I am trying to implement in R the formula used by Nahorniak et al. (2015) to calculate inverse sample probabilities. But, unfortunately, I don't have the necessary knowledge to do it. For context, the authors use those probabilities to resample from sample data produced by complex survey designs (e.g., an unequal probability sample) and generate data that might be analyzed as produced by simple random sampling. This approach is called "inverse probability bootstrap sampling" by the authors. It is considered a type of "pseudo-inverse sampling" by Seeskin et al. (2017). The objective is to use techniques not yet implemented by specialized software like the survey package in R.
The equation is this one.
where:
- Pi is the probability that a given element, i, of a sample of size N, is included in the original, unequal probability sample.
- Pi,ipb is the inverse sample probability assigned to element i.
- The quantity Pi,ipb is the inverse of the original sampling probability, scaled such that the sum of all Pi,ipb is equal to one.
Normally, I would use some R package that is already programmed. Still, in this case, I don't know what package I could use, either for obtaining the results of this formula applied to my data or, even better, for imitating the whole process followed by the authors and apply it to my data.
I'm not sure I understand the formula correctly and how I should implement it. I have tried to code it but without success.
References:
- Nahorniak, M., Larsen, D. P., Volk, C., & Jordan, C. E. (2015). Using Inverse Probability Bootstrap Sampling to Eliminate Sample Induced Bias in Model-Based Analysis of Unequal Probability Samples. PLOS ONE, 10(6). https://doi.org/10.1371/journal.pone.0131765
- Seeskin, Z. H., Mulrow, E., Bechara, J., & Ma, Q. (2017). Inverse Sampling: Investigating a Tool for Model Estimation with Complex Survey Data.