Identification of Expected Outcomes in a Data Error Mixing Model With Multiplicative Mean Independence

We consider the problem of identifying a mean outcome in corrupt sampling where the observed outcome is drawn from a mixture of the distribution of interest and another distribution. Relaxing the contaminated sampling assumption that the outcome is statistically independent of the mixing process, we assess the identifying power of an assumption that the conditional means of the distributions differ by a factor of proportionality. For binary outcomes, we consider the special case that all draws from the alternative distribution are erroneous. We illustrate how these models can inform researchers about illicit drug use in the presence of reporting errors.