Using Mixture Models for Heaped Data with Rounded Responses and True Spikes

• Activity Number: 426
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Minsun Riddles* and Sharon Lohr and Ardeshir Eftekharzadeh
• Companies: Westat and Westat and IRS
• Keywords: Rounding ; Density estimation ; Missing data ; Income data

Abstract

Survey respondents often round their answers to questions about quantities such as number of cigarettes smoked, annual income, or amount of time or money spent on tax preparation. This rounding can create heaping at particular values. For example, a person might report an income of $50,000 when the actual value is $47,332. This will cause a histogram of the data to have a higher value at $50,000 than in neighboring bins. In some cases, however, there may be a true spike causing the heaping: if many persons use a tax preparation software package that is priced at $40, some of the data heaping at $40 may represent the true value rather than a rounded quantity. We develop a likelihood-based approach for estimating the underlying distribution of a quantity of interest when the values are heaped, using a mixture model to capture components of true spikes as well as rounding.