I have a data set that includes locations of where certain rocks were observed on the Earth. Populated areas have a higher number of observations in general. Remote areas have less observations. I'm confident that the low number of observations in rural areas does not mean there are fewer rocks of that type present.

Is there a way to correct/reduce this bias? I've looked into oversampling and bias correction and have not been able to find something I think is appropriate.

My current thought is to look at each observation point, count the number of points that are near it, and use a PDF (Normal or Gaussian) to generate new points around that point. If the number of points near the original point is low, I will generate a larger number of new points. If there are a lot of points around the point, I will generate few (if any) new points. (Basically using rough estimates of the PDF parameters and number of surrounding points to add points to the data set).

Is this an acceptable way to supplement the data set with the goal of overcoming some of the bias? Is there something similar or a different approach I should use?

  • $\begingroup$ "generating new points" is a feasible approach. Basically it is imputation, and you would have to use multiple imputation: undersampling is basically a missing data problem when you know something about the observations you didn't sample: most importantly how many of them there are. In survey sciences, we would usually create a weighting variable which I think is more appropriate for your analysis. Your cursory explanation suggests to me you should just create a survey weight for your observations to downweight oversampled units. $\endgroup$ – AdamO Dec 13 '16 at 20:28
  • $\begingroup$ Thanks for the pointers. Maybe I'm not understanding the concept of missing data. The data is not missing values. I'm basically looking at x, y, z data where x = longitude, y = latitude, and z = rock type. All rows have all data. My main problem is there just aren't a lot of data points for Arizona where I know a lot of rocks are and there are a lot of data points for Georgia (which I doubt has 100 times more rocks than Arizona even though there are 100 times more observations). I'll look more into multiple imputation and survey weighting but at this point I still think I'm missing something. $\endgroup$ – JKU Dec 13 '16 at 20:45
  • $\begingroup$ I'm sure Arizona has many rocks. You should be thinking about the "rows" of X,Y,Z that you don't have. $\endgroup$ – AdamO Dec 13 '16 at 21:28
  • $\begingroup$ Thank you, that is exactly what I'm thinking about! I suppose I just don't yet understand how survey weighting or multiple imputation help me find those missing rows. $\endgroup$ – JKU Dec 13 '16 at 21:35
  • $\begingroup$ probably off-topic for a SE post. It's far too broad of a question. $\endgroup$ – AdamO Dec 13 '16 at 21:36

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