Methods for Imputing Missing Values and Synthesizing Confidential Values for Continuous and Magnitude Data

Abstract

Continuous variable is one of the major data types collected by the survey organizations. It can be incomplete such that the data collectors need to fill in the missingness. Or, it can contain sensitive information which needs protection from re-identification. One of the approaches to protect continuous microdata is to sum them up according to different cells of features. In this thesis, I represents novel methods of multiple imputation (MI) that can be applied to impute missing values and synthesize confidential values for continuous and magnitude data.

The first method is for limiting the disclosure risk of the continuous microdata whose marginal sums are fixed. The motivation for developing such a method comes from the magnitude tables of non-negative integer values in economic surveys. I present approaches based on a mixture of Poisson distributions to describe the multivariate distribution so that the marginals of the synthetic data are guaranteed to sum to the original totals. At the same time, I present methods for assessing disclosure risks in releasing such synthetic magnitude microdata. The illustration on a survey of manufacturing establishments shows that the disclosure risks are low while the information loss is acceptable.

The second method is for releasing synthetic continuous micro data by a nonstandard MI method. Traditionally, MI fits a model on the confidential values and then generates multiple synthetic datasets from this model. Its disclosure risk tends to be high, especially when the original data contain extreme values. I present a nonstandard MI approach conditioned on the protective intervals. Its basic idea is to estimate the model parameters from these intervals rather than the confidential values. The encouraging results of simple simulation studies suggest the potential of this new approach in limiting the posterior disclosure risk.

The third method is for imputing missing values in continuous and categorical variables. It is extended from a hierarchically coupled mixture model with local dependence. However, the new method separates the variables into non-focused (e.g., almost-fully-observed) and focused (e.g., missing-a-lot) ones. The sub-model structure of focused variables is more complex than that of non-focused ones. At the same time, their cluster indicators are linked together by tensor factorization and the focused continuous variables depend locally on non-focused values. The model properties suggest that moving the strongly associated non-focused variables to the side of focused ones can help to improve estimation accuracy, which is examined by several simulation studies. And this method is applied to data from the American Community Survey.

(Table 1) Comparison of diatom-bound and bulk sedimentary d15N values of ODP Holes 175-1082A and 175-1084A

The Matuyama Diatom Maximum (MDM) is a time of peak opal accumulation from 2.6 to ~2.0 Ma within the Benguela Current upwelling system that was initiated by increased influence of Southern Ocean water on the eastern South Atlantic. We measured opal, total organic carbon (TOC), and CaCO3 fluxes and C and N stable isotopes in sediments deposited from 2.4 to 1.95 Ma at Sites 1082 and 1084 to explore the biogeochemical dynamics within the Benguela region. The infusion of Southern Ocean water delivered dissolved nutrients and Southern Ocean flora and fauna, resulting in local opal accumulation increasing up to 8 g/cm**2/ky and the production of diatom mats. Some d15N measurements of diatom-bound organic matter indicate that the mats grew within the Benguela region. The bulk sediment d15N records are taken to reflect changes in the d15N of nitrate in the incoming water, where lower values at 2.4 Ma reflect less nitrate utilization in the Antarctic. A long-term increase in relative nitrate uptake in the Southern Ocean is evidenced by the gradual increase in d15N toward 1.9 Ma.

Global distributions of diazotrophs abundance and biomass - Depth integrated values computed from a collection of source datasets - Contribution to the MAREDAT World Ocean Atlas of Plankton Functional Types

The MAREDAT atlas covers 11 types of plankton, ranging in size from bacteria to jellyfish. Together, these plankton groups determine the health and productivity of the global ocean and play a vital role in the global carbon cycle. Working within a uniform and consistent spatial and depth grid (map) of the global ocean, the researchers compiled thousands and tens of thousands of data points to identify regions of plankton abundance and scarcity as well as areas of data abundance and scarcity. At many of the grid points, the MAREDAT team accomplished the difficult conversion from abundance (numbers of organisms) to biomass (carbon mass of organisms). The MAREDAT atlas provides an unprecedented global data set for ecological and biochemical analysis and modeling as well as a clear mandate for compiling additional existing data and for focusing future data gathering efforts on key groups in key areas of the ocean. The present data set presents depth integrated values of diazotrophs abundance and biomass, computed from a collection of source data sets.