scholarly journals Comparison between Highly Complex Location Models and GAMLSS

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 469
Author(s):  
Thiago G. Ramires ◽  
Luiz R. Nakamura ◽  
Ana J. Righetto ◽  
Renan J. Carvalho ◽  
Lucas A. Vieira ◽  
...  
Keyword(s):  
Regression Models ◽  
Generalized Additive Models ◽  
Real Data ◽  
Additive Models ◽  
Location Model ◽  
Main Motivation ◽  
Location Models ◽  
Location Class ◽  
Response Variables

This paper presents a discussion regarding regression models, especially those belonging to the location class. Our main motivation is that, with simple distributions having simple interpretations, in some cases, one gets better results than the ones obtained with overly complex distributions. For instance, with the reverse Gumbel (RG) distribution, it is possible to explain response variables by making use of the generalized additive models for location, scale, and shape (GAMLSS) framework, which allows the fitting of several parameters (characteristics) of the probabilistic distributions, like mean, mode, variance, and others. Three real data applications are used to compare several location models against the RG under the GAMLSS framework. The intention is to show that the use of a simple distribution (e.g., RG) based on a more sophisticated regression structure may be preferable than using a more complex location model.

scholarly journals Non-Parametric Generalized Additive Models as a Tool for Evaluating Policy Interventions

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 299
Author(s):  
Jaime Pinilla ◽  
Miguel Negrín
Keyword(s):  
Linear Regression ◽  
Regression Models ◽  
Linear Trend ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Linear Regression Models ◽  
Non Linear ◽  
Nonlinear Trends ◽  
The Impact ◽  
Non Parametric

The interrupted time series analysis is a quasi-experimental design used to evaluate the effectiveness of an intervention. Segmented linear regression models have been the most used models to carry out this analysis. However, they assume a linear trend that may not be appropriate in many situations. In this paper, we show how generalized additive models (GAMs), a non-parametric regression-based method, can be useful to accommodate nonlinear trends. An analysis with simulated data is carried out to assess the performance of both models. Data were simulated from linear and non-linear (quadratic and cubic) functions. The results of this analysis show how GAMs improve on segmented linear regression models when the trend is non-linear, but they also show a good performance when the trend is linear. A real-life application where the impact of the 2012 Spanish cost-sharing reforms on pharmaceutical prescription is also analyzed. Seasonality and an indicator variable for the stockpiling effect are included as explanatory variables. The segmented linear regression model shows good fit of the data. However, the GAM concludes that the hypothesis of linear trend is rejected. The estimated level shift is similar for both models but the cumulative absolute effect on the number of prescriptions is lower in GAM.

scholarly journals Functional Location-Scale Model to Forecast Bivariate Pollution Episodes

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 941
Author(s):  
Manuel Oviedo-de La Fuente ◽  
Celestino Ordóñez ◽  
Javier Roca-Pardiñas
Keyword(s):  
Generalized Additive Models ◽  
Real Data ◽  
Additive Models ◽  
Scale Model ◽  
Power Station ◽  
Specific Level ◽  
Uncertainty Region ◽  
Corrective Measures ◽  
Pollution Episodes

Predicting anomalous emission of pollutants into the atmosphere well in advance is crucial for industries emitting such elements, since it allows them to take corrective measures aimed to avoid such emissions and their consequences. In this work, we propose a functional location-scale model to predict in advance pollution episodes where two pollutants are involved. Functional generalized additive models (FGAMs) are used to estimate the means and variances of the model, as well as the correlation between both pollutants. The method not only forecasts the concentrations of both pollutants, it also estimates an uncertainty region where the concentrations of both pollutants should be located, given a specific level of uncertainty. The performance of the model was evaluated using real data of SO 2 and NO x emissions from a coal-fired power station, obtaining good results.

scholarly journals Interactively visualizing distributional regression models with distreg.vis

2021 ◽  
pp. 1471082X2110073
Author(s):  
Stanislaus Stadlmann ◽  
Thomas Kneib
Keyword(s):  
Regression Models ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Estimation Model ◽  
Response Distribution ◽  
Conditional Response ◽  
Link Functions ◽  
Covariate Effects ◽  
Parametric Response ◽  
Distributional Regression

