A new improved randomized response model with application to compulsory motor insurance.

Area of Science:

• Statistics
• Survey Methodology
• Privacy-Preserving Data Analysis

Background:

• Investigating sensitive attributes in surveys presents privacy challenges.
• Traditional randomized response (RR) methods like Warner's model balance confidentiality with estimation but can lack efficiency.
• Increased likelihood of sensitive questions in RR models leads to higher estimation variance.

Purpose of the Study:

• To introduce a novel three-stage RR model as a more efficient and practical alternative to Warner's model.
• To assess the privacy protection and efficiency trade-offs of the proposed RR model.
• To apply the new RR model for estimating noncompliance in compulsory motor insurance.

Main Methods:

• Development of a new three-stage randomized response (RR) model.
• Calculation of a privacy protection measure for comparison.
• Application of the proposed model to estimate the noncompliance ratio in compulsory motor insurance.

Main Results:

• The proposed three-stage RR model demonstrates greater efficiency compared to Warner's and Mangat & Singh's RR models.
• The new model exhibits practical reliability when applied to a selected population.
• The study successfully estimated the noncompliance ratio for compulsory motor insurance using the proposed model.

Conclusions:

• The novel three-stage RR model offers an efficient and credible approach for surveying sensitive attributes.
• The model provides a reliable method for estimating noncompliance in compulsory motor insurance.
• This research contributes to improved data collection methods for sensitive information and policy prediction.