  Social scientists are interested in studying the impact that citizenship
status has on health insurance coverage among immigrants in the United States.
This can be done using data from the Survey of Income and Program Participation
(SIPP); however, two primary challenges emerge. First, statistical models must
account for the survey design in some fashion to reduce the risk of bias due to
informative sampling. Second, it has been observed that survey respondents
misreport citizenship status at nontrivial rates. This too can induce bias
within a statistical model. Thus, we propose the use of a weighted
pseudo-likelihood mixture of categorical distributions, where the mixture
component is determined by the latent true response variable, in order to model
the misreported data. We illustrate through an empirical simulation study that
this approach can mitigate the two sources of bias attributable to the sample
design and misreporting. Importantly, our misreporting model can be further
used as a component in a deeper hierarchical model. With this in mind, we
conduct an analysis of the relationship between health insurance coverage and
citizenship status using data from the SIPP.
