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Income distributions tend to be highly skewed. Yet the American Community Survey (ACS) provides only two summary statistics for its median income estimates in small areas: the mean estimate and a standard error. I want to build a Bayesian error-in-variables model that uses a latent unknown zip-code-level income estimate as a covariate, with the the latent median income variable estimated from the zip-code-level estimate and standard error from the ACS. I don't want to assume a normal error distribution because, for many small zip codes with low median income, that allows for negative income. I don't want to use a higher level of geographic aggregation because the problem remains anyway and because there is a much more linear (thus more tractably estimated) relationship between zip-code-level median income estimates and the outcome variable of interest, but not so at higher levels of aggregation.

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