Fitting the truncated negative binomial distribution to count data

Population-averaged and subject-specific models are available to evaluate count data when repeated observations per subject are present. The latter are also known in the literature as generalised linear mixed models (GLMM). In GLMM repeated measures are taken into account explicitly through random animal effects in the linear predictor. In this paper the relevant GLMMs are presented based on conditional Poisson or negative binomial distribution of the response variable for given random animal effects. Equations for the repeatability of count data are derived assuming normal distribution and logarithmic gamma distribution for the random animal effects. Using count data on aggressive behaviour events of pigs (barrows, sows and boars) in mixed-sex housing, we demonstrate the use of the Poisson »log-gamma intercept«, the Poisson »normal intercept« and the »normal intercept« model with negative binomial distribution. Since not all count data can definitely be seen as Poisson or negative-binomially distributed, questions of model selection and model checking are examined. Emanating from the example, we also interpret the least squares means, estimated on the link as well as the response scale. Options provided by the SAS procedure NLMIXED for estimating model parameters and for estimating marginal expected values are presented.

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COMPARATIVE STUDY OF CATTLE TICK RESISTANCE USING GENERALIZED LINEAR MIXED MODELS

REVISTA BRASILEIRA DE BIOMETRIA ◽

10.28951/rbb.v37i1.341 ◽

2019 ◽

Vol 37 (1) ◽

pp. 41

Author(s):

Amanda Marchi MAIORANO ◽

Thiago Santos MOTA ◽

Ana Carolina VERDUGO ◽

Ricardo Antonio da Silva FARIA ◽

Beatriz Pressi Molina da SILVA ◽

...

Keyword(s):

Negative Binomial Distribution ◽

Count Data ◽

Binomial Distribution ◽

Mixed Models ◽

Negative Binomial ◽

Bos Taurus ◽

Generalized Linear Mixed Models ◽

Linear Mixed Models ◽

Tick Count ◽

Tick Resistance

Comparison of tick resistance in Bos taurus indicus (Nelore) and Bos taurus taurus (Simmental and Caracu) subspecies was investigated utilizing generalized linear mixed models (GLMMs) with Poisson and Negative binomial distributions. Nelore animals (NE) are known to present greater resistance than t. taurus. Difference between tick resistance in Simmental (SI) and Caracu (CA) breeds has never been reported previously. Three artificial tick infestations were conducted to evaluate tick resistance in these breeds. The statistic point of the present study was to show alternative models for the evaluation of tick count data, the GLMMs. Analysis for tick resistance by GLMM with Negative binomial distribution has never been assessed previously. The analyses were performed by the use of the PROC GLIMMIX procedure of the SAS program. The results showed that GLMM with Negative binomial distribution is appropriated to evaluate tick count data with excess of zero observations avoiding overdispersion problems. Finally, considering multiple comparisons with the Bonferroni test, different pattern of tick infestation was observed for the studied breeds, suggesting that NE is the most resistant breed followed by CA.

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A Novel Bayesian Outlier Score Based on the Negative Binomial Distribution for Detecting Aberrantly Expressed Genes in RNA-Seq Gene Expression Count Data

IEEE Access ◽

10.1109/access.2021.3082311 ◽

2021 ◽

pp. 1-1

Author(s):

Edin Salkovic ◽

Halima Bensmail

Keyword(s):

Gene Expression ◽

Negative Binomial Distribution ◽

Count Data ◽

Binomial Distribution ◽

Negative Binomial ◽

Rna Seq

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Graphic Model-based Gene Regulatory Network Reconstruction using RNA Sequencing Count Data

JOURNAL OF ADVANCES IN BIOTECHNOLOGY ◽

10.24297/jbt.v8i0.8298 ◽

2019 ◽

Vol 8 ◽

pp. 1078-1085

Author(s):

Liliana Lopez-Kleine ◽

Cristian Andres Gonzalez-Prieto

Keyword(s):

Rna Sequencing ◽

Negative Binomial Distribution ◽

Count Data ◽

Binomial Distribution ◽

Regulatory Networks ◽

Graphical Model ◽

Negative Binomial ◽

Sequencing Data ◽

Model Based ◽

Gene Regulatory

Interactions between genes, such as regulations are best represented by gene regulatory networks (GRN). These are often constructed based on gene expression data. Few methods for the construction of GRN exist for RNA sequencing count data. One of the most used methods for microarray data is based on graphical Gaussian networks. Considering that count data have different distributions, a method assuming RNA sequencing counts distribute Poisson has been proposed recently. Nevertheless, it has been argued that the most likely distribution of RNA sequencing counts is not Poisson due to overdispersion. Therefore, the negative binomial distribution is much more likely. For this distribution, no model-based method for the construction of GRN has been proposed until now. Here, we present a graphical, model-based method for the construction of GRN assuming a negative binomial distribution of the RNA sequencing count data. The R code is available under request. We used the method proposed both on simulated RNA sequencing count data and on real data. The graph is showed, and its descriptive measurements were assessed. They were found some interesting biological conclusions. We confirm that using negative binomial distribution for fitting the model is suitable because RNA sequencing data present overdispersion.

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Analysis of Frequency Count Data Using the Negative Binomial Distribution

Ecology ◽

10.2307/2265753 ◽

1996 ◽

Vol 77 (8) ◽

pp. 2549-2557 ◽

Cited By ~ 250

Author(s):

Gary C. White ◽

Robert E. Bennetts

Keyword(s):

Negative Binomial Distribution ◽

Count Data ◽

Binomial Distribution ◽

Negative Binomial ◽

Frequency Count

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Analysis of correlated count data using generalised linear mixed models exemplified by field data on aggressive behaviour of boars

Archives Animal Breeding ◽

10.7482/0003-9438-57-026 ◽

2015 ◽

Vol 57 (1) ◽

pp. 1-19

Author(s):

Norbert Mielenz ◽

Joachim Spilke ◽

Eberhard von Borell

Keyword(s):

Negative Binomial Distribution ◽

Count Data ◽

Binomial Distribution ◽

Mixed Models ◽

Aggressive Behaviour ◽

Negative Binomial ◽

Linear Mixed Models ◽

Model Parameters ◽

Generalised Linear Mixed Models ◽

Animal Effects

Abstract. Population-averaged and subject-specific models are available to evaluate count data when repeated observations per subject are present. The latter are also known in the literature as generalised linear mixed models (GLMM). In GLMM repeated measures are taken into account explicitly through random animal effects in the linear predictor. In this paper the relevant GLMMs are presented based on conditional Poisson or negative binomial distribution of the response variable for given random animal effects. Equations for the repeatability of count data are derived assuming normal distribution and logarithmic gamma distribution for the random animal effects. Using count data on aggressive behaviour events of pigs (barrows, sows and boars) in mixed-sex housing, we demonstrate the use of the Poisson »log-gamma intercept«, the Poisson »normal intercept« and the »normal intercept« model with negative binomial distribution. Since not all count data can definitely be seen as Poisson or negative-binomially distributed, questions of model selection and model checking are examined. Emanating from the example, we also interpret the least squares means, estimated on the link as well as the response scale. Options provided by the SAS procedure NLMIXED for estimating model parameters and for estimating marginal expected values are presented.

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