Mathematics

Research

19 pages, 358 KiB

Open AccessArticle

Methods to Counter Self-Selection Bias in Estimations of the Distribution Function and Quantiles

by María del Mar Rueda, Sergio Martínez-Puertas and Luis Castro-Martín

Mathematics 2022, 10(24), 4726; https://doi.org/10.3390/math10244726 - 12 Dec 2022

Viewed by 2560

Many surveys are performed using non-probability methods such as web surveys, social networks surveys, or opt-in panels. The estimates made from these data sources are usually biased and must be adjusted to make them representative of the target population. Techniques to mitigate this [...] Read more.

Many surveys are performed using non-probability methods such as web surveys, social networks surveys, or opt-in panels. The estimates made from these data sources are usually biased and must be adjusted to make them representative of the target population. Techniques to mitigate this selection bias in non-probability samples often involve calibration, propensity score adjustment, or statistical matching. In this article, we consider the problem of estimating the finite population distribution function in the context of non-probability surveys and show how some methodologies formulated for linear parameters can be adapted to this functional parameter, both theoretically and empirically, thus enhancing the accuracy and efficiency of the estimates made. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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20 pages, 444 KiB

Open AccessArticle

Single Imputation Methods and Confidence Intervals for the Gini Index

by Encarnación Álvarez-Verdejo, Pablo J. Moya-Fernández and Juan F. Muñoz-Rosas

Mathematics 2021, 9(24), 3252; https://doi.org/10.3390/math9243252 - 15 Dec 2021

Cited by 3 | Viewed by 2432

Abstract

The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods [...] Read more.

The problem of missing data is a common feature in any study, and a single imputation method is often applied to deal with this problem. The first contribution of this paper is to analyse the empirical performance of some traditional single imputation methods when they are applied to the estimation of the Gini index, a popular measure of inequality used in many studies. Various methods for constructing confidence intervals for the Gini index are also empirically evaluated. We consider several empirical measures to analyse the performance of estimators and confidence intervals, allowing us to quantify the magnitude of the non-response bias problem. We find extremely large biases under certain non-response mechanisms, and this problem gets noticeably worse as the proportion of missing data increases. For a large correlation coefficient between the target and auxiliary variables, the regression imputation method may notably mitigate this bias problem, yielding appropriate mean square errors. We also find that confidence intervals have poor coverage rates when the probability of data being missing is not uniform, and that the regression imputation method substantially improves the handling of this problem as the correlation coefficient increases. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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24 pages, 1340 KiB

Open AccessArticle

Comparison of the Average Kappa Coefficients of Two Binary Diagnostic Tests with Missing Data

by José Antonio Roldán-Nofuentes and Saad Bouh Regad

Mathematics 2021, 9(21), 2834; https://doi.org/10.3390/math9212834 - 08 Nov 2021

Cited by 2 | Viewed by 1452

Abstract

The average kappa coefficient of a binary diagnostic test is a parameter that measures the average beyond-chance agreement between the diagnostic test and the gold standard. This parameter depends on the accuracy of the diagnostic test and also on the disease prevalence. This [...] Read more.

The average kappa coefficient of a binary diagnostic test is a parameter that measures the average beyond-chance agreement between the diagnostic test and the gold standard. This parameter depends on the accuracy of the diagnostic test and also on the disease prevalence. This article studies the comparison of the average kappa coefficients of two binary diagnostic tests when the gold standard is not applied to all individuals in a random sample. In this situation, known as partial disease verification, the disease status of some individuals is a missing piece of data. Assuming that the missing data mechanism is missing at random, the comparison of the average kappa coefficients is solved by applying two computational methods: the EM algorithm and the SEM algorithm. With the EM algorithm the parameters are estimated and with the SEM algorithm their variances-covariances are estimated. Simulation experiments have been carried out to study the sizes and powers of the hypothesis tests studied, obtaining that the proposed method has good asymptotic behavior. A function has been written in R to solve the proposed problem, and the results obtained have been applied to the diagnosis of Alzheimer's disease. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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40 pages, 2469 KiB

Open AccessArticle

A Map of the Poor or a Poor Map?

by Paul Corral, Kristen Himelein, Kevin McGee and Isabel Molina

Mathematics 2021, 9(21), 2780; https://doi.org/10.3390/math9212780 - 02 Nov 2021

Cited by 5 | Viewed by 2135

Abstract

This paper evaluates the performance of different small area estimation methods using model and design-based simulation experiments. Design-based simulation experiments are carried out using the Mexican Intra Censal survey as a census of roughly 3.9 million households from which 500 samples are drawn [...] Read more.

