Weighting Adjustment and Multiple Imputation for Addressing Nonresponse in A Multi-Day Diary Survey

Abstract In multi-day diary surveys, participants decide daily whether to continue. The day-level nonresponse can introduce nonresponse errors, and underreporting tends to increase over the data collection period. To address these problems, we propose an adjustment by either the construction of person-day level survey weights or multiple imputation (MI). This study used data from the US National Household Food Acquisition and Purchase Survey (FoodAPS) and focused on four key outcomes in this survey: the occurrence and expenditure of daily food-at-home (FAH) and food-away-from-home (FAFH) events reported by individuals. We employed logistic regression models and conditional inference trees to predict daily response propensities and used the inverse of predicted response propensity as an adjustment factor for the existing FoodAPS household weights. As an alternative, we conducted MI for the key outcome variables using chained equations and fit zero-inflated imputation models for counts and semi-continuous variables to allow bounds and subset restrictions. The results show that raw estimates for the key variables are consistently smaller than those produced by any weighting or imputation techniques, indicating that some form of adjustment is necessary. Person-day level weights and MI show varying impacts across outcome variables, with MI offering a modest efficiency gain. We also performed a sensitivity analysis that employs an alternative definition of missingness, which yielded different MI estimates. This study offers valuable insights into addressing nonresponse errors in multi-day diary surveys and contributes to methodological approaches for conducting innovative weighting and imputation with complex data structures.