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Fractional hot deck imputation (FHDI), proposed by Kalton and Kish (1984) and investigated by Kim and Fuller (2004), is a tool for handling item nonresponse in survey sampling. In FHDI, each missing item is filled with multiple observed values yielding a single completed data set for subsequent analyses. An R package FHDI is developed to perform FHDI and also the fully efficient fractional imputation (FEFI) method of (Fuller and Kim, 2005) to impute multivariate missing data with arbitrary missing patterns. FHDI substitutes missing items with a few observed values jointly obtained from a set of donors whereas the FEFI uses all the possible donors. This paper introduces FHDI as a tool for implementing the multivariate version of fractional hot deck imputation discussed in Im et al. (2015) as well as FEFI. For variance estimation of FHDI and FEFI, the Jackknife method is implemented, and replicated weights are provided as a part of the output.

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Propensity score weighting adjustment is commonly used to handle unit nonresponse. When the response mechanism is nonignorable in the sense that the response probability depends directly on the study variable, a followup sample is commonly used to obtain an unbiased estimator using the framework of two-phase sampling, where the follow-up sample is assumed to respond completely. In practice, the followup sample is also subject to missingness. We consider propensity score weighting adjustment for nonignorable nonresponse when there are several follow-ups and the final follow-up sample is also subject to missingness. We propose two methods, one using calibration weighting and the other using a conditional likelihood using a so-called reverse conditional probability. Both methods provides consistent estimates under correct specification of the response model. A limited simulation study is used to compare the estimators. The proposed methods are applied to the real data example in a Korean household survey of employment.

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