More generalized linear modelling.

2021 ◽  
pp. 171-186
Author(s):  
Donald Quicke ◽  
Buntika A. Butcher ◽  
Rachel Kruft Welton
Keyword(s):  
Generalized Linear Models ◽  
Count Data ◽  
Binary Data ◽  
Linear Models ◽  
Explanatory Variable ◽  
Response Variable ◽  
Explanatory Variables ◽  
Continuous Response ◽  
Generalized Linear Modelling ◽  
Linear Modelling

Abstract This chapter employs generalized linear modelling using the function glm when we know that variances are not constant with one or more explanatory variables and/or we know that the errors cannot be normally distributed, for example, they may be binary data, or count data where negative values are impossible, or proportions which are constrained between 0 and 1. A glm seeks to determine how much of the variation in the response variable can be explained by each explanatory variable, and whether such relationships are statistically significant. The data for generalized linear models take the form of a continuous response variable and a combination of continuous and discrete explanatory variables.

scholarly journals Generalized Linear Spatial Models to Predict Slate Exploitability

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Angeles Saavedra ◽  
Javier Taboada ◽  
María Araújo ◽  
Eduardo Giráldez
Keyword(s):  
Spatial Distribution ◽  
Generalized Linear Models ◽  
Spatial Dependence ◽  
Spatial Model ◽  
Linear Models ◽  
Spatial Models ◽  
Response Variable ◽  
Explanatory Variables ◽  
Model Residuals

The aim of this research was to determine the variables that characterize slate exploitability and to model spatial distribution. A generalized linear spatial model (GLSMs) was fitted in order to explore relationship between exploitability and different explanatory variables that characterize slate quality. Modelling the influence of these variables and analysing the spatial distribution of the model residuals yielded a GLSM that allows slate exploitability to be predicted more effectively than when using generalized linear models (GLM), which do not take spatial dependence into account. Studying the residuals and comparing the prediction capacities of the two models lead us to conclude that the GLSM is more appropriate when the response variable presents spatial distribution.

scholarly journals Generalized lineal models for the analysis of binary data from propagation experiments of Brazilian orchids

2008 ◽  
Vol 51 (5) ◽  
pp. 963-970 ◽  
Author(s):  
Freddy Mora ◽  
Letícia de Menezes Gonçalves ◽  
Carlos Alberto Scapim ◽  
Elias Nunes Martins ◽  
Maria de Fátima Pires da Silva Machado
Keyword(s):  
Generalized Linear Models ◽  
Binary Data ◽  
Linear Models ◽  
Storage Temperature ◽  
Culture Media ◽  
Seed Viability ◽  
Response Variable ◽  
Statistical Approaches ◽  
Germination Experiment ◽  
Storage Temperatures

This study aimed at applying the generalized linear models (GLM) for the analysis of a germination experiment of Cattleya bicolor in which the response variable was binary. The purpose of this experiment was to assess the effects of the storage temperatures and culture mediums on the seed viability. The analyses of variance was also carried out either with or without the data transformation. All the statistical approaches indicated the importance of the storage temperature on the seed viability. But, the culture media and interaction effects were significant only by the GLM. Based on the GLM, the seeds stored at 10°C increased viability, in which the coconut medium achieved the best performance. The results emphasized the importance of adopting the GLM to improve the reliability in many situations where the response variable followed a non-normal distribution.

Analysis of variance (ANOVA).

2021 ◽  
pp. 155-165
Author(s):  
Donald Quicke ◽  
Buntika A. Butcher ◽  
Rachel Kruft Welton
Keyword(s):  
Linear Model ◽  
Analysis Of Variance ◽  
Explanatory Variable ◽  
T Test ◽  
Specific Function ◽  
Real Numbers ◽  
Response Variable ◽  
Explanatory Variables ◽  
Student’S T ◽  
One Way Anova

Abstract Analysis of variance is used to analyze the differences between group means in a sample, when the response variable is numeric (real numbers) and the explanatory variable(s) are all categorical. Each explanatory variable may have two or more factor levels, but if there is only one explanatory variable and it has only two factor levels, one should use Student's t-test and the result will be identical. Basically an ANOVA fits an intercept and slopes for one or more of the categorical explanatory variables. ANOVA is usually performed using the linear model function lm, or the more specific function aov, but there is a special function oneway.test when there is only a single explanatory variable. For a one-way ANOVA the non-parametric equivalent (if variance assumptions are not met) is the kruskal.test.

