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Title:

Simultaneous Inference in General Parametric Models

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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the o...

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth of the results. For the analyses we use the R add-on package multcomp, which provides a convenient interface to the general approach adopted here. Key words: multiple tests, multiple comparisons, simultaneous confidence intervals, adjusted p-values, multivariate normal distribution, robust statistics. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-12-04

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http://epub.ub.uni-muenchen.de/2120/1/tr019.pdf

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310 Collections of general statistics *(computed)*

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On multiple comparisons

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The multiplicity problem arises when several inferences are considered simulta-neously as a group. If each inference has a 5 % error rate, then the error rate over the entire group can be much higher than 5%. This article shows practical examples of multiple comparisons procedures that control the error of making any incorrect inference. The mul...

The multiplicity problem arises when several inferences are considered simulta-neously as a group. If each inference has a 5 % error rate, then the error rate over the entire group can be much higher than 5%. This article shows practical examples of multiple comparisons procedures that control the error of making any incorrect inference. The multcomp package for the R statistical environment allows for multiple comparisons of parameters whose estimates are generally correlated, including comparisons of k groups in general linear models. The package has many com-mon multiple comparison procedures “hard-coded”, including Dunnett, Tukey, sequential pairwise contrasts, comparisons with the average, changepoint anal-ysis, Williams’, Marcus’, McDermott’s, and tetrad contrasts. In addition, a free input interface for the contrast matrix allows for more general comparisons. The comparisons themselves are not restricted to balanced or simple designs. Instead, the package is designed to provide general multiple comparisons, thus allowing for covariates, nested effects, correlated means, likelihood-based esti- Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2015-01-16

Source:

http://math.furman.edu/~dcs/courses/math47/R/library/multcomp/doc/Rmc.pdf

http://math.furman.edu/~dcs/courses/math47/R/library/multcomp/doc/Rmc.pdf Minimize

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text

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en

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310 Collections of general statistics *(computed)*

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multcomp: Simultaneous Inference in General Parametric Models, 2008. URL http://CRAN. R-project.org. R package version

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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thuscontroltheover...

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thuscontroltheoveralltypeIerrorrate. Inthispaperwedescribesimultaneousinference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth This is a preprint of an article published in Biometrical Journal, Volume 50, Number 3, 346–363. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-24

Source:

http://cran.r-project.org/web/packages/multcomp/vignettes/generalsiminf.pdf

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text

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multcomp: Simultaneous Inference in General Parametric Models, 2008. URL http://CRAN. R-project.org. R package version

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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the o...

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth This is a preprint of an article published in Biometrical Journal, Volume 50, Number 3, 346–363. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-07-25

Source:

http://cran.at.r-project.org/web/packages/multcomp/vignettes/generalsiminf.pdf

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multcomp: Simultaneous Inference in General Parametric Models, 2008. URL http://CRAN. R-project.org. R package version

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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the o...

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth This is a preprint of an article published in Biometrical Journal, Volume 50, Number 3, 346–363. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-01-17

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http://cran.r-project.org/web/packages/multcomp/vignettes/generalsiminf.pdf

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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting erroneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous inference procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The framework described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth This is a preprint of an article published in Biometrical Journal, Volume 50, Number 3, 346–363. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-03-25

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http://cran.r-project.org/web/packages/multcomp/vignettes/generalsiminf.pdf

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Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting er-roneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the ...

Simultaneous inference is a common problem in many areas of application. If multiple null hypotheses are tested simultaneously, the probability of rejecting er-roneously at least one of them increases beyond the pre-specified significance level. Simultaneous inference procedures have to be used which adjust for multiplicity and thus control the overall type I error rate. In this paper we describe simultaneous infer-ence procedures in general parametric models, where the experimental questions are specified through a linear combination of elemental model parameters. The frame-work described here is quite general and extends the canonical theory of multiple comparison procedures in ANOVA models to linear regression problems, generalized linear models, linear mixed effects models, the Cox model, robust linear models, etc. Several examples using a variety of different statistical models illustrate the breadth ∗This is a preprint of an article published in Biometrical Journal, Volume 50, Number 3, 346–363. Copyright ➞ 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim; available online http://www. biometrical-journal.com. 1 of the results. For the analyses we use the R add-on package multcomp, which pro-vides a convenient interface to the general approach adopted here. Key words: multiple tests, multiple comparisons, simultaneous confidence intervals, adjusted p-values, multivariate normal distribution, robust statistics. 1 Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2014-12-10

Source:

http://cran.fhcrc.org/web/packages/multcomp/vignettes/generalsiminf.pdf

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en

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310 Collections of general statistics *(computed)*

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2010-04-15

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http://cran.r-project.org/web/packages/multcomp/vignettes/generalsiminf.pdf

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Chairperson of the Committee

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I would first like to thank my committee members for their patience and comments throughout writing this dissertation. I would especially like to thank Dr. Tanja Karp for her guidance and willingness to always discuss any questions I had. I would also like to thank my wonderful parents whose love and support has been constant and unwavering. My ...

I would first like to thank my committee members for their patience and comments throughout writing this dissertation. I would especially like to thank Dr. Tanja Karp for her guidance and willingness to always discuss any questions I had. I would also like to thank my wonderful parents whose love and support has been constant and unwavering. My in-laws have also been great to me throughout this dissertation. Thank you for all the encouragement, but most of all thank you for not coming close to my computer while I finished!! I thank God for giving me the wonderful opportunity and experience I had at Texas Tech, and for providing wisdom and encouragement when I needed it most. Lastly and most importantly I would like to thank my loving wife. Her support and encouragement was crucial in me finishing this dissertation. Her patience with me while I spent the late nights was unbelievable. Thank you. I owe you one!! Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://etd.lib.ttu.edu/theses/available/etd-04252006-004528/unrestricted/Patterson_Andrew_Diss.pdf

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CONTENTS ACKNOWLEDGEMENTS. ii ABSTRACT. vi

CONTENTS ACKNOWLEDGEMENTS. ii ABSTRACT. vi Minimize

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Chairperson of the Committee

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Copyright 2006, Engku-Ngah S. Engku-Chik ACKNOWLEDGEMENTS I have been greatly aided in this dissertation by the insightful suggestions and guidance provided

Copyright 2006, Engku-Ngah S. Engku-Chik ACKNOWLEDGEMENTS I have been greatly aided in this dissertation by the insightful suggestions and guidance provided Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-01

Source:

http://etd.lib.ttu.edu/theses/available/etd-07162006-141253/unrestricted/Engku-Chik_Engku-Ngah.pdf

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LIST OF TABLES ……………………………………………………………………

LIST OF TABLES …………………………………………………………………… Minimize

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