Beyond Multiple Linear Regression: Applied Generalized Linear Models and Multilevel Models in R

Air pollution is a risk factor for the population health. Its harmful effects on the population are observed even when the atmospheric pollutants are within the parameters set out in specific legislation, and they develop mainly through respiratory diseases. The aim of this study was to analyze the relationship between the concentrations of air pollutants and the incidence of respiratory diseases in the city of Porto Alegre, in 2005 and 2006. Applied multiple linear regression analysis, ordinal logistic regression and generalized linear models were used in the work. The results show good adjustment by the three techniques. The ordinal logistic regression detected only positive influence of air temperature and relative humidity in hospitalizations for respiratory diseases. Multiple linear regression related negatively hospitalizations with meteorological variables and positively with the particulate matter (PM10). The generalized linear model detected negative influence of meteorological variables and positive of pollutants, tropospheric ozone (O3) and PM10 in hospitalizations. Comparing the three statistical techniques to analyze the same data set, it can be concluded that all of them had a model with good fit to the data, but the technique of generalized linear models showed higher sensitivity in capturing the influence of pollutants, except in ordinal logistic regression and multiple linear regression.

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Chemometric approach in the development of the colorimetric method for the estimation of food colorants in meat products

Hemijska industrija ◽

10.2298/hemind131204004p ◽

2014 ◽

Vol 68 (6) ◽

pp. 781-791 ◽

Cited By ~ 2

Author(s):

Radivoj Petronijevic ◽

Vesna Matekalo-Sverak ◽

Aurelija Spiric ◽

Ilija Vukovic ◽

Jelena Babic ◽

...

Keyword(s):

Linear Regression ◽

Mathematical Models ◽

Multiple Linear Regression ◽

Linear Models ◽

Colorimetric Method ◽

Meat Products ◽

Food Colorants ◽

Food Colorant ◽

Control Batch

The aim of this research was to develop a novel colorimetric method based on mathematical models, by multiple linear regression (MLR), from the CIE L*a*b* measurements and data of the HPLC determination of food colorants. Calibration set of 10 production batches of finely grinded cooked sausage with food colorants added was manufactured in industrial conditions as follows: one control batch and 9 products with various quantities of added food colorants: E120 (3.4, 7.5 and 12.5 mg/kg), E 124 (5.0, 15.0, 25.0 mg/kg) and E 129 (5.0, 15.0, 25.0 mg/kg). The estimation of the added food colorants was assessed by measuring L*, a*, b* parameters of cross-section. The quantification of food colorants was achieved by HPLC-PDA. Food colorants were extracted from meat products using Accelerated Solvent Extraction (ASE). Quantification of food colorants was achieved in the range from 1 to 100 mg / kg, and recovery values were from 76.15% to 107.04%, for E 120, from 97.61% to 101.03%, for E 124 and from 99.91% to 101.67%, for E 129. Correlation of the results obtained using HPLC and colorimetric measuring data was assessed by Multiple Linear Regression (MLR). The results from colorimetric and chromatographic determinations in four experimental batches (three batches with different quantities of food colorants and one control batch) were used for calibration. Coefficients of determination (R2) for linear models in experimental batches were 0.954, for E 124, 0.987, for E 120 and 0.993, for E 129. Correlation functions of food colorant quantities and corresponding L*a*b* values were established. The obtained mathematical models were tested for the estimation of the content of dyes in 21 samples of finely grinded cooked sausages purchased in retail stores. Food colorants were confirmed in 20 samples (95.24 %), and one sample (4.76 %) did not contain any of these compounds. Out of the positive samples, sixteen samples (80.00 %) contained E 120, while four samples (20.00 %) contained E 129. Food colorant E124 was not established in any of the analyzed samples. Colorimetric CIE L*a*b* method might be used during sensory evaluation of meat products for the assessment of the added food colorants.

