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Title:

Locating Multiple Interacting Quantitative Trait Loci with the Zero-Inflated Generalized Poisson Regression

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We consider the problem of locating multiple interacting quantitative trait loci (QTL) influencing traits measured in counts. In many applications the distribution of the count variable has a spike at zero. Zero-inflated generalized Poisson regression (ZIGPR) allows for an additional probability mass at zero and hence an improvement in the detec...

We consider the problem of locating multiple interacting quantitative trait loci (QTL) influencing traits measured in counts. In many applications the distribution of the count variable has a spike at zero. Zero-inflated generalized Poisson regression (ZIGPR) allows for an additional probability mass at zero and hence an improvement in the detection of significant loci. Classical model selection criteria often overestimate the QTL number. Therefore, modified versions of the Bayesian Information Criterion (mBIC and EBIC) were successfully used for QTL mapping. We apply these criteria based on ZIGPR as well as simpler models. An extensive simulation study shows their good power detecting QTL while controlling the false discovery rate. We illustrate how the inability of the Poisson distribution to account for over-dispersion leads to an overestimation of the QTL number and hence strongly discourages its application for identifying factors influencing count data. The proposed method is used to analyze the mice gallstone data of Lyons et al. (2003). Our results suggest the existence of a novel QTL on chromosome 4 interacting with another QTL previously identified on chromosome 5. We provide the corresponding code in R. ; Computational Biology/Bioinformatics, Statistical Models, quantitative trait loci, count data, model selection criteria, zero inflated Poisson regression Minimize

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Title:

Sampling Count Variables with specified Pearson Correlation -- a Comparison between a naive and a C-vine Sampling Approach

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Erhardt and Czado (2008) suggest an approximative method for sampling highdimensional count random variables with a specified Pearson correlation. They utilize Gaussian copulae for the construction of multivariate discrete distributions. A major task is to determine the appropriate copula parameters for the achievement of a specified target corr...

Erhardt and Czado (2008) suggest an approximative method for sampling highdimensional count random variables with a specified Pearson correlation. They utilize Gaussian copulae for the construction of multivariate discrete distributions. A major task is to determine the appropriate copula parameters for the achievement of a specified target correlation. Erhardt and Czado (2008) develop an optimization routine to determine these copula parameters sequentially. Thereby, they use pair-copula decompositions of n-dimensional distributions, i.e. a decomposition consisting only of bivariate copula with one parameter each. C-vines, a graphical tool to organize such pair-copula decompositions, are used to select a possible decomposition. In the paper mentioned, the approach was compared to the NORTA method for discrete margins described in Avramidis, Channouf, and L’Ecuyer (2008). Here we will compare it to a widely used naive sampling approach for an even larger variety of marginal distributions such as the Poisson, generalized Poisson, Negative Binomial and zero-inflated Generalized Poisson distribution. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-10-25

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/cvinevsnaivewebpage.pdf

http://www-m4.ma.tum.de/Papers/Erhardt/cvinevsnaivewebpage.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

including zero-claims

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Modelling dependent yearly claim totals

Modelling dependent yearly claim totals Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-03-19

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/pcc-marginals-erhardt-czado.pdf

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Modelling dependent yearly claim totals including zero-claims in . . .

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-10-25

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/pcc-marginals-erhardt-czado.pdf

Document Type:

text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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A method for approximately sampling high-dimensional countvariableswithprespecifiedPearsoncorrelation.Submitted for publication.Preprint available at http://www-m4.ma.tum.de/Papers/index.html

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We suggest an approximative method for sampling high-dimensional random variables with a specified Pearson correlation matrix. We sample from dependent vectors using pair-copula constructions (PCC) and use C-vines, a graphical tool to organize such PCC. Thereby, we choose bivariate Gaussian copulas for the construction. A major task is to determ...

