  We analyze longitudinal self-reported counts of sexual partners from youth
living with HIV. In self-reported survey data, subjects recall counts of events
or behaviors such as the number of sexual partners or the number of drug uses
in the past three months. Subjects with small counts may report the exact
number, whereas subjects with large counts may have difficulty recalling the
exact number. Thus, self-reported counts are noisy, and mis-reporting induces
errors in the count variable. As a naive method for analyzing self-reported
counts, the Poisson random effects model treats the observed counts as true
counts and reporting errors in the outcome variable are ignored. Inferences are
therefore based on incorrect information and may lead to conclusions
unsupported by the data. We describe a Bayesian model for analyzing
longitudinal self-reported count data that formally accounts for reporting
error. We model reported counts conditional on underlying true counts using a
linear birth-death process and use a Poisson random effects model to model the
underlying true counts. A regression version of our model can identify
characteristics of subjects with greater or lesser reporting error. We
demonstrate several approaches to prior specification.
