I have a dataset with socioeconomic information of the poorest households of a country. Each observation is associated with a vulnerability index (in a 0-100 scale) calculated using some of the variables of the dataset. This index is used to prioritize which households should have access to public programs. I want to replicate this index in other datasets that collected the same information (i.e that derive from questionnares that included the same questions). However, I don't know which variables were used to calculate it (some information was collected for a different purpose than construction of the index) nor the weight that was given to those that were actually used.
I was planning to predict the index using the variables of the dataset but I really don't know which method I should use. Any ideas?
Dear Santiago Valdivieso
Generally, One common approach to index replication involves using a subset of the assets present in the benchmark portfolio. Typically, replicating portfolios will hold the assets that have the largest weights in the benchmark, which are often the most liquid.
I think this article (https://lipperalpha.refinitiv.com/2015/08/index-replication-principles-and-applications/), Have a look.
Kind Regards
Qamar Ul Islam
Considering simply, I would suggest regression models. Of course, since you are not aware of the exact variables used to create the index, it would be difficult to refigure out the original relationship between features and the scores. Split the original scored dataset into train and test, train the model to get acceptable performance and apply the model to the new data afterwards, given that the features collected are in the same scales and setting as the original scored data.
Getting even more naive, I would think a clustering-like algorithm such K-nearest neighbors should work fine as well. The advantage would be that the model is not assuming a relationship between features and target, but the similarity between the original scored data and the new data.
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