This paper evaluates the performance of different small area estimation methods using model and design-based simulation experiments. Design-based simulation experiments are carried out using the Mexican Intra Censal survey as a census of roughly 3.9 million households from which 500 samples are drawn using a two-stage selection procedure similar to that of Living Standards Measurement Study (LSMS) surveys. The estimation methods considered are that of Elbers, Lanjouw and Lanjouw (2003), the empirical best predictor of Molina and Rao (2010), the twofold nested error extension presented by Marhuenda et al. (2017), and finally an adaptation, presented by Nguyen (2012), that combines unit and area level information, and which has been proposed as an alternative when the available census data is outdated. The findings show the importance of selecting a proper model and data transformation so that model assumptions hold. A proper data transformation can lead to a considerable improvement in mean squared error (MSE). Results from design-based validation show that all small area estimation methods represent an improvement, in terms of MSE, over direct estimates. However, methods that model unit level welfare using only area level information suffer from considerable bias. Because the magnitude and direction of the bias is unknown ex ante, methods relying only on aggregated covariates should be used with caution, but may be an alternative to traditional area level models when these are not applicable. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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34 pages, 4156 KiB

Open AccessArticle

Multimorbidity from Diabetes, Heart Failure, and Related Conditions: Assessing a Panel of Depressive Symptoms as Both Formative and Reflective Indicators of a Latent Trait

by Richard B. Francoeur

Mathematics 2021, 9(21), 2715; https://doi.org/10.3390/math9212715 - 26 Oct 2021

Cited by 1 | Viewed by 2188

Abstract

Through exploring specific conditions (diabetes, heart failure, related vascular/metabolic diagnoses) and their multimorbidities, I develop a more thorough means to adjust confounders of clinical targets within main or interactive contexts in epidemiological panel studies. Regression-based multiple indicators-multiple causes (MIMIC) models combine multiple or [...] Read more.

Through exploring specific conditions (diabetes, heart failure, related vascular/metabolic diagnoses) and their multimorbidities, I develop a more thorough means to adjust confounders of clinical targets within main or interactive contexts in epidemiological panel studies. Regression-based multiple indicators-multiple causes (MIMIC) models combine multiple or moderated regression and confirmatory factor analysis. In a novel specification, each of twenty depressive symptoms is both a “formative” (causal) indicator and a “reflective” (effect) indicator of a latent trait (Depression). Although both indicators provide identical information (under different variable names), formative indicators provide “exogenous” information (outside the model) to estimate, within groups or subgroups, “endogenous” effects (recovered by the model) from the latent trait and its reflective indicators. Formative indicators within the multiple regressions constitute comprehensive proxies for unspecified confounders by completely mediating all unspecified confounder effects on the endogenous latent trait and its reflective indicators, the latter estimated through confirmatory factor analysis. Findings of symptom clusters of Depression in these specific conditions, and in subgroups that capture their synergies, corroborate parallel MIMIC models with instrumental variables that specify several known confounders, but suggest some confounding biases remain. All multimorbidities involve synergy from co-occurring diabetes and heart failure. There may be opportunities to target screening and optimize metformin treatment for these co-occurring conditions. This strategy avoids the need to specify all confounders, which may not be possible or verifiable. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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12 pages, 320 KiB

Open AccessArticle

Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion

by Hua Xin, Jianping Zhu, Tzong-Ru Tsai and Chieh-Yi Hung

Mathematics 2021, 9(19), 2518; https://doi.org/10.3390/math9192518 - 07 Oct 2021

Cited by 1 | Viewed by 1399

Abstract

In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of [...] Read more.

In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of the SNP is obtained via using a hierarchical Bayesian modeling procedure. Moreover, a hybrid algorithm using Gibbs sampling in Metropolis–Hastings algorithms is used to obtain the Bayes estimator of the SNP. The highest posterior density interval of the SNP is obtained based on the empirical distribution of Markov chains. We use the term 3RR-HB to denote the proposed method here. Monte Carlo simulations show that the quality of 3RR-HB procedure is good and that it can improve the drawback of the maximum likelihood estimation method. The proposed 3RR-HB procedure is simple for use. An example regarding the homosexual proportion of college freshmen is used for illustration. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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23 pages, 497 KiB

Open AccessArticle

Normalized Information Criteria and Model Selection in the Presence of Missing Data

by Nitzan Cohen and Yakir Berchenko

Mathematics 2021, 9(19), 2474; https://doi.org/10.3390/math9192474 - 03 Oct 2021

Cited by 3 | Viewed by 1900

Abstract

Information criteria such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are commonly used for model selection. However, the current theory does not support unconventional data, so naive use of these criteria is not suitable for data with missing values. [...] Read more.

