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amended zc diffs #2

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amended zc diffs #2

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Alickbird
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Step 3 in https://sawtoothsoftware.com/forum/6140/is-there-a-formula-for-calculating-the-zero-centered-diffs seems to suggest multiplying 100 by the number of items before dividing by the sum of zc beta differences. Updated code to reflect this calculation.

@cnchapman
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Thank you! I'll test this and appreciate the review. BTW, besides the bug, we have been thinking about changes to this, and whether (for example) to default to exponentiated scores (e.g., e^beta/(1+e^beta)) as another option. We wonder if they might be easier to interpret.

@Alickbird
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No problem :) Yep, personally I think the exponentiated probability scores are easier to explain when presenting the results of maxdiff - mainly because (as I understand it) they'll be ratio scaled whereas the zero-centered diffs are not.

@cnchapman
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Thanks again! and apologies for the slow reply. IIUC multiplication by #items is not needed, because for MaxDiff -- as opposed to conjoint -- there is only 1 "attribute". The items are all part of a single attribute. This is slightly confusing in the Sawtooth doc, which is assuming multiple attributes (like price + size + brand, etc.)

@Alickbird
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A ha... I see, thanks for clarifying - in which case I've made the wrong change. Instead, I think for line 175 in maxdiff-estimate which reads: cmr.beta.zc.sumdiffs <- sum(colMaxs(as.matrix(cmr.beta.zc))-colMins(as.matrix(cmr.beta.zc))) should just be
cmr.beta.zc.sumdiffs <- max(cmr.beta.zc)-min(cmr.beta.zc), because all items are part of a single attribute?

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