Generalized Linear Models for Count Data

2015 ◽  
pp. 429-504
Author(s):  
Michael Friendly ◽  
David Meyer ◽  
Achim Zeileis
Keyword(s):  
Generalized Linear Models ◽  
Count Data ◽  
Linear Models

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 glmGamPoi: Fitting Gamma-Poisson Generalized Linear Models on Single Cell Count Data

2020 ◽  
Author(s):  
Constantin Ahlmann-Eltze ◽  
Wolfgang Huber
Keyword(s):  
Single Cell ◽  
Poisson Distribution ◽  
Generalized Linear Models ◽  
Count Data ◽  
Linear Models ◽  
Differential Expression Analysis ◽  
Source Code ◽  
Principal Component ◽  
R Package ◽  
Single Cell Rna Sequencing

Abstract Motivation The Gamma-Poisson distribution is a theoretically and empirically motivated model for the sampling variability of single cell RNA-sequencing counts (Grün et al., 2014; Svensson, 2020; Silverman et al., 2018; Hafemeister and Satija, 2019) and an essential building block for analysis approaches including differential expression analysis (Robinson et al., 2010; McCarthy et al., 2012; Anders and Huber, 2010; Love et al., 2014), principal component analysis (Townes et al., 2019) and factor analysis (Risso et al., 2018). Existing implementations for inferring its parameters from data often struggle with the size of single cell datasets, which can comprise millions of cells; at the same time, they do not take full advantage of the fact that zero and other small numbers are frequent in the data. These limitations have hampered uptake of the model, leaving room for statistically inferior approaches such as logarithm(-like) transformation. Results We present a new R package for fitting the Gamma-Poisson distribution to data with the characteristics of modern single cell datasets more quickly and more accurately than existing methods. The software can work with data on disk without having to load them into RAM simultaneously. Availability The package glmGamPoi is available from Bioconductor for Windows, macOS, and Linux, and source code is available on github.com/const-ae/glmGamPoi under a GPL-3 license.

scholarly journals Generalized linear models for analyzing count data of rainfall occurrences

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
Sharmin Nahar Sumi ◽  
Narayan Chandra Sinha ◽  
M. Ataharul Islam
Keyword(s):  
Relative Humidity ◽  
Generalized Linear Models ◽  
Count Data ◽  
Linear Models ◽  
Monsoon Season ◽  
Summer Season ◽  
Climatic Variables ◽  
Rainfall Occurrences ◽  
Regional Rainfall ◽  
Rainy Days

AbstractHaving the adequate knowledge about the behavior of climatic variables on the occurrences of rainfall is needed to the country’s economists and agriculturists for saving the country’s people from the devastating natural hazards like flash flood, drought, heavy rainfall, etc. Therefore, the study has been taken initiative to identify the influence of climatic variables for the occurrences of rainfall. The study has been developed generalized linear models (GLMs) for Poisson distribution for weekly and fortnightly count data of daily rainfall occurrences for the summer and monsoon seasons for five regional rainfall stations of Bangladesh. For these models, minimum and maximum temperatures and relative humidity are considered as explanatory variables. For five regional rainfall stations, the model selection procedures AIC and BIC indicate that the GLMs for the Poisson distribution satisfactorily explain the influence of climatic variables for the fortnightly occurrences of rainfall in the summer and monsoon seasons. The GLMs for the summer season of fortnightly occurrences of rainfall indicate that if one unit of relative humidity increases, then the probability of rainy days will be increased by 12 percent in Feni station, 6 percent in Sylhet, Khulna and Rajshahi stations, and 7 percent in Dhaka station. Besides, the GLMs for the monsoon season of fortnightly occurrences of rainfall indicate that if one unit increases of minimum temperature, then the probability of rainy days will be increased by 22 percent, 19 percent, 24 percent, 17 percent and 19 percent in Feni, Sylhet, Khulna, Rajshahi and Dhaka stations, respectively. Further, maximum temperature indicates negative influence on the occurrences of rainfall for all the stations and seasons of the period. The study indicates that the relative humidity for summer season and minimum temperature for monsoon season play remarkable role for changing fortnightly occurrences of rainfall in all the regions of the country.

