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Social scientists are interested in studying the impact that citizenshipstatus 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 mustaccount for the survey design in some fashion to reduce the risk of bias due toinformative sampling. Second, it has been observed that survey respondentsmisreport citizenship status at nontrivial rates. This too can induce biaswithin a statistical model. Thus, we propose the use of a weightedpseudo-likelihood mixture of categorical distributions, where the mixturecomponent is determined by the latent true response variable, in order to modelthe misreported data. We illustrate through an empirical simulation study thatthis approach can mitigate the two sources of bias attributable to the sampledesign and misreporting. Importantly, our misreporting model can be furtherused as a component in a deeper hierarchical model. With this in mind, weconduct an analysis of the relationship between health insurance coverage andcitizenship status using data from the SIPP.

The Link Between Health Insurance Coverage and Citizenship Among  Immigrants: Bayesian Unit-Level Regression Modeling of Categorical Survey  Data Observed with Measurement Error