How to account for missing observations in multivariate regression?

My research concerns the eBay feedback mechanism. users have a "feedback score" (total positive reviews less negative reviews) and a "feedback percentage " $\frac{positives}{positives+negatives}$.

Obviously feedback score can be set zero as a continuous explanatory variable, but how would I account for an impossible feedback percentage? For example if a seller has no feedback he cannot have a feedback percentage.

Would I just leave these blank in the dataset or should I account for them in some other way? Only 7/605 of the auction observations in my dataset have this problem but I do not want to simply omit them.

@Tom your idea is a standard way to cope with missing values - to create indicator column describing whether the filled-in value was actually missing or not. This does not lose any information and - depending on the further processing / model though - should go well. E.g. linear regression or tree-like modes will handle that.

• I disagree with the idea that this is considered "standard". It's like saying that the lack of a value has some kind of effect. It would be useful to include it if the OP was interested in studying the effect that a missing value has on his response variable, but in general is not standard. – Kevin Li Jul 18 '18 at 17:07
• Ah cheers man, really appreciate that! so when i come to interpret the results i would say something like "a seller that has a feedback percentage can expect an x% increase/derease in revenue and, for those that do, each additional percentage point loss decreases revenue by x amount" ? would that be correct? – Tom Witten Jul 18 '18 at 17:07
• Right, if I got your "rule" correctly, your model should learn kind of that way. And addtionally some "rule" for the case where the indicator column is 0 saying feedback percentage is not avaialble. – MkL Jul 18 '18 at 17:22

I would draw parallels to survey analysis. And as is the case with any survey analysis, imputation of survey responses will lead to the wrong conclusion on the survey. It is highly recommended to remove them from the data and you are not going to lose out a lot on your sample size anyways.

• could i create a binary dummy variable that states weather a user even has a feedback scrore and then examine the effect (of less than perfect percentages) for those that do? would that capture any additional effect? for project specific reasons i really don;t want to loose those observations – Tom Witten Jul 18 '18 at 16:26
• *should read dummy for feedback percentage, not feedback score – Tom Witten Jul 18 '18 at 17:02
• Could you give some more context on what you would be doing with the scores and percentages? – Srikrishna Jul 18 '18 at 17:16
• sure, i want to determine the effect of seller reputations on both likelihood of sale and effect on auction revenue on ebay. for likelihood of sale i was thinking of a probit model (althoug would appreciate any thoughts of better methods) of different variables on a binary indicator "SOLD". I then need to do a multivariate regression (on auction revenue) using reputation variables as well as other auction parameter controls (eg time of auction, opening price etc...). my main problem then is these missing values. – Tom Witten Jul 18 '18 at 17:48
• Got your problem. Yes, in that case it would certainly make sense to create a dummy for no feedback received, along with positive and negative feedback dummies as well. Also, the percentage you have penalises the positive feedback, maybe you should add in a percentage for negative as well. If you do that, I think you could impute blank percentages to zero for both. Let me know if this makes sense contextually. – Srikrishna Jul 18 '18 at 18:15