Fluctuating abundance of humpback whales (Megaptera novaeangliae) in a calving ground off coastal Brazil

2008 ◽  
Vol 88 (6) ◽  
pp. 1229-1235 ◽  
Author(s):  
Maria E. Morete ◽  
Tatiana L. Bisi ◽  
Richard M. Pace ◽  
Sergio Rosso
Keyword(s):  
Generalized Linear Models ◽  
Count Data ◽  
Linear Models ◽  
East Coast ◽  
General Pattern ◽  
Time Of Day ◽  
Megaptera Novaeangliae ◽  
Humpback Whales ◽  
Breeding Ground ◽  
Increasing Trend

The humpback whale (Megaptera novaeangliae) population that uses Abrolhos Bank, off the east coast of Brazil as a breeding ground is increasing. To describe temporal changes in the relative abundance of humpback whales around Abrolhos, seven years (1998–2004) of whale count data were collected during July through to November. During one-hour-scans, observers determined group size within 9.3 km (5 n.m.) of a land-based observing station. A total of 930 scans, comprising 7996 sightings of adults and 2044 calves were analysed using generalized linear models that included variables for time of day, day of the season, years and two-way interactions as possible predictors. The pattern observed was the gradual build-up and decline in whale counts within seasons. Patterns and peaks of adult and calf counts varied among years. Although fluctuation was observed, there was generally an increasing trend in adult counts among years. Calf counts increased only in 2004. These fluctuations may have been caused by some environmental conditions in humpback whales' summering grounds and also by changes in spatial–temporal concentrations in Abrolhos Bank. The general pattern observed within the study area mirrored what was observed in the whole Abrolhos Bank. Knowledge of the consistency with which humpback whales use this important nursing area should prove beneficial for designing future monitoring programmes especially related to whale watching activities around Abrolhos Archipelago.

scholarly journals glmGamPoi: Fitting Gamma-Poisson Generalized Linear Models on Single Cell Count Data

2020 ◽  
Author(s):  
Constantin Ahlmann-Eltze ◽  
Wolfgang Huber
Keyword(s):  
Principal Component Analysis ◽  
Single Cell ◽  
Poisson Distribution ◽  
Generalized Linear Models ◽  
Count Data ◽  
Linear Models ◽  
Differential Expression Analysis ◽  
Source Code ◽  
Principal Component ◽  
Single Cell Rna Sequencing

AbstractMotivationThe Gamma-Poisson distribution is a theoretically and empirically motivated model for the sampling variability of single cell RNA-sequencing counts (Grün et al., 2014; Townes et al., 2019; Svensson, 2020; Silverman et al., 2018; Hafemeister and Satija, 2019) and an essential building block for analysis approaches including differential expression analysis (Robinson et al., 2010; McCarthy et al., 2012; Anders and Huber, 2010; Love et al., 2014), principal component analysis (Townes et al., 2019) and factor analysis (Risso et al., 2018). Existing implementations for inferring its parameters from data often struggle with the size of single cell datasets, which typically comprise thousands or millions of cells; at the same time, they do not take full advantage of the fact that zero and other small numbers are frequent in the data. These limitations have hampered uptake of the model, leaving room for statistically inferior approaches such as logarithm(-like) transformation.ResultsWe present a new R package for fitting the Gamma-Poisson distribution to data with the characteristics of modern single cell datasets more quickly and more accurately than existing methods. The software can work with data on disk without having to load them into RAM simultaneously.AvailabilityThe package glmGamPoi is available from Bioconductor (since release 3.11) for Windows, macOS, and Linux, and source code is available on GitHub under a GPL-3 license. The scripts to reproduce the results of this paper are available on GitHub as [email protected]

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