Information criteria such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are commonly used for model selection. However, the current theory does not support unconventional data, so naive use of these criteria is not suitable for data with missing values. Imputation, at the core of most alternative methods, is both distorted as well as computationally demanding. We propose a new approach that enables the use of classic well-known information criteria for model selection when there are missing data. We adapt the current theory of information criteria through normalization, accounting for the different sample sizes used for each candidate model (focusing on AIC and BIC). Interestingly, when the sample sizes are different, our theoretical analysis finds that

A I C_{j} / n_{j}

is the proper correction for

A I C_{j}

that we need to optimize (where

n_{j}

is the sample size available to the

j th

model) while

- (B I C_{j} - B I C_{i}) / (n_{j} - n_{i})

is the correction of BIC. Furthermore, we find that the computational complexity of normalized information criteria methods is exponentially better than that of imputation methods. In a series of simulation studies, we find that normalized-AIC and normalized-BIC outperform previous methods (i.e., normalized-AIC is more efficient, and normalized BIC includes only important variables, although it tends to exclude some of them in cases of large correlation). We propose three additional methods aimed at increasing the statistical efficiency of normalized-AIC: post-selection imputation, Akaike sub-model averaging, and minimum-variance averaging. The latter succeeds in increasing efficiency further. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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18 pages, 2072 KiB

Open AccessFeature PaperArticle

COVID-19 and Changes in Social Habits. Restaurant Terraces, a Booming Space in Cities. The Case of Madrid

by Virgilio Pérez, Cristina Aybar and Jose M. Pavía

Mathematics 2021, 9(17), 2133; https://doi.org/10.3390/math9172133 - 02 Sep 2021

Cited by 11 | Viewed by 3714

Abstract

The COVID-19 pandemic and the fear experienced by some of the population, along with the lack of mobility due to the restrictions imposed, has modified the social behaviour of Spaniards. This has had a significant effect on the hospitality sector, viewed as being [...] Read more.

The COVID-19 pandemic and the fear experienced by some of the population, along with the lack of mobility due to the restrictions imposed, has modified the social behaviour of Spaniards. This has had a significant effect on the hospitality sector, viewed as being an economic and social driver in Spain. From the analysis of data collected in two of our own non-probabilistic surveys (N ~ 8400 and N ~ 2000), we show how, during the first six months of the pandemic, Spaniards notably reduced their consumption in bars and restaurants, also preferring outdoor spaces to spaces inside. The restaurant sector has needed to adapt to this situation and, with the support of the authorities (regional and local governments), new terraces have been allowed on pavements and public parking spaces, modifying the appearance of the streets of main towns and cities. This study, focused on the city of Madrid, analyses the singular causes that have prompted this significant impact on this particular city, albeit with an uneven spatial distribution. It seems likely that the new measures will leave their mark and some of the changes will remain. The positive response to these changes from the residents of Madrid has ensured the issue is being widely debated in the public arena. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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27 pages, 7438 KiB

Open AccessArticle

Imputation for Repeated Bounded Outcome Data: Statistical and Machine-Learning Approaches

by Urko Aguirre-Larracoechea and Cruz E. Borges

Mathematics 2021, 9(17), 2081; https://doi.org/10.3390/math9172081 - 28 Aug 2021

Viewed by 1710

Abstract

Real-life data are bounded and heavy-tailed variables. Zero-one-inflated beta (ZOIB) regression is used for modelling them. There are no appropriate methods to address the problem of missing data in repeated bounded outcomes. We developed an imputation method using ZOIB (i-ZOIB) and compared its [...] Read more.

