Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables

• Published in: Mathematics (Basel) Vol. 9; no. 6; p. 609
• Main Authors: Rueda, María del Mar, Cobo, Beatriz, Arcos, Antonio
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.03.2021
• Subjects: complex sampling designs; Crime; Food science; Generalized linear models; Population; Random variables; randomized response techniques; Regression analysis; Regression coefficients; Regression models; Statistical analysis
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math9060609

Randomized response (RR) techniques are widely used in research involving sensitive variables, such as drugs, violence or crime, especially when a population mean or prevalence must be estimated. However, they are not generally applied to examine relationships between a sensitive variable and other characteristics. This type of technique was initially applied to qualitative variables, and studies later showed that a logistic regression may be performed with RR data. Since many of the variables considered in this context are quantitative, RR techniques were extended to these cases to estimate the values required. Regression analysis is a valuable statistical tool for exploring relationships among variables and for establishing associations between responses and covariates. In this article, we propose a design-based regression analysis for complex sample designs based on the unified RR approach. We present estimators of the regression coefficients, study their theoretical properties and consider different ways to estimate their variance. The properties of these estimation techniques were simulated using various quantitative randomized models. The method proposed was also used to analyse the findings from a real-world survey.