Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables

María del Mar Rueda, Beatriz Cobo and Antonio Arcos
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María del Mar Rueda: Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain
Beatriz Cobo: Department of Quantitative Methods for the Economy and Business, University of Granada, 18011 Granada, Spain
Antonio Arcos: Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain

Mathematics, 2021, vol. 9, issue 6, 1-13

Abstract: 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.

Keywords: regression models; randomized response techniques; complex sampling designs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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