Sex, lies and self-reported counts: Bayesian mixture models for heaping in longitudinal count data via birth–death processes

Abstract

Surveys often ask respondents to report non-negative counts, but respondents may misremember or round to a nearby multiple of 5 or 10. This phenomenon is called heaping, and the error inherent in heaped self-reported numbers can bias estimation. Heaped data may be collected cross-sectionally or longitudinally and there may be covariates that complicate the inferential task. Heaping is a well-known issue in many survey settings, and inference for heaped data is an important statistical problem. We propose a novel reporting distribution whose underlying parameters are readily interpretable as rates of misremembering and rounding. The process accommodates a variety of heaping grids and allows for quasi-heaping to values nearly but not equal to heaping multiples. We present a Bayesian hierarchical model for longitudinal samples with covariates to infer both the unobserved true distribution of counts and the parameters that control the heaping process. Finally, we apply our methods to longitudinal self-reported counts of sex partners in a study of high-risk behavior in HIV-positive youth.

Generalized Inflated Discrete Models: A Strategy to Work with Multimodal Discrete Distributions

“…In addition, the current study adopted a mixed method that used a logit model for the inflated probabilities without further elaborating the mechanism of inflation. Previous studies have shown that the inflation or heaping on certain values may be due to rounding to nearby popular values (Crawford et al, 2015;Wang & Heitjan, 2008). We hope that the current work can stimulate further developments that incorporate various measurement models.…”

“…Data inflation may take various forms. It could be that respondents forget the information, or round to a nearby number of convenience (Crawford, Weiss, & Suchard, 2015); it can also be the result of hiding one's ignorance in situations where face-saving is deemed important (Bagozzi & Mukherjee, 2012). In other scenarios, measures on counts or summarized items, e.g., the number of hospital visits and the delinquency scale, may naturally concentrate on values of zero, or low occurrences such as one or two.…”

Kernel Density Estimation for Heaped Data

“…Wang and Heitjan (2008) proposed a model for heaped cigerate counts. A recent work of Crawford et al (2014) formulated a general model for count data involving birth-death processes and applied this to the self-reported counts of the number of sex-partners. In addition, Bar and Lillard (2012) lately developed an approach for event time data by modeling the density by a mixture of two parametric distributions.…”

“…Both applications indicated that these assumptions are not completely fullfilled in real-world data. As Crawford et al (2014) remarks, the assumption that, for example, a reported value of W i = 100 with rounding value R i = 10 means that the true unobserved value X i lies inside the interval (95,105) is rather strong. A possible solution would be to decompose the reporting process into an recall error (i.e.…”

Estimating the number of casualties in the American Indian war: A Bayesian analysis using the power law distribution

“…A further source of error that is present is rounding or heaping (Crawford, Weiss and Suchard, 2015). From Table 1 there is clear evidence that the number casualties have been rounded to the nearest five: for the Native American's there were 69 and 51 events where the number of casualties was 4 and 6 respectively, whereas there were 126 recorded conflicts where the number of casualties was 5.…”