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Abstract:
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“All or nothing” data is an instance where the response variable, y, is either equal to its auxiliary variable, x, with probability p, or 0 with probability 1-p, where p is a constant, but typically unknown, value between 0 and 1. The accuracy of estimating total values using design based and model based estimation for “all or nothing” data is a studied in this paper. An auxiliary variable (x) was simulated using the gamma distribution as it is a common distribution found in tax data. The response variable (y) was randomly assigned for a specified probability, p. Mean squared error and confidence interval coverage was assessed across different scenarios, using different population sizes, sample sizes, and probability rates. The scenarios detected under coverage in extreme settings where there were both small sample sizes and a p near 0 or 1. The research is directly applicable to many tax applications studies that estimate a tax credit or a tax deduction. In all cases costs (x) are known for an entire population, but the qualifying costs (y) amount are unknown except on sampled records. Due to complicated tax laws, either the entire cost (x) qualifies or none of it.
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