispersed variants, which would be implicitly multiplicative i.e. multiplicative by virtue of having a log link function.  But that would be primarily your choice rather than the data's.  
ANOVA?
A badly fitting ANOVA model would be a sign you might have jumped the wrong way on the function form (although it might be a sign of lots of other things too).  But in any case, ANOVA is a model that assumes with various levels of strictness, Normally and homoskedastically distributed cell values, so a priori it's an odd choice for zero bounded things like distance.  
Learning an appropriate transformation
You could, I suppose, also 'learn' that a multiplicative transformation would fit the Normality constraints by using a Box-Cox transformation and discovering that its preferred parameter transformation is one that amounts to logging the data.  Interpretation will be a little bit harder, and you will have forced the data into the model rather than matching the model to the data.  But that would work, if you're wedded to using ANOVA.
