Multiple Imputation for Combined-Survey Estimation with Incomplete Regressors in One but Not Both Surveys

Within-survey multiple imputation (MI) methods are adapted to pooled-survey regression estimation where one survey has more regressors, but typically fewer observations, than the other. This adaptation is achieved through (1) larger numbers of imputations to compensate for the higher fraction of missing values, (2) model-fit statistics to check the assumption that the two surveys sample from a common universe, and (3) specifying the analysis model completely from variables present in the survey with the larger set of regressors, thereby excluding variables never jointly observed. In contrast to the typical within-survey MI context, cross-survey missingness is monotonic and easily satisfies the missing at random assumption needed for unbiased MI. Large efficiency gains and substantial reduction in omitted variable bias are demonstrated in an application to sociodemographic differences in the risk of child obesity estimated from two nationally representative cohort surveys.