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Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03

Mathematik, Informatik und Statistik - Open Access LMU - Teil 01/03

Ludwig-Maximilians-Universität München 250 Episoden Neueste vor 24 Jahren
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Quantifying overdispersion effects in count regression data

1 minute
The Poisson regression model is often used as a first model for count data with covariates. Since this model is a GLM with canonical link, regression parameters can be easily fitted using standard software. However the model requires equidispersion, which might not be valid for the data set under consideration. There have been many models proposed in the literature to allow for overdispersion. One such model is the negative binomial regression model. In addition, score tests have been commonly used to detect overdispersion in the data. However these tests do not allow to quantify the effects of overdispersion. In this paper we propose easily interpretable discrepancy measures which allow to quantify the overdispersion effects when comparing a negative binomial regression to Poisson regression. We propose asymptotic $\alpha$-level tests for testing the size of overdispersion effects in terms of the developed discrepancy measures. A graphical display of p-values curves can then be used to allow for an exact quantification of the overdispersion effects. This can lead to a validation of the Poisson regression or a discrimination of the Poisson regression with respect to the negative binomial regression. The proposed asymptotic tests are investigated in small samples using simulation and applied to two examples.

Graphical chain models for the analysis of complex genetic diseases: an application to hypertension

1 minute
A crucial task in modern genetic medicine is the understanding of complex genetic diseases. The main complicating features are that a combination of genetic and environmental risk factors is involved, and the phenotype of interest may be complex. Traditional statistical techniques based on lod-scores fail when the disease is no longer monogenic and the underlying disease transmission model is not defined. Different kinds of association tests have been proved to be an appropriate and powerful statistical tool to detect a candidate gene for a complex disorder. However, statistical techniques able to investigate direct and indirect influences among phenotypes, genotypes and environmental risk factors, are required to analyse the association structure of complex diseases. In this paper we propose graphical models as a natural tool to analyse the multifactorial structure of complex genetic diseases. An application of this model to primary hypertension data set is illustrated.

Geo-additive models of Childhood Undernutrition in three Sub-Saharan African Countries

1 minute
We investigate the geographical and socioeconomic determinants of childhood undernutrition in Malawi, Tanzania and Zambia, three neighboring countries in Southern Africa using the 1992 Demographic and Health Surveys. We estimate models of undernutrition jointly for the three countries to explore regional patterns of undernutrition that transcend boundaries, while allowing for country-specific interactions. We use semiparametric models to flexibly model the effects of selected so-cioeconomic covariates and spatial effects. Our spatial analysis is based on a flexible geo-additive model using the district as the geographic unit of anal-ysis, which allows to separate smooth structured spatial effects from random effect. Inference is fully Bayesian and uses recent Markov chain Monte Carlo techniques. While the socioeconomic determinants generally confirm what is known in the literature, we find distinct residual spatial patterns that are not explained by the socioeconomic determinants. In particular, there appears to be a belt run-ning from Southern Tanzania to Northeastern Zambia which exhibits much worse undernutrition, even after controlling for socioeconomic effects. These effects do transcend borders between the countries, but to a varying degree. These findings have important implications for targeting policy as well as the search for left-out variables that might account for these residual spatial patterns.

Parametric and Nonparametric Regression with Missing X's - A Review

1 minute
This paper gives a detailed overview of the problem of missing data in parametric and nonparametric regression. Theoretical basics, properties as well as simulation results may help the reader to get familiar with the common problem of incomplete data sets. Of course, not all occurences can be discussed so this paper could be seen as an introduction to missing data within regression analysis and as an extension to the early paper of Little (1992).

A Selection Model for Bivariate Normal Data, with a Flexible Nonparametric Missing Model and a Focus on Variance Estimates

1 minute
Nonignorable nonresponse is a common problem in bivariate or multivariate data. Here a selection model for bivariate normal distributed data (Y1 ; Y2) is proposed. The missingness of Y2 is supposed to depend on its own values. The model for missingness describes the probability of nonresponse in dependency of Y2 itself and it is chosen nonparametrically to allow exible patterns. We try to get a reasonable estimate for the expectation and especially for the variance of Y2 . Estimation is done by data augmentation and computation by common sampling methods.
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Die Universitätsbibliothek (UB) verfügt über ein umfangreiches Archiv an elektronischen Medien, das von Volltextsammlungen über Zeitungsarchive, Wörterbücher und Enzyklopädien bis hin zu ausführlichen Bibliographien und mehr als 1000 Datenbanken reicht. Auf iTunes U stellt die UB unter anderem eine Auswahl an elektronischen Publikationen der Wissenschaftlerinnen und Wissenschaftler an der LMU bereit. (Dies ist der 1. von 3 Teilen der Sammlung 'Mathematik, Informatik und Statistik - Open Access LMU'.)
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Ludwig-Maximilians-Universität München
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