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I want to model the effect of Level (continuous) of different Additives (categorical) on Y (continuous) by fitting a linear model, so my data is going to look like this:

Additive   Level   Y
A            1     2.3
A            2     4.5
A            3     6.7
 <snip>
B            1     8.9
B            2     1.0
 etc.

I could fit that with something like Y ~ Level %in% Additive

But what about zero level? At zero level additive identity doesn't mean anything. I don't want to include another variable indicating whether any additive is present because that would split off the zero level data. I want the zero level data to be used in estimating the regressions for all the Additives, but I don't know how to enter the data, never mind how to specify the model!

It feels as if this must be a recognised situation with "standard" approaches. I've hit it before but never resolved it to my own satisfaction, now it's arisen again. Can anyone point me in the right direction?

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  • $\begingroup$ Answering my own question, at least to an extent. I think I was seeing a problem where there wasn't one, perhaps because Minitab gave me an "insufficient rank" error when fitting a nested model to data containing several 'Additive = None, Level = 0' rows. R gave me an answer with Y ~ Level %in% Additive. Perhaps the way to think of it is to lose the categorical 'Additive' column and have a different continuous 'Level' column for each Additive; no additive is just zero in all the Level columns. I think Minitab may be able to fit such a model by multiple linear regression; I'll try on Monday. $\endgroup$
    – user20637
    Mar 23, 2013 at 9:57
  • $\begingroup$ My previous comment was correct. R fits just the model I need with Y ~ Level %in% Additive. In Minitab I can get the same fit but I need a separate Level column for each 'Additive'. Sorry for the waste of bandwidth. $\endgroup$
    – user20637
    Mar 25, 2013 at 12:53

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