Real-life data are bounded and heavy-tailed variables. Zero-one-inflated beta (ZOIB) regression is used for modelling them. There are no appropriate methods to address the problem of missing data in repeated bounded outcomes. We developed an imputation method using ZOIB (i-ZOIB) and compared its performance with those of the naïve and machine-learning methods, using different distribution shapes and settings designed in the simulation study. The performance was measured employing the absolute error (MAE), root-mean-square-error (RMSE) and the unscaled mean bounded relative absolute error (UMBRAE) methods. The results varied depending on the missingness rate and mechanism. The i-ZOIB and the machine-learning ANN, SVR and RF methods showed the best performance. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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16 pages, 534 KiB

Open AccessArticle

Respondent Burden Effects on Item Non-Response and Careless Response Rates: An Analysis of Two Types of Surveys

by Álvaro Briz-Redón

Mathematics 2021, 9(17), 2035; https://doi.org/10.3390/math9172035 - 24 Aug 2021

Cited by 2 | Viewed by 2006

Abstract

The respondent burden refers to the effort required by a respondent to answer a questionnaire. Although this concept was introduced decades ago, few studies have focused on the quantitative detection of such a burden. In this paper, a face-to-face survey and a telephone [...] Read more.

The respondent burden refers to the effort required by a respondent to answer a questionnaire. Although this concept was introduced decades ago, few studies have focused on the quantitative detection of such a burden. In this paper, a face-to-face survey and a telephone survey conducted in Valencia (Spain) are analyzed. The presence of burden is studied in terms of both item non-response rates and careless response rates. In particular, two moving-window statistics based on the coefficient of unalikeability and the average longstring index are proposed for characterizing careless responding. Item non-response and careless response rates are modeled for each survey by using mixed-effects models, including respondent-level and question-level covariates and also temporal random effects to assess the existence of respondent burden during the questionnaire. The results suggest that the sociodemographic characteristics of the respondents and the typology of the question impact item non-response and careless response rates. Moreover, the estimates of the temporal random effects indicate that item non-response and careless response rates are time-varying, suggesting the presence of respondent burden. In particular, an increasing trend in item non-response rates in the telephone survey has been found, which supports the hypothesis of the burden. Regarding careless responding, despite the presence of some temporal variation, no clear trend has been identified. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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17 pages, 371 KiB

Open AccessArticle

Estimation of the Average Kappa Coefficient of a Binary Diagnostic Test in the Presence of Partial Verification

by José Antonio Roldán-Nofuentes and Saad Bouh Regad

Mathematics 2021, 9(14), 1694; https://doi.org/10.3390/math9141694 - 19 Jul 2021

Cited by 5 | Viewed by 1690

Abstract

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In [...] Read more.

The average kappa coefficient of a binary diagnostic test is a measure of the beyond-chance average agreement between the binary diagnostic test and the gold standard, and it depends on the sensitivity and specificity of the diagnostic test and on disease prevalence. In this manuscript the estimation of the average kappa coefficient of a diagnostic test in the presence of verification bias is studied. Confidence intervals for the average kappa coefficient are studied applying the methods of maximum likelihood and multiple imputation by chained equations. Simulation experiments have been carried out to study the asymptotic behaviors of the proposed intervals, given some application rules. The results obtained in our simulation experiments have shown that the multiple imputation by chained equations method provides better results than the maximum likelihood method. A function has been written in R to estimate the average kappa coefficient by applying multiple imputation. The results have been applied to the diagnosis of liver disease. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

16 pages, 327 KiB

Open AccessArticle

Multiple Ordinal Correlation Based on Kendall’s Tau Measure: A Proposal

by Juan M. Muñoz-Pichardo, Emilio D. Lozano-Aguilera, Antonio Pascual-Acosta and Ana M. Muñoz-Reyes

Mathematics 2021, 9(14), 1616; https://doi.org/10.3390/math9141616 - 08 Jul 2021

Cited by 4 | Viewed by 2283

Abstract

The joint analysis of various ordinal variables is necessary in many experimental studies within research fields such as sociology and psychology. Therefore, the necessary measures of multiple ordinal dependence must be easy to interpret and facilitate the interpretation of multivariate models that fit [...] Read more.

The joint analysis of various ordinal variables is necessary in many experimental studies within research fields such as sociology and psychology. Therefore, the necessary measures of multiple ordinal dependence must be easy to interpret and facilitate the interpretation of multivariate models that fit ordinal data. The main objective of this article is to propose a multiple ordinal correlation measure based on a bivariate correlation measure: Kendall’s tau. A sample version of the measure is proposed for its estimation. Furthermore, a confidence interval and a multiple ordinal independence test are proposed. The measure is applied to various simulations, covering a wide range of multiple ordinal dependency scenarios, in order to illustrate the adequacy of the measure and the proposed inferential techniques. Finally, the measure is applied to a real-world study based on a social survey of the levels of life satisfaction and the happiness index of a population. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

17 pages, 537 KiB

Open AccessArticle

About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model

by Alexander Robitzsch

Mathematics 2021, 9(13), 1465; https://doi.org/10.3390/math9131465 - 22 Jun 2021

Cited by 2 | Viewed by 2003

Abstract

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model [...] Read more.

