disclosure_z

Author: Source: Unknown - Date unknown Please cite: Data Used in "A BAYESIAN APPROACH TO DATA DISCLOSURE: OPTIMAL INTRUDER BEHAVIOR FOR CONTINUOUS DATA" by Stephen E. Fienberg, Udi E. Makov, and Ashish P. Sanil Background: ========== In this paper we develop an approach to data disclosure in survey settings by adopting a probabilistic definition of disclosure due to Dalenius. Our approach is based on the principle that a data collection agency must consider disclosure from the perspective of an intruder in order to efficiently evaluate data disclosure limitation procedures. The probabilistic definition and our attempt to study optimal intruder behavior lead naturally to a Bayesian formulation. We apply the methods in a small-scale simulation study using data adapted from an actual survey conducted by the Institute for Social Research at York University. (See Sections 1-3 of the paper for details oF the model formulation and related issues.) The Data: ======== Our case study uses data from the survey data Elite Canadian Decision-Makers collected by the Institute for Social Research at York University. This survey was conducted in 1981 using telephone interviews and there were 1348 respondents, but many of these did not supply complete data. We have extracted data on 12 variables, each of which was measured on a 5-point scale: Civil-liberties: - --------------- C1 - Free speech is just not worth it. C2 - We have gone too far in pushing equal rights in this country. C3 - It is better to live in an orderly society than to allow people so much freedom. C5 - Free speech ought to be allowed for all political groups. Attitudes towards Jews: - ---------------------- A15 - Most Jews don't care what happens to people who are not Jews. A18 - Jews are more willing than others to use shady practices to get ahead. Canada-US relationship: - ---------------------- CUS1 - Ensure independent Canada. CUS5 - Canada should have free trade with the USA. CUS6 - Canada's way of life is influenced strongly by USA. CUS7 - Canada benefits from US investments. In addition, we have data on two approximately continuous variables: Personal information: - -------------------- Income - Total family income before taxes (with top-coding at \$80,000). Age - Based on year of birth. We transformed the original survey data as follows in order to create a database of approximately continuous variables: [A] We add categorical variables (all but income) to increase the number of levels. (When necessary we reversed the order of levels of a response to a question.) The new variables are defined as follows: Civil = C1 + C2 + C3 + (8 - C5) Attitude = A15 + A18 Can/US = (5 - CUS1) + CUS5 + (5 - CUS6) + CUS7 After we removed cases with missing observations and two cases involving young children, we had a data-base consisting of 662 observations. [B] In order to enhance continuity, we took the following measures: Age: We added normal distributed variates, with 0 mean and variance 4 to all observations. Income: We added uniform variates on the range of $0 - $10,000 to all incomes below $80,000. Since all cases of incomes exceeding $80,000 were lumped together in the survey, we simulated their values by means of a t(8) distribution. Drawing values from the upper 38% tail of t(8), we evaluated the values of income as $60,000 + 25,000*t(8). Other variables: We added normal distributed variates, with 0 mean and variance 0.5 to the variables. We assume that the agency releases information about all variables, except for Attitudes (towards Jews), which is unavailable to the intruder and is at the center of the intruder's investigation. We denote the released data by Z = (( z(i,j) )) with i=1,..,662; j=1,2,3,4. We assume that the intruder's data, X, are accurate and are related to Z via the following transformation: x(0,j) = z(i,j)*theta(i,j) + xi(j), where theta(i,j) is a bias removing parameter normally distributed with mean 1 and variance v(j), and xi(j) is normally distributed disturbance with 0 mean and variance sigma2(j). The following table provides the values of v(j), sigma2(j) used in the study: v(j) sigma2(j) Civil 0.1732 25 Can/US 0.1732 25 Age 0.1732 9 Income (in $10000's) 0.1732 4 We first generated several realizations of the above transformation on small subsets of the data to ascertain the impact of the process of the error on the data. In Table 4-1 in the paper we present 10 records the the intruder's accurate data, X, and the biased and corrupted released data, Z, which we obtained from one realization of the transformation. Section 4.2 of the paper contains details of the implementation of our Bayesian model. Data Used in the Computations: ============================= We conducted a complete simulation of the procedures for the complete set of 662 cases. We considered four different scenarios for the simulation. (The names of datasets used in each of the scenarios appear in brackets below. The datasets are appended to this text.) * The released data contains no bias or noise (i.e. v(j)=0 and sigma2(j)=0 for all j). [Z.DATA] * The released data contains only noise (i.e., v(j)=0 for all j and and $sigma2(j)$ as given in the above Table). [X_NOISE.DATA] * The released data contains only bias (i.e., sigma2(j)=0 for all j and v(j) as given in the above Table). [X_BIAS.DATA] * The released data contains both bias and noise (i.e., v(j) and sigma2(j) as given in the above Table). [X_TAMPERED.DATA] We took each individual in turn as the object of the intruder's efforts and carried out the calculations. Structure of the Datasets: - ------------------------- Each attached dataset consists of four space-separated columns containing the data on Age, Civil, Can/US and Income ($) respectively. Dataset: Z Information about the dataset CLASSTYPE: numeric CLASSINDEX: none specific