We suggest an approximative method for sampling high-dimensional random variables with a specified Pearson correlation matrix. We sample from dependent vectors using pair-copula constructions (PCC) and use C-vines, a graphical tool to organize such PCC. Thereby, we choose bivariate Gaussian copulas for the construction. A major task is to determine the appropriate copula parameterstoobtainthespecifiedtargetcorrelation.Wewillintroduceasequentialandveryfastrootfinding routine to approximate them using bisection. We will illustrate that our sampling approach generates accurate results even in high dimensions and for relatively small sample sizes in several settings with Poisson, generalized Poisson, zero-inflated generalized Poisson and Negative Binomial margins in a variety of settings. We show its advantages over the NORTA method for discrete margins. An implementation of our algorithm for R is available as package corcounts on CRAN. Keywords: algorithm; longitudinal count data; pair copula construction; C-vine; input modeling. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-04-20

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/erhardt-sampling.pdf

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Title:

A Method for approximately sampling high-dimensional Count Variables with prespecified Pearson Correlation

Description:

We suggest an approximative method for sampling high-dimensional count random variables with a specified Pearson correlation. As in the continuous case copulas can be used to construct multivariate discrete distributions. We utilize Gaussian copulas for the construction. A major task is to determine the appropriate copula parameters to obtain th...

We suggest an approximative method for sampling high-dimensional count random variables with a specified Pearson correlation. As in the continuous case copulas can be used to construct multivariate discrete distributions. We utilize Gaussian copulas for the construction. A major task is to determine the appropriate copula parameters to obtain the specified target correlation. Very often, the fact that for the Gaussian copula the correlation matrix of the multivariate normal distribution is not equal to the correlation of the sampled (discrete) outcomes, is simply neglected. We will introduce an optimization routine to determine the copula parameters sequentially using bisection. Thereby, we need to break our T-dimensional copula down to a decomposition of bivariate copulas with only one parameter each. We use C-vines, a graphical tool to organize such pair-copula decompositions of highdimensional distributions. We will illustrate that our sampling approach generates accurate results even in high dimensions in several settings with Poisson, generalized Poisson, zero-inflated generalized Poisson and Negative Binomial margins for a variety of marginal parameters and outperforms a widely used ’naive ’ sampling approach. An implementation of our algorithm for R is available as package corcounts on ’The Comprehensive R Archive Network ’ (CRAN). Keywords: algorithm; longitudinal; pair copula construction; C-vine; partial correlation. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-11-19

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/erhardt-sampling.pdf

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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1

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multiple interacting quantitative trait loci

multiple interacting quantitative trait loci Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-03-19

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/erhardt-bogdan-czado.pdf

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text

Language:

en

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Generalized estimating equations for longitudinal generalized Poisson count data with regression effects on the mean and dispersion level

Generalized estimating equations for longitudinal generalized Poisson count data with regression effects on the mean and dispersion level Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-04-20

Source:

http://www-m4.ma.tum.de/Papers/Erhardt/ec-gee-web.pdf

http://www-m4.ma.tum.de/Papers/Erhardt/ec-gee-web.pdf Minimize

Document Type:

text

Language:

en

Subjects:

generalized estimating equations ; generalized Poisson regression ; longitudinal count data

generalized estimating equations ; generalized Poisson regression ; longitudinal count data Minimize

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outsourcing

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Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent

Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://www-m4.ma.tum.de/Papers/Czado/Czado-Erhardt-Min-Wagner.ps

http://www-m4.ma.tum.de/Papers/Czado/Czado-Erhardt-Min-Wagner.ps Minimize

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text

Language:

en

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maximum likelihood estimator ; overdispersion ; patent outsourcing ; Vuong test ; zero-inflated generalized Poisson regression ; zero-inflation 1 Corresponding author

maximum likelihood estimator ; overdispersion ; patent outsourcing ; Vuong test ; zero-inflated generalized Poisson regression ; zero-inflation 1 Corresponding author Minimize

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Corresponding author.

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Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent

Zero-inflated generalized Poisson models with regression effects on the mean, dispersion and zero-inflation level applied to patent Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-08

Source:

http://www.statistik.lmu.de/sfb386/papers/dsp/paper482.pdf

http://www.statistik.lmu.de/sfb386/papers/dsp/paper482.pdf Minimize

Document Type:

text

Language:

en

Subjects:

maximum likelihood estimator ; overdispersion ; patent outsourcing ; Vuong test ; zero-inflated generalized Poisson regression ; zero-inflation 1

maximum likelihood estimator ; overdispersion ; patent outsourcing ; Vuong test ; zero-inflated generalized Poisson regression ; zero-inflation 1 Minimize

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