A newly emerging field in statistics is distributional regression, where not only the mean but each parameter of a parametric response distribution can be modelled using a set of predictors. As an extension of generalized additive models, distributional regression utilizes the known link functions (log, logit, etc.), model terms (fixed, random, spatial, smooth, etc.) and available types of distributions but allows us to go well beyond the exponential family and to model potentially all distributional parameters. Due to this increase in model flexibility, the interpretation of covariate effects on the shape of the conditional response distribution, its moments and other features derived from this distribution is more challenging than with traditional mean-based methods. In particular, such quantities of interest often do not directly equate the modelled parameters but are rather a (potentially complex) combination of them. To ease the post-estimation model analysis, we propose a framework and subsequently feature an implementation in R for the visualization of Bayesian and frequentist distributional regression models fitted using the bamlss, gamlss and betareg R packages.

scholarly journals Larger Democratic swings in United States counties with Black Lives Matter protests in preliminary results of the 2020 presidential election

2021 ◽  
Author(s):  
Drew Thomas
Keyword(s):  
Presidential Election ◽  
Regression Models ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Democratic Candidate ◽  
Black Lives Matter ◽  
Percentage Points ◽  
Voting Age ◽  
Us Presidential Election ◽  
Hispanic Voters

Media commentary has suggested that recent Black Lives Matter (BLM) protests, particularly riots, drove voters, particularly Hispanic voters, away from Democratic candidate Joe Biden in the 2020 US presidential election. I test these hypotheses with county-level regression models of 2016-to-2020 swing towards the Democratic presidential candidate, using the presence and intensity of BLM non-riot protests and riots as regressors, controlling for state and many background demographic factors (population density, household size, racial composition, etc.). The models (generalized additive models) that control most aggressively for background factors find small and positive associations between BLM protests and Democratic swing: counties with non-riot BLM protests swung more towards Joe Biden by 0.2 percentage points, and counties with BLM-associated riots swung more towards Joe Biden by (a statistically insignificant) 0.1 percentage points. The extra BLM-protest swing was not statistically significantly different in counties with relatively many Hispanic voting-age citizens, although it was weaker in counties with relatively many Asian voting-age citizens. Inasmuch as these results reflect causal impacts of BLM protests, the protests enhanced the Democratic swing but were probably not electorally decisive. My most elaborate model suggests that a lack of BLM protests in 2020 would have flipped only one state: Biden might have narrowly lost Arizona.

scholarly journals A general framework for functional regression modelling

2017 ◽  
Vol 17 (1-2) ◽  
pp. 1-35 ◽  
Author(s):  
Sonja Greven ◽  
Fabian Scheipl
Keyword(s):  
Functional Data ◽  
Regression Models ◽  
Generalized Additive Models ◽  
Large Body ◽  
Imaging Study ◽  
Additive Models ◽  
Gradient Boosting ◽  
Functional Regression ◽  
Functional Responses ◽  
Additive Mixed Models

Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for ‘generalized’ functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases—particularly splines and functional principal components—and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost , respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.

Abstract 17174: Revisiting the QT Correction Formulas: A Generalized Additive Models for Location, Scale, and Shape Approach

Circulation ◽  
2020 ◽  
Vol 142 (Suppl_3) ◽  
Author(s):  
Hai Nguyen ◽  
Patrick Y Jay ◽  
William Scott ◽  
Janos Molnar ◽  
Henry Huang ◽  
...  
Keyword(s):  
Heart Rate ◽  
Clinical Practice ◽  
Regression Models ◽  
Generalized Additive Models ◽  
Additive Models ◽  
Correction Function ◽  
Coefficient Of Determination ◽  
Male And Female ◽  
Regression Slope ◽  
Significant Difference

Introduction: Various mathematical equations have been proposed to correct QT interval for heart rate (QTc). However, with most formulas, QTc remains dependent on heart rate (HR) especially at low and high HR values. Hypothesis: A spline correction function would perform better than standard mathematical formulas by allowing the data to determine the form of the relationship. Methods: A series of regression models using the generalized additive models for location, scale, and shape framework was applied to 10,000 completely normal electrocardiogram data from the National Health and Nutrition Examination Surveys II and III. Evaluation of the model’s performance was performed using the R 2 coefficient of determination and the root mean squared of the errors between the predicted and observed QTc. The new regression models were compared to the Bazett’s and Fredericia’s formulas, which are the 2 most widely used formulas in clinical practice. Results: When boxplots of the QTc for each formula are plotted, grouped by HR in intervals of 5 beats/minute, QTc determined by the penalized spline regression was almost heart rate independent for both male and female as the slope of the regression line was almost zero (-0.003 for female and -0.001 for male) (Figure 1 A—B). By contrast, QTc by Bazett had a positive correlation (regression slope of 0.86 for female and 0.89 for male) while Fredericia’s had a negative correlation (regression slope of -0.14 for female and -0.13 for male) with HR (Figure 1C—F). In all 3 formulas, there was no significant difference between male and female. Conclusions: A new QTc formula was developed, which is almost independent of HR thereby providing a more accurate estimate of QTc for clinical management. Automatic QTc calculation and percentiles estimation could easily be incorporated in an online calculator or app for easy integration in everyday clinical practice.

