A joint regression modeling framework for analyzing bivariate binary data in R

Marra, Giampiero; Radice, Rosalba

doi:10.1515/demo-2017-0016

Cited by 31 publications

(50 citation statements)

References 48 publications

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“…C : [0,1] 2 →[0,1] is a two-place copula function and θ , known as the copula parameter, is an association parameter which measures the dependence between the two random variables [ 33 ]. If Y i 1 and Y i 2 were both continuous, the copula C would be unique.…”

Section: Methodsmentioning

confidence: 99%

Copula geoadditive modelling of anaemia and malaria in young children in Kenya, Malawi, Tanzania and Uganda

Roberts

Zewotir

2020

J Health Popul Nutr

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Background Anaemia and malaria are the leading causes of sub-Saharan African childhood morbidity and mortality. This study aimed to explore the complex relationship between anaemia and malaria in young children across the districts or counties of four contiguous sub-Saharan African countries, namely Kenya, Malawi, Tanzania and Uganda, while accounting for the effects of socio-economic, demographic and environmental factors. Geospatial maps were constructed to visualise the relationship between the two responses across the districts of the countries. Methods A joint bivariate copula regression model was used, which estimates the correlation between the two responses conditional on the linear, non-linear and spatial effects of the explanatory variables considered. The copula framework allows the dependency structure between the responses to be isolated from their marginal distributions. The association between the two responses was set to vary according to the district of residence across the four countries. Results The study revealed a positive association between anaemia and malaria throughout the districts, the strength of which varied across the districts of the four countries. Due to this heterogeneous association between anaemia and malaria, we further considered the joint probability of each combination of outcome of anaemia and malaria to further reveal more about the relationship between the responses. A considerable number of districts had a high joint probability of a child being anaemic but not having malaria. This might suggest the existence of other significant drivers of childhood anaemia in these districts. Conclusions This study presents an alternative technique to joint modelling of anaemia and malaria in young children which assists in understanding more about their relationship compared to techniques of multivariate modelling. The approach used in this study can aid in visualising the relationship through mapping of their correlation and joint probabilities. These maps produced can then help policy makers target the correct set of interventions, or prevent the use of incorrect interventions, particularly for childhood anaemia, the causes of which are multiple and complex.

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Section: Methodsmentioning

confidence: 99%

Copula geoadditive modelling of anaemia and malaria in young children in Kenya, Malawi, Tanzania and Uganda

Roberts

Zewotir

2020

J Health Popul Nutr

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“…We applied this theoretical framework on tree species distribution modelling by estimating BSMs (Marra et al ., ) that included both ecological and economic drivers. BSMs were estimated with the package ‘SemiParBIVProbit’ available on CRAN (Marra et al ., ).…”

Section: Methodsmentioning

confidence: 99%

W_{i}

for technical reasons presented in Section 1.3 of the Supporting Information.…”

Section: Methodsmentioning

confidence: 99%

The economics of land use reveals a selection bias in tree species distribution models

Guillemot

Martin‐StPaul

et al. 2016

Global Ecol. Biogeogr.

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In human-dominated ecosystems, the presence of a given species is the result of both the ecological suitability of the site and human impacts such as land-use choices. The influence of land-use choices on the predictions of species distribution models (SDMs) has, however, been often neglected. Here, we provide a theoretical analysis of the land-use selection bias affecting classical SDMs in the case of either presence-only or presence–absence datasets. Land-use selection bias in the predictions of SDMs is then quantified for four widespread European tree species

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“…The probability of default is π ( x i )= exp [−{1+ ξ ( β ′ x i )} −1/ ξ ]. The corresponding linear predictor can be derived as

\frac{{[- ln false{π (x_{i}) false}]}^{- ξ} - 1}{ξ} = β^{'} x_{i} .

We fitted this model by using the generalized joint regression modelling package GJRM in the R statistical software (Marra and Radice, ).…”

Section: Models and Predictive Accuracy Measuresmentioning

confidence: 99%

“…We fitted this model by using the generalized joint regression modelling package GJRM in the R statistical software (Marra and Radice, 2017).…”

Section: Generalized Extreme Value Regression Modelmentioning

confidence: 99%

Prediction of Default Probability by using Statistical Models for rare Events

Ogundimu

2019

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

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Summary Prediction models in credit scoring usually involve the use of data sets with highly imbalanced distributions of the event of interest (default). Logistic regression, which is widely used to estimate the probability of default, PD, often suffers from the problem of separation when the event of interest is rare and consequently poor predictive performance of the minority class in small samples. A common solution is to discard majority class examples, to duplicate minority class examples or to use a combination of both to balance the data. These methods may overfit data. It is unclear how penalized regression models such as Firth's estimator, which reduces bias and mean‐square error relative to classical logistic regression, performs in modelling PD. We review some methods for class imbalanced data and compare them in a simulation study using the Taiwan credit card data. We emphasize the effect of events per variable for developing an accurate model—an often neglected concept in PD‐modelling. The data balancing techniques that are considered are the random oversampling examples and synthetic minority oversampling technique methods. The results indicate that the synthetic minority oversampling technique improved predictive accuracy of PD regardless of sample size. Among the penalized regression models that are analysed, the log‐F prior and ridge regression methods are preferred.

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A joint regression modeling framework for analyzing bivariate binary data in R

Cited by 31 publications

References 48 publications

Copula geoadditive modelling of anaemia and malaria in young children in Kenya, Malawi, Tanzania and Uganda

Copula geoadditive modelling of anaemia and malaria in young children in Kenya, Malawi, Tanzania and Uganda

The economics of land use reveals a selection bias in tree species distribution models

Prediction of Default Probability by using Statistical Models for rare Events

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