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Forecasting of Daily PM10 Concentrations in Brno and Graz by Different Regression Approaches

Austrian Journal of Statistics ◽

10.17713/ajs.v41i4.169 ◽

2016 ◽

Vol 41 (4) ◽

Cited By ~ 6

Author(s):

Ernst Stadlober ◽

Zuzana Hübnerová ◽

Jaroslav Michálek ◽

Miroslav Kolář

Keyword(s):

Linear Regression ◽

Generalized Linear Models ◽

Linear Models ◽

Prediction Models ◽

Winter Season ◽

Ambient Air ◽

Quality Measures ◽

Limit Value ◽

Two Cities ◽

Daily Pm10

Brno and Graz, the second largest cities of their countries, observe in each winter season PM10 concentrations of daily means which regularly exceed the limit value of 50 ?g/m3. This is mainly caused by unfavorable dissemination conditions of the ambient air. Hence, partial regulation measureshave to be taken in Brno and Graz where specific decisions for certain regulations may be based on the average PM10 concentration of the next day provided that reliable forecasts of these values are available. For several sites in the two cities we establish forecasts of daily PM10 concentrations based onmultiple linear regression and generalized linear models utilizing both measured covariates of the present day and meteorological forecasts of the next day. The comparisons, based on different quality measures demonstrate the usefulness of both model approaches as they yield results of similar quality.Our prediction models may support future decisions concerning possible traffic restrictions or other regulations.

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Linear Regression and Generalized Linear Models

Categorical and Nonparametric Data Analysis ◽

10.4324/9780203122860-16 ◽

2014 ◽

pp. 277-304

Keyword(s):

Linear Regression ◽

Generalized Linear Models ◽

Linear Models

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Multiple Linear Regression Model of Meningococcal Disease in Ukraine: 1992–2015

Computational and Mathematical Methods in Medicine ◽

10.1155/2020/5105120 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Hennadii Mokhort

Keyword(s):

Linear Regression ◽

Multiple Linear Regression ◽

Meningococcal Disease ◽

Total Population ◽

Linear Models ◽

National Level ◽

Multiple Linear Regression Model ◽

National Database ◽

Linear Regression Models ◽

Susceptible Population

Estimating the rates of invasive meningococcal disease (IMD) from epidemiologic data remains critical for making public health decisions. In Ukraine, such estimations have not been performed. We used epidemiological data to develop a national database. These data were used to estimate the population susceptible to IMD and identify the prevalence of asymptomatic carriers of N. meningitidis using simple epidemiological models of meningococcal disease that may be used by the national policy makers. The goal was to create simple, easily understood analysis of patterns of the infection within Ukraine that would capture the major features of the infection dynamics. Studies used nationally reported data during 1992–2015. A logic model identified the prevalence of carriage and the proportion of the population susceptible to IMD as key drivers of IMD incidence. Multiple linear regression models for all ages (total population) and for children ≤14 years old were fit to national-level data. Linear models with the incidence of IMD as an outcome were highly associated with carriage and estimated susceptible population in both total population and children (R2 = 0.994 and R2 = 0.978, respectively). The susceptibility rate to IMD in the study total population averaged 0.0034 ± 0.0009% annually. At the national level, IMD can be characterized by the simple interaction between the prevalence of asymptomatic carriage and the proportion of the susceptible population. IMD association with prevalence rates of carriage and the proportion of susceptible population is sufficiently strong for national-level planning of intervention strategies for IMD.

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Fear of falling in older adults living at home: associated factors

Revista da Escola de Enfermagem da USP ◽

10.1590/s1980-220x2016223703215 ◽

2017 ◽

Vol 51 (0) ◽

Cited By ~ 5

Author(s):

Luciano Magalhães Vitorino ◽

Carla Araujo Bastos Teixeira ◽

Eliandra Laís Vilas Boas ◽

Rúbia Lopes Pereira ◽

Naiana Oliveira dos Santos ◽

...

