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I'm in a situation where I'm fitting a GLM to a multivariate data set and presenting the outputs to a client. However (long story ...) I have just found out that the client needs the results to take an additive/multiplicative format. In other words, the model would be structured along the lines (I think) of:

Predicted Value = Base Value * (1 + additive_rel_1 + additive_rel_2 + ...) * multiplicative_rel_1 * multiplicative_rel_2 * ...

("rel": relativity)

If just additive, no problem with GLMs. If multiplicative, no problem with GLMs (using a log link function). With a hybrid of the two, what are my modelling options? Is there some modelling framework I can use to give me what I need?

Alan
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  • Could you give some more context? What does your variables represent? Why do you need this strange form? Look at https://stats.stackexchange.com/questions/142338/goodness-of-fit-and-which-model-to-choose-linear-regression-or-poisson/142353#142353, what you have can be seen as a (quasi)poisson regression with offset, log link and a nonlinear predictor function in place of the usual linear predictor. Such models can be estimated with the R gnm package, see this list. – kjetil b halvorsen Mar 03 '20 at 13:56
  • Just edited my post - I must have been half-asleep because the formula wasn't the one I wanted to show. The reason for needing to conform to this structure is that it's in use already to derive a price for an item using various lookup tables. I can change the numbers in the lookup tables but I can't change the lookup tables in the short term. – Alan Mar 03 '20 at 21:30
  • I still think you should have a go with gnm. Maybe you clarify your post even better by using mathemathical notation? – kjetil b halvorsen Mar 03 '20 at 21:51
  • Thank you. I’ve just found https://cran.r-project.org/web/packages/gnm/vignettes/gnmOverview.pdf so I’ll read through that when I have a moment, – Alan Mar 03 '20 at 21:59

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