The Effect of Microaggregation Procedures on the Estimation of Linear Models: A Simulation Study

Microaggregation is a set of procedures that distort empirical data in order to guarantee the factual anonymity of the data. At the same time the information content of data sets should not be reduced too much and should still be useful for scientific research. This paper investigates the effect of microaggregation on the estimation of a linear regression by ordinary least squares. It studies, by way of an extensive simulation experiment, the bias of the slope parameter estimator induced by various microaggregation techniques. Some microaggregation procedures lead to consistent estimates while others imply an asymptotic bias for the estimator

p-probabilistic k-anonymous microaggregation for the anonymization of surveys with uncertain participation

We develop a probabilistic variant of k-anonymous microaggregation which we term p-probabilistic resorting to a statistical model of respondent participation in order to aggregate quasi-identifiers in such a manner that k-anonymity is concordantly enforced with a parametric probabilistic guarantee. Succinctly owing the possibility that some respondents may not finally participate, sufficiently larger cells are created striving to satisfy k-anonymity with probability at least p. The microaggregation function is designed before the respondents submit their confidential data. More precisely, a specification of the function is sent to them which they may verify and apply to their quasi-identifying demographic variables prior to submitting the microaggregated data along with the confidential attributes to an authorized repository. We propose a number of metrics to assess the performance of our probabilistic approach in terms of anonymity and distortion which we proceed to investigate theoretically in depth and empirically with synthetic and standardized data. We stress that in addition to constituting a functional extension of traditional microaggregation, thereby broadening its applicability to the anonymization of statistical databases in a wide variety of contexts, the relaxation of trust assumptions is arguably expected to have a considerable impact on user acceptance and ultimately on data utility through mere availability.Peer ReviewedPostprint (author's final draft

Estimation of a Linear Regression under Microaggregation with the Response Variable as a Sorting Variable

Microaggregation is one of the most frequently applied statistical disclosure control techniques for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. However, while reducing the disclosure risk of data files, the technique also affects the results of statistical analyses. The paper deals with the impact of microaggregation on a linear model in continuous variables. We show that parameter estimates are biased if the dependent variable is used to form the groups. Using this result, we develop a consistent estimator that removes the aggregation bias. Moreover, we derive the asymptotic covariance matrix of the corrected least squares estimator

The Effect of Single-Axis Sorting on the Estimation of a Linear Regression

Microaggregation is one of the most important statistical disclosure control techniques for continuous data. The basic principle of microaggregation is to group the observations in a data set and to replace them by their corresponding group means. In this paper, we consider single-axis sorting, a frequently applied microaggregation technique where the formation of groups depends on the magnitude of a sorting variable related to the variables in the data set. The paper deals with the impact of this technique on a linear model in continuous variables. We show that parameter estimates are asymptotically biased if the sorting variable depends on the response variable of the linear model. Using this result, we develop a consistent estimator that removes the aggregation bias. Moreover, we derive the asymptotic covariance matrix of the corrected least squares estimator

DATA CLUSTERING AND MICRO-PERTURBATION FOR PRIVACY-PRESERVING DATA SHARING AND ANALYSIS

Clustering-based data masking approaches are widely used for privacy-preserving data sharing and data mining. Existing approaches, however, cannot cope with the situation where confidential attributes are categorical. For numeric data, these approaches are also unable to preserve important statistical properties such as variance and covariance of the data. We propose a new approach that handles these problems effectively. The proposed approach adopts a minimum spanning tree technique for clustering data and a micro-perturbation method for masking data. Our approach is novel in that it (i) incorporates an entropy-based measure, which represents the disclosure risk of the categorical confidential attribute, into the traditional distance measure used for clustering in an innovative way; and (ii) introduces the notion of cluster-level microperturbation (as opposed to conventional micro-aggregation) for masking data, to preserve the statistical properties of the data. We provide both analytical and empirical justification for the proposed methodology

Modeling projections in microaggregation

Microaggregation is a method used by statistical agencies to limit the disclosure of sensitive microdata. It has been proven that microaggregation is an NP-hard problem when more than one variable is microaggregated at the same time. To solve this problem in a heuristic way, a few methods based on projections have been introduced in the literature. The main drawback of such methods is that the projected axis is computed maximizing a statistical property (e.g., the global variance of the data), disregarding the fact that the aim of microaggregation is to keep the disclosure risk as low as possible for all records. In this paper we present some preliminary results on the application of aggregation functions for computing the projected axis. We show that, using the Sugeno integral to calculate the projected axis, we can reduce in some cases the disclosure risk of the protected data (when projected microaggregation is used).Postprint (author’s final draft