Keyword(s):

Older Adults ◽

Linear Regression ◽

Multiple Linear Regression ◽

Older Adult ◽

Linear Models ◽

Fear Of Falling ◽

Multiple Linear Regression Model ◽

Cross Sectional ◽

Modifiable Factors ◽

At Home

Abstract OBJECTIVE To identify the factors associated with the fear of falling in the older adultliving at home. METHOD Cross-sectional study with probabilistic sampling of older adultenrolled in two Family Health Strategies (FHS). The fear of falling was measured by the Brazilian version of the Falls Efficacy Scale-International and by a household questionnairethat contained the explanatory variables. Multiple Linear Regression using the stepwise selection technique and the Generalized Linear Models were used in the statistical analyses. RESULTS A total of170 older adultsparticipated in the research, 85 from each FHS. The majority (57.1%) aged between 60 and 69; 67.6% were female; 46.1% fell once in the last year. The majority of the older adults(66.5%) had highfear of falling. In the final multiple linear regression model, it was identified that a higher number of previous falls, female gender, older age, and worse health self-assessment explained 37% of the fear of falling among the older adult. CONCLUSION The findings reinforce the need to assess the fear of falling among the older adultliving at home, in conjunction with the development and use ofstrategies based on modifiable factors by professionalsto reduce falls and improve health status, which may contribute to the reduction of the fear of falling among the older adult.

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Interpretation and Implications of Lognormal Linear Regression Used for Bacterial Enumeration

Journal of AOAC International ◽

10.1093/jaoacint/qsaa005 ◽

2020 ◽

Vol 103 (4) ◽

pp. 1105-1111

Author(s):

Anli Gao ◽

Jennifer Fischer-Jenssen ◽

Charles Wroblewski ◽

Perry Martos

Keyword(s):

Linear Regression ◽

Normal Distribution ◽

Generalized Linear Models ◽

Error Term ◽

Linear Models ◽

Target Concentration ◽

Percent Recovery ◽

Significant Difference ◽

Bacterial Enumeration ◽

Statistical Results

Abstract Background Bacterial enumeration data are typically log transformed to realize a more normal distribution and stabilize the variance. Unfortunately, statistical results from log transformed data are often misinterpreted as data within the arithmetic domain. Objective To explore the implication of slope and intercept from an unweighted linear regression and compare it to the results of the regression of log transformed data. Method Mathematical formulae inferencing explained using real dataset. Results For y=Ax+B+ε, where y is the recovery (CFU/g) and x is the target concentration (CFU/g) with error ε homogeneous across x. When B=0, slope A estimates percent recovery R. In the regression of log transformed data, logy=αlogx+β+εz (equivalent to equation y=Axα·ω), it is the intercept β=logyx=logA that estimates the percent recovery in logarithm when slope α=1, which means that R doesn’t vary over x. Error term ω is multiplicative to x, while εz or log(ω) is additive to log(x). Whether the data should be transformed or not is not a choice, but a decision based on the distribution of the data. Significant difference was not found between the five models (the linear regression of log transformed data, three generalized linear models and a nonlinear model) regarding their predicted percent recovery when applied to our data. An acceptable regression model should result in approximately the best normal distribution of residuals. Conclusions Statistical procedures making use of log transformed data should be studied separately and documented as such, not collectively reported and interpreted with results studied in arithmetic domain. Highlights The way to interpret statistical results developed from arithmetic domain does not apply to that of the log transformed data.

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Regression models

Epidemiology with R ◽

10.1093/oso/9780198841326.003.0005 ◽

2020 ◽

pp. 65-92

Author(s):

Bendix Carstensen

Keyword(s):

Linear Regression ◽

Regression Model ◽

Generalized Linear Models ◽

Linear Regression Model ◽

Regression Models ◽

Linear Models ◽

General Linear Model ◽

Simple Linear Regression ◽

Response Variable ◽

Quantitative Response

This chapter evaluates regression models, focusing on the normal linear regression model. The normal linear regression model establishes a relationship between a quantitative response (also called outcome or dependent) variable, assumed to be normally distributed, and one or more explanatory (also called regression, predictor, or independent) variables about which no distributional assumptions are made. The model is usually referred to as 'the general linear model'. The chapter then differentiates between simple linear regression and multiple regression. The term 'simple linear regression' covers the regression model where there is one response variable and one explanatory variable, assuming a linear relationship between the two. The chapter also discusses the model formulae in R; generalized linear models; collinearity and aliasing; and logarithmic transformations.

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