Document Type : Original Paper
Authors
1 Statistics Dept, Faculty of Mathematical Sciences and Computer, Shahid Chamran university of Ahvaz, Ahvaz, Iran
2 Statistics dept., Mathematical Sciences and computer college, shahid Chamran university of Ahvaz, Ahvaz, Iran
3 Dept. of Statistics, Faculty Mathematical Sciences and Computer, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Abstract
Some social surveys address sensitive topics for which respondents do not report reliable responses. Randomized response techniques (RRTs) are employed to increase privacy levels and provide honest answers. However, estimates obtained from this method tend to exhibit increased variances. Repeating randomized responses for each individual increases the sample size, and the mean of observations for each individual reduces the variance of the parameter’s estimator, bringing them closer to reality. In this study, considering continuous additive repeated randomized responses (RRRs), we apply the averaged RR of each individual using the linear regression model for sensitive variable mean. Data on the income of family heads were collected from students and each respondent was asked to randomize their responses five times. The maximum likelihood estimators of parameters are obtained by two methods. In the first method, the response variable is the first reported observation and in the second method, we considered the averaged RR for each individual. The results emphasize that the estimators from the second method are closer to reality and have lower variance.
Keywords
- Randomized response
- Repeated randomized response
- linear regression model
- continuous sensitive variable
- repeated individual observations
Main Subjects
)