Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation

Bianchi, Annamaria; Fabrizi, Enrico; Salvati, Nicola; Tzavidis, Nikos

doi:10.1111/insr.12267

Cited by 30 publications

(36 citation statements)

References 53 publications

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“…As such, this regression does not assume there is normality nor uniformity in how COVID-19 is diffused and transmitted between and within countries. This regression revealed how the influences of log-transformed rate of COVID-19 confirmed cases vary across the quantiles of the distribution (69). As such, this regression does not assume there is normality nor uniformity in how COVID-19 is diffused and transmitted between and within countries.…”

Section: Methodsmentioning

confidence: 98%

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The Socio-Spatial Determinants of COVID-19 Diffusion: The Impact of Globalisation, Settlement Characteristics and Population

Sigler

Mahmuda

Kimpton

et al. 2020

Preprint

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Background: COVID-19 is an emergent infectious disease that has spread geographically to become a global pandemic. While much research focuses on the epidemiological and virological aspects of the COVID-19 transmission, there remains a gap in knowledge regarding the drivers of geographical diffusion between places. Here, we use quantile regression to model the roles of globalisation, human settlement and population characteristics as socio-spatial determinants of COVID-19 diffusion over a six-week period in March and April 2020. Results: The quantile regression model suggest that globalisation and settlement population characteristics related to high human mobility predict disease diffusion. Human development level (HDI) and total population predict COVID-19 diffusion in countries with a high number of total confirmed cases per million whereas larger household size, older populations, and globalisation tied to human interaction predict COVID-19 diffusion in countries with a low number of total confirmed cases per million. Conclusions: The analysis confirms that globalisation, settlement and population characteristics lead to greater disease diffusion, and primarily variables tied to high human mobility. These outcomes serve to inform policies around ‘flattening the curve’, particularly as they related to anticipated relocation diffusion from more- to less-developed countries and regions, and hierarchical diffusion from countries with higher population and density. Epidemiological strategies must be tailored to suit the range of human mobility patterns, as well as the variety of settlement and population characteristics.

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Section: Methodsmentioning

confidence: 98%

“…confirmed cases vary across the quantiles of the distribution (69). As such, this regression does not assume there is normality nor uniformity in how COVID-19 is diffused and transmitted between and within countries.…”

Section: Methodsmentioning

confidence: 99%

The Socio-Spatial Determinants of COVID-19 Diffusion: The Impact of Globalisation, Settlement Characteristics and Population

Sigler

Mahmuda

Kimpton

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…As such, this regression does not assume there is normality nor uniformity in how COVID-19 is diffused and transmitted between and within countries. This regression revealed how the in uences of log-transformed rate of COVID-19 con rmed cases vary across the quantiles of the distribution (65). As such, this regression does not assume there is normality nor uniformity in how COVID-19 is diffused and transmitted between and within countries.…”

mentioning

confidence: 96%

The Socio-Spatial Determinants of COVID-19 Diffusion: The Impact of Globalisation, Settlement Characteristics and Population

Sigler

Mahmuda

Kimpton

et al. 2020

Preprint

View full text Add to dashboard Cite

Background: COVID-19 is an emergent infectious disease that has spread geographically to become a global pandemic. While much research focuses on the epidemiological and virological aspects of the COVID-19 transmission, there remains a gap in knowledge regarding the drivers of geographical diffusion between places. Here, we use quantile regression to model the roles of globalisation, human settlement and population characteristics as socio-spatial determinants of COVID-19 diffusion over a six-week period in March and April 2020.Results: The quantile regression model suggest that globalisation and settlement population characteristics related to high human mobility predict disease diffusion. Human development level (HDI) and total population predict COVID-19 diffusion in countries with a high number of total confirmed cases per million whereas larger household size, older populations, and globalisation tied to human interaction predict COVID-19 diffusion in countries with a low number of total confirmed cases per million. Conclusions: The analysis confirms that globalisation, settlement and population characteristics lead to greater disease diffusion, and primarily variables tied to high human mobility. These outcomes serve to inform policies around ‘flattening the curve’, particularly as they related to anticipated relocation diffusion from more- to less-developed countries and regions, and hierarchical diffusion from countries with higher population and density. Epidemiological strategies must be tailored to suit the range of human mobility patterns, as well as the variety of settlement and population characteristics.

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“…Because the scale parameter σ ( τ ) must also be estimated, it is convenient to define

(\overset{false^}{bold-italicβ} false(τ false), \overset{false^}{σ} false(τ false))

to be the minimizers of

L_{n} false{bold-italicβ (τ), σ (τ) false} = n^{- 1} 2.047em2.047emtrue[n log false{σ (τ) false} + {false\sum}_{i = 1}^{n} ρ_{τ} {\frac{y_{i} - x_{i}^{T} β (τ)}{σ false(τ false)}} 2.047em2.047emtrue],

where y i is a realization from Y i . The quantity expressed in equation corresponds, up to an additive constant, to the negative log‐likelihood of a generalized asymmetric least informative distribution (Bianchi et al ., ). This model is not assumed to reflect the true data distribution but provides a unified framework for joint estimation of β ( τ ) and σ ( τ ).…”

Section: An Overview Of M‐quantile Regression Models and Their Applicmentioning

confidence: 97%

“…the small area quantiles; Tzavidis et al (2008) and Pratesi et al (2008)). For a complete review of MQR models in SAE, we refer to Bianchi et al (2018).…”

Section: Introductionmentioning

confidence: 99%

Parametric Modelling ofM-Quantile Regression Coefficient Functions with Application to Small Area Estimation

Frumento

Salvati

2019

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Small area estimation methods can be used to obtain reliable estimates of a parameter of interest within an unplanned domain or subgroup of the population for which only a limited sample size is available. A standard approach to small area estimation is to use a linear mixed model in which the heterogeneity between areas is accounted for by area level effects. An alternative solution, which has gained popularity in recent years, is to use M‐quantile regression models. This approach requires much weaker assumptions than the standard linear mixed model and enables computing outlier robust estimators of the area means. We introduce a new framework for M‐quantile regression, in which the model coefficients, β(τ), are described by (flexible) parametric functions of τ. We illustrate the advantages of this approach and its application to small area estimation. Using the European Union Survey on Income and Living Conditions data, we estimate the average equivalized household income in three Italian regions. The paper is accompanied by an R package Mqrcm that implements the necessary procedures for estimation, inference and prediction.

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Estimation and Testing in M‐quantile Regression with Applications to Small Area Estimation

Cited by 30 publications

References 53 publications

The Socio-Spatial Determinants of COVID-19 Diffusion: The Impact of Globalisation, Settlement Characteristics and Population

The Socio-Spatial Determinants of COVID-19 Diffusion: The Impact of Globalisation, Settlement Characteristics and Population

The Socio-Spatial Determinants of COVID-19 Diffusion: The Impact of Globalisation, Settlement Characteristics and Population

Parametric Modelling ofM-Quantile Regression Coefficient Functions with Application to Small Area Estimation

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