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REGRESSION ANALYSIS USING SCRAMBLED RESPONSES
Author(s) -
Singh Sarjinder,
Joarder A.H.,
King Maxwell L.
Publication year - 1996
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1996.tb00676.x
Subject(s) - scrambling , null hypothesis , wald test , statistics , linear regression , confidence interval , regression analysis , regression , mathematics
Summary This paper investigates the general linear regression model Y = Xβ + e assuming the dependent variable is observed as a scrambled response using Eichhorn & Hayre's (1983) approach to collecting sensitive personal information. The estimates of the parameters in the model remain unbiased, but the variances of the estimates increase due to scrambling. The Wald test of the null hypothesis H 0 : β=β 0 , against the alternative hypothesis H a : β#β 0 , is also investigated. Parameter estimates obtained from scrambled responses are compared to those from conventional or direct‐question surveys, using simulation. The coverage by nominal 95% confidence intervals is also reported.