This article shows that the recently proposed latent D-scoring model of Dimitrov is statistically equivalent to the two-parameter logistic item response model. An analytical derivation and a numerical illustration are employed for demonstrating this finding. Hence, estimation techniques for the two-parameter logistic model can be used for estimating the latent D-scoring model. In an empirical example using PISA data, differences of country ranks are investigated when using different metrics for the latent trait. In the example, the choice of the latent trait metric matters for the ranking of countries. Finally, it is argued that an item response model with bounded latent trait values like the latent D-scoring model might have advantages for reporting results in terms of interpretation. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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19 pages, 347 KiB

Open AccessArticle

Confidence Intervals and Sample Size to Compare the Predictive Values of Two Diagnostic Tests

by José Antonio Roldán-Nofuentes and Saad Bouh Regad

Mathematics 2021, 9(13), 1462; https://doi.org/10.3390/math9131462 - 22 Jun 2021

Cited by 3 | Viewed by 2160

Abstract

A binary diagnostic test is a medical test that is applied to an individual in order to determine the presence or the absence of a certain disease and whose result can be positive or negative. A positive result indicates the presence of the [...] Read more.

A binary diagnostic test is a medical test that is applied to an individual in order to determine the presence or the absence of a certain disease and whose result can be positive or negative. A positive result indicates the presence of the disease, and a negative result indicates the absence. Positive and negative predictive values represent the accuracy of a binary diagnostic test when it is applied to a cohort of individuals, and they are measures of the clinical accuracy of the binary diagnostic test. In this manuscript, we study the comparison of the positive (negative) predictive values of two binary diagnostic tests subject to a paired design through confidence intervals. We have studied confidence intervals for the difference and for the ratio of the two positive (negative) predictive values. Simulation experiments have been carried out to study the asymptotic behavior of the confidence intervals, giving some general rules for application. We also study a method to calculate the sample size to compare the parameters using confidence intervals. We have written a program in R to solve the problems studied in this manuscript. The results have been applied to the diagnosis of colorectal cancer. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

27 pages, 4452 KiB

Open AccessArticle

Self-Perceived Health, Life Satisfaction and Related Factors among Healthcare Professionals and the General Population: Analysis of an Online Survey, with Propensity Score Adjustment

by Ramón Ferri-García, María del Mar Rueda and Andrés Cabrera-León

Mathematics 2021, 9(7), 791; https://doi.org/10.3390/math9070791 - 06 Apr 2021

Cited by 3 | Viewed by 2161

Abstract

Healthcare professionals (HCPs) often suffer high levels of depression, stress, anxiety and burnout. Our main study aimswereto estimate the prevalences of poor self-perceived health, life dissatisfaction, chronic disease and unhealthy habits among HCPs and to explore the use of machine learning classification algorithms [...] Read more.

Healthcare professionals (HCPs) often suffer high levels of depression, stress, anxiety and burnout. Our main study aimswereto estimate the prevalences of poor self-perceived health, life dissatisfaction, chronic disease and unhealthy habits among HCPs and to explore the use of machine learning classification algorithms to remove selection bias. A sample of Spanish HCPs was asked to complete a web survey. Risk factors were identified by multivariate ordinal regression models. To counteract the absence of probabilistic sampling and representation, the sample was weighted by propensity score adjustment algorithms. The logistic regression algorithm was considered the most appropriate for dealing with misestimations. Male HCPs had significantly worse lifestyle habits than their female counterparts, together with a higher prevalence of chronic disease and of health problems. Members of the general population reported significantly poorer health and less satisfaction with life than the HCPs. Among HCPs, the prior existence of health problems was most strongly associated with worsening self-perceived health and decreased life satisfaction, while obesity had an important negative impact on female practitioners’ self-perception of health. Finally, the HCPs who worked as nurses had poorer self-perceptions of health than other HCPs, and the men who worked in primary care had less satisfaction with their lives than those who worked in other levels of healthcare. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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13 pages, 295 KiB

Open AccessArticle

Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables

by María del Mar Rueda, Beatriz Cobo and Antonio Arcos

Mathematics 2021, 9(6), 609; https://doi.org/10.3390/math9060609 - 12 Mar 2021

Cited by 1 | Viewed by 1514

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 [...] Read more.

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. Full article

(This article belongs to the Special Issue Methods and Applications of Statistics in the Social and Health Sciences)

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