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Suppose I have 5 predictor variables, a binary response variable, and 100 data points. I want to try to predict what the chance of the binary response being -1 or 1 is, but 99 of the response values are -1.

What is the best way to go about making predictions on this data set (with heavily 'skewed' responses) without collecting additional data?

To clarify, it is clear that a model fitted to this data will probably do a bad job classifying new data. Can we, for example, make up data in order to improve the results? What are some other ways to try to get a better idea of what the data might look like at 1000 samples?

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I guess that by "make predictions" you mean find a predictively accurate model, since you already know the true response values for this data.

Logistic regression is the usual tool for probabilistic classification. It's hard to guess in advance whether it will be able to beat the trivial model that guesses a probability of .99 for every case, but you can try it. Fancier models are unlikely to do better in this situation.

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  • $\begingroup$ I've added a follow up to my question, I think there might have been some confusion. Thanks! $\endgroup$
    – 114
    Commented Oct 5, 2016 at 19:25
  • $\begingroup$ @114 Regarding your first question, I'm not sure what you would expect to get out of simulated data here. Regarding your second, under the usual assumption of IID sampling, a sample of 1,000 would be most likely to look like the sample of 100 you already have. $\endgroup$
    – Kodiologist
    Commented Oct 5, 2016 at 22:06

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