  We present an approach for modeling and imputation of nonignorable missing
data under Gaussian copulas. The analyst posits a set of quantiles of the
marginal distributions of the study variables, for example, reflecting
information from external data sources or elicited expert opinion. When these
quantiles are accurately specified, we prove it is possible to consistently
estimate the copula correlation and perform multiple imputation in the presence
of nonignorable missing data. We develop algorithms for estimation and
imputation that are computationally efficient, which we evaluate in simulation
studies of multiple imputation inferences. We apply the model to analyze
associations between lead exposure levels and end-of-grade test scores for
170,000 students in North Carolina. These measurements are not missing at
random, as children deemed at-risk for high lead exposure are more likely to be
measured. We construct plausible marginal quantiles for lead exposure using
national statistics provided by the Centers for Disease Control and Prevention.
Complete cases and missing at random analyses appear to underestimate the
relationships between certain variables and end-of-grade test scores, while
multiple imputation inferences under our model support stronger adverse
associations between lead exposure and educational outcomes.