scholarly journals Comparing regression methods to predict species richness patterns

Web Ecology ◽  
2009 ◽  
Vol 9 (1) ◽  
pp. 58-67 ◽  
Author(s):  
D. Nogués-Bravo
Keyword(s):  
Species Richness ◽  
Regression Models ◽  
Linear Models ◽  
Predictive Accuracy ◽  
Generalized Additive Models ◽  
Bird Species ◽  
Spatial Modelling ◽  
Additive Models ◽  
Northern Spain ◽  
Bird Species Richness

Abstract. Multivariable regression models have been used extensively as spatial modelling tools. However, other regression approaches are emerging as more efficient techniques. This paper attempts to present a synthesis of Generalised Regression Models (Generalized Linear Models, GLMs, Generalized Additive Models, GAMs), and a Geographically Weighted Regression, GWR, implemented in a GAM, explaining their statistical formulations and assessing improvements in predictive accuracy compared with linear regressions. The problems associated with these approaches are also discussed. A digital database developed with Geographic Information Systems (GIS), including environmental maps and bird species richness distribution in northern Spain, is used for comparison of the techniques. GWR using splines has shown the highest improvement in accounted deviance when compared with traditional linear regression approach, followed by GAM and GLM.

scholarly journals High-density Lipoprotein Cholesterol Is Negatively Correlated with Bone Mineral Density and Has Potential Predictive Value for Bone Loss

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Yuchen Tang ◽  
Shenghong Wang ◽  
Qiong Yi ◽  
Yayi Xia ◽  
Bin Geng
Keyword(s):  
Bone Mineral Density ◽  
Linear Regression ◽  
Regression Models ◽  
Generalized Additive Models ◽  
Density Lipoprotein ◽  
Additive Models ◽  
Nonlinear Relationship ◽  
Linear Regression Models ◽  
Mineral Density ◽  
Increased Risk

Abstract Background Many studies have shown that lipids play important roles in bone metabolism. However, the association between high-density lipoprotein cholesterol (HDL-C) and bone mineral density (BMD) is unclear. Therefore, this study aimed to investigate the linear or nonlinear relation between HDL-C levels and BMD and addressed whether the HDL-C levels had the potential values for predicting the risk of osteoporosis or osteopenia. Methods Two researchers independently extracted all information from the National Health and Nutrition Examination Survey (NHANES) database. Participants over 20 years of age with available HDL-C and BMD data were enrolled in the final analysis. The linear relationship between HDL-C levels and BMD was assessed using multivariate linear regression models. Moreover, the nonlinear relationship was also characterized by fitted smoothing curves and generalized additive models. In addition, the odds ratio (OR) for osteopenia and osteoporosis was evaluated with multiple logistic regression models. Results The weighted multivariable linear regression models demonstrated that HDL-C levels displayed an inverse association with BMD, especially among females and subjects aged 30 to 39 or 50 to 59. Moreover, the nonlinear relationship characterized by smooth curve fittings and generalized additive models suggested that (i) HDL-C levels displayed an inverted U-shaped relationship with BMD among women 30 to 39 or over 60 years of age; (ii) HDL-C levels exhibited a U-shaped association with BMD among women 20 to 29 or 50 to 59 years of age. In addition, females with high HDL levels (62-139 mg/dL) had an increased risk of osteopenia or osteoporosis. Conclusion This study demonstrated that HDL-C levels exhibit an inverse correlation with BMD. Especially in females, clinicians need to be alert to patients with high HDL-C levels, which may indicate an increased risk of osteoporosis or osteopenia. For these patients, close monitoring of BMD and early intervention may be necessary.

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