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"description": "**Author**: \n**Source**: Unknown - Date unknown \n**Please cite**: \n\nData Used in \"A BAYESIAN APPROACH TO DATA DISCLOSURE: OPTIMAL\nINTRUDER BEHAVIOR FOR CONTINUOUS DATA\"\nby Stephen E. Fienberg, Udi E. Makov, and Ashish P. Sanil\n\nBackground:\n==========\nIn this paper we develop an approach to data disclosure in survey settings by\nadopting a probabilistic definition of disclosure due to Dalenius. Our approach\nis based on the principle that a data collection agency must consider\ndisclosure from the perspective of an intruder in order to efficiently evaluate\ndata disclosure limitation procedures. The probabilistic definition and our\nattempt to study optimal intruder behavior lead naturally to a Bayesian\nformulation. We apply the methods in a small-scale simulation study using data\nadapted from an actual survey conducted by the Institute for Social Research at\nYork University. (See Sections 1-3 of the paper for details oF the model\nformulation and related issues.)\n\nThe Data:\n========\nOur case study uses data from the survey data Elite Canadian\nDecision-Makers collected by the Institute for Social Research at York\nUniversity. This survey was conducted in 1981 using telephone\ninterviews and there were 1348 respondents, but many of these did not\nsupply complete data. We have extracted data on 12 variables, each of which\nwas measured on a 5-point scale:\n\nCivil-liberties:\n- ---------------\nC1 - Free speech is just not worth it.\nC2 - We have gone too far in pushing equal rights in this country.\nC3 - It is better to live in an orderly society than to allow people so\nmuch freedom.\nC5 - Free speech ought to be allowed for all political groups.\n\nAttitudes towards Jews:\n- ----------------------\nA15 - Most Jews don't care what happens to people who are not Jews.\nA18 - Jews are more willing than others to use shady practices to\nget ahead.\n\nCanada-US relationship:\n- ----------------------\nCUS1 - Ensure independent Canada.\nCUS5 - Canada should have free trade with the USA.\nCUS6 - Canada's way of life is influenced strongly by USA.\nCUS7 - Canada benefits from US investments.\n\n\nIn addition, we have data on two approximately continuous variables:\n\nPersonal information:\n- --------------------\nIncome - Total family income before taxes (with top-coding at \\$80,000).\nAge - Based on year of birth.\n\n\nWe transformed the original survey data as follows in order to create\na database of approximately continuous variables:\n\n[A] We add categorical variables (all but income) to increase the number\nof levels. (When necessary we reversed the order of levels of a response to a\nquestion.) The new variables are defined as follows:\n\nCivil = C1 + C2 + C3 + (8 - C5)\nAttitude = A15 + A18\nCan\/US = (5 - CUS1) + CUS5 + (5 - CUS6) + CUS7\n\nAfter we removed cases with missing observations and two cases involving\nyoung children, we had a data-base consisting of 662 observations.\n\n[B] In order to enhance continuity, we took the following measures:\n\nAge: We added normal distributed variates, with 0 mean and\nvariance 4 to all observations.\nIncome: We added uniform variates on the range of $0 - $10,000 to all incomes\nbelow $80,000. Since all cases of incomes exceeding $80,000 were\nlumped together in the survey, we simulated their values by means\nof a t(8) distribution. Drawing values from the upper 38% tail of t(8),\nwe evaluated the values of income as $60,000 + 25,000*t(8).\nOther variables: We added normal distributed variates, with 0 mean and\nvariance 0.5 to the variables.\n\nWe assume that the agency releases information about all\nvariables, except for Attitudes (towards Jews), which is unavailable to\nthe intruder and is at the center of the intruder's investigation.\n\nWe denote the released data by\n\nZ = (( z(i,j) )) with i=1,..,662; j=1,2,3,4.\n\nWe assume that the intruder's data, X, are accurate and are related to Z via\nthe following transformation:\nx(0,j) = z(i,j)*theta(i,j) + xi(j),\n\nwhere theta(i,j) is a bias removing parameter normally distributed with mean 1\nand variance v(j), and xi(j) is normally distributed disturbance with 0 mean\nand variance sigma2(j).\n\nThe following table provides the values of\nv(j), sigma2(j) used in the study:\n\nv(j) sigma2(j)\nCivil 0.1732 25\nCan\/US 0.1732 25\nAge 0.1732 9\nIncome (in $10000's) 0.1732 4\n\n\nWe first generated several realizations of the above transformation on small\nsubsets of the data to ascertain the impact of the process of the error\non the data. In Table 4-1 in the paper we present 10 records the the intruder's\naccurate data, X, and the biased and corrupted released data, Z, which we\nobtained from one realization of the transformation.\n\nSection 4.2 of the paper contains details of the implementation of our Bayesian\nmodel.\n\nData Used in the Computations:\n=============================\nWe conducted a complete simulation of the procedures for the complete set of\n662 cases. We considered four different scenarios for the simulation. (The\nnames of datasets used in each of the scenarios appear in brackets below. The\ndatasets are appended to this text.)\n\n* The released data contains no bias or noise (i.e. v(j)=0 and sigma2(j)=0 for\nall j). [Z.DATA]\n* The released data contains only noise (i.e., v(j)=0 for all j and\nand $sigma2(j)$ as given in the above Table). [X_NOISE.DATA]\n* The released data contains only bias (i.e., sigma2(j)=0 for all j and v(j)\nas given in the above Table). [X_BIAS.DATA]\n* The released data contains both bias and noise (i.e., v(j) and sigma2(j) as\ngiven in the above Table). [X_TAMPERED.DATA]\n\nWe took each individual in turn as the object of the intruder's efforts and\ncarried out the calculations.\n\nStructure of the Datasets:\n- -------------------------\nEach attached dataset consists of four space-separated columns containing the\ndata on Age, Civil, Can\/US and Income ($) respectively.\n\n\n\nDataset: Z\n\n\nInformation about the dataset\nCLASSTYPE: numeric\nCLASSINDEX: none specific",
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