Climate Influences on Meningitis Incidence in Northwest Nigeria

2014 ◽  
Vol 6 (1) ◽  
pp. 62-76 ◽  
Author(s):  
Auwal F. Abdussalam ◽  
Andrew J. Monaghan ◽  
Vanja M. Dukić ◽  
Mary H. Hayden ◽  
Thomas M. Hopson ◽  
...  
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Generalized Additive Models ◽  
Skill Score ◽  
Additive Models ◽  
Maximum Temperature ◽  
Daily Maximum Temperature ◽  
Daily Maximum ◽  
Explanatory Variables ◽  
Score Statistics

Abstract Northwest Nigeria is a region with a high risk of meningitis. In this study, the influence of climate on monthly meningitis incidence was examined. Monthly counts of clinically diagnosed hospital-reported cases of meningitis were collected from three hospitals in northwest Nigeria for the 22-yr period spanning 1990–2011. Generalized additive models and generalized linear models were fitted to aggregated monthly meningitis counts. Explanatory variables included monthly time series of maximum and minimum temperature, humidity, rainfall, wind speed, sunshine, and dustiness from weather stations nearest to the hospitals, and the number of cases in the previous month. The effects of other unobserved seasonally varying climatic and nonclimatic risk factors that may be related to the disease were collectively accounted for as a flexible monthly varying smooth function of time in the generalized additive models, s(t). Results reveal that the most important explanatory climatic variables are the monthly means of daily maximum temperature, relative humidity, and sunshine with no lag; and dustiness with a 1-month lag. Accounting for s(t) in the generalized additive models explains more of the monthly variability of meningitis compared to those generalized linear models that do not account for the unobserved factors that s(t) represents. The skill score statistics of a model version with all explanatory variables lagged by 1 month suggest the potential to predict meningitis cases in northwest Nigeria up to a month in advance to aid decision makers.

scholarly journals Penalized Likelihood Estimation of Gamma Distributed Response Variable via Corrected Solution of Regression Coefficients

2021 ◽  
Vol 19 (1) ◽  
Author(s):  
Rasaki Olawale Olanrewaju
Keyword(s):  
Generalized Linear Models ◽  
Linear Models ◽  
Penalized Likelihood ◽  
Likelihood Estimation ◽  
Regression Coefficients ◽  
Response Variable ◽  
Penalized Likelihood Estimation ◽  
Selection Operator ◽  
Minimax Concave Penalty

A Gamma distributed response is subjected to regression penalized likelihood estimations of Least Absolute Shrinkage and Selection Operator (LASSO) and Minimax Concave Penalty via Generalized Linear Models (GLMs). The Gamma related disturbance controls the influence of skewness and spread in the corrected path solutions of the regression coefficients.

Regression and correlation analyses.

2021 ◽  
pp. 119-146
Author(s):  
Donald Quicke ◽  
Buntika A. Butcher ◽  
Rachel Kruft Welton
Keyword(s):  
Regression Analysis ◽  
Explanatory Variable ◽  
Continuous Variable ◽  
The Other ◽  
Strongly Correlated ◽  
Regression Analyses ◽  
Response Variable ◽  
Explanatory Variables ◽  
Correlation Analyses ◽  
Initial Assumption

Abstract This chapter focuses on regression and correlation analyses. Correlation and regression analyses are used to test whether, and to what degree, variation in one continuous variable is related to variation in another continuous variable. In correlation analysis, there are no control over either variable, they are just data collected, and indeed, even if two variables are strongly correlated, they may not be influencing one another but simply both being affected by a third which perhaps was not measured. The initial assumption of the analysis is that the values of both variables are drawn from a normal distribution. In regression analysis one of the variables are being controlled seeing whether changing its value affects the other. The variable being controlled is the explanatory variable (sometimes called the treatment) and the other is the response variable. As the explanatory variables are being controlled, they are probably going to be set at specified values or set increments and are therefore not normally distributed. There may be more than one explanatory variable. If all the explanatory variables are categorical then the regression is called an ANOVA.

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