scholarly journals Algebraic geometry of Poisson regression

2016 ◽  
Vol 7 (1) ◽  
Author(s):  
Thomas Kahle ◽  
Kai-Friederike Oelbermann ◽  
Rainer Schwabe
Keyword(s):  
Algebraic Geometry ◽  
Generalized Linear Models ◽  
Poisson Regression ◽  
Linear Models ◽  
Optimal Designs ◽  
Local Optimality ◽  
Unknown Parameters ◽  
Explanatory Variables ◽  
Saturated Design ◽  
Poisson Counts

Designing experiments for generalized linear models is difficultbecause optimal designs depend on unknown parameters.  Here weinvestigate local optimality.  We propose to study for a given designits region of optimality in parameter space.  Often these regions aresemi-algebraic and feature interesting symmetries.  We demonstratethis with the Rasch Poisson counts model.  For any given interactionorder between the explanatory variables we give a characterization ofthe regions of optimality of a special saturated design. This extendsknown results from the case of no interaction.  We also give analgebraic and geometric perspective on optimality of experimentaldesigns for the Rasch Poisson counts model using polyhedral andspectrahedral geometry.

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.

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.

The properties of partial trace and block trace operators of partitioned matrices

2018 ◽  
Vol 33 ◽  
pp. 3-15 ◽  
Author(s):  
Katarzyna Filipiak ◽  
Daniel Klein ◽  
Erika Vojtková
Keyword(s):  
Linear Models ◽  
Positive Definiteness ◽  
Linear Operators ◽  
Optimal Designs ◽  
Trace Operator ◽  
Multivariate Models ◽  
Unknown Parameters ◽  
Partial Trace ◽  
Multi Level

The aim of this paper is to give the properties of two linear operators defined on non-square partitioned matrix: the partial trace operator and the block trace operator. The conditions for symmetry, nonnegativity, and positive-definiteness are given, as well as the relations between partial trace and block trace operators with standard trace, vectorizing and the Kronecker product operators. Both partial trace as well as block trace operators can be widely used in statistics, for example in the estimation of unknown parameters under the multi-level multivariate models or in the theory of experiments for the determination of an optimal designs under the linear models.

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 Determinants of social startups in Italy

2021 ◽  
pp. 85-90
Author(s):  
Lucio Palazzo ◽  
Pietro Sabatino ◽  
Riccardo Ievoli
Keyword(s):  
Generalized Linear Models ◽  
Social Impact ◽  
Linear Models ◽  
Well Being ◽  
Explanatory Variables ◽  
Technological Value ◽  
Demographic Indicators ◽  
Italian Provinces ◽  
Tax Benefits ◽  
The Empirical Analysis

The so called "Startup Act" (Decree Law 179/2012, converted into Law 221/2012), has introduced in Italy the notion of innovative companies with a high technological value, denoted as the innovative startups. Among them, the Italian government includes the category of SIAVS ("Startup Innovative A Vocazione Sociale"), which represents a relatively new field of interest in both scientific and normative perspective. A social startup must satisfy the same requirement of other innovative startups, usually operating in sectors such as social assistance, education, health, social tourism and culture which can have a direct (social) impact on collective well-being. Furthermore, they must produce specific reporting of the produced social impact, enjoying also some tax benefits. In 2020 more than 200 SIAVS are registered in Italy, more than doubled with respect to 2015. This work is concerned with the empirical analysis of innovative companies focused in funding and implementing solutions to social, cultural, or environmental issues. Specifically, the aim of the paper is to investigate what are the relevant factors for the arise of SIAVS in Italy. The response variable is based on the number of active social startups in Italian provinces while the set of explanatory variables is composed by economic and demographic indicators at the provincial level. Generalized linear models (GLM) for discrete outcomes are applied and compared, even taking into account the zero-inflated issue arising due to the distribution of these particular data.

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