The generalized additive model is a well established and strong tool that allows to model smooth effects of predictors on the response. However, if the link function, which is typically chosen as the canonical link, is misspecified, substantial bias is to be expected. A procedure is proposed that simultaneously estimates the form of the link function and the unknown form of the predictor functions including selection of predictors. The procedure is based on boosting methodology, which obtains estimates by using a sequence of weak learners. It strongly dominates fitting procedures that are unable to modify a given link function if the true link function deviates from the fixed function. The performance of the procedure is shown in simulation studies and illustrated by a real world example.

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May 21, 2013

In this paper, individual differences scaling (INDSCAL) is revisited, considering INDSCAL as being embedded within a hierarchy of individual difference scaling models. We explore the members of this family, distinguishing (i) models, (ii) the role of identification and substantive constraints, (iii) criteria for fitting models and (iv) algorithms to optimise the criteria. Model formulations may be based either on data that are in the form of proximities or on configurational matrices. In its configurational version, individual difference scaling may be formulated as a form of generalized Procrustes analysis. Algorithms are introduced for fitting the new models. An application from sensory evaluation illustrates the performance of the methods and their solutions.

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May 10, 2013

We discuss two-sample global permutation tests for sets of multivariate ordinal data in possibly high-dimensional setups, motivated by the analysis of data collected by means of the World Health Organisation's International Classification of Functioning, Disability and Health. The tests do not require any modelling of the multivariate dependence structure. Specifically, we consider testing for marginal inhomogeneity and direction-independent marginal order. Max-T test statistics are known to lead to good power against alternatives with few strong individual effects. We propose test statistics that can be seen as their counterparts for alternatives with many weak individual effects. Permutation tests are valid only if the two multivariate distributions are identical under the null hypothesis. By means of simulations, we examine the practical impact of violations of this exchangeability condition. Our simulations suggest that theoretically invalid permutation tests can still be 'practically valid'. In particular, they suggest that the degree of the permutation procedure's failure may be considered as a function of the difference in group-specific covariance matrices, the proportion between group sizes, the number of variables in the set, the test statistic used, and the number of levels per variable.

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Apr 17, 2013

In linear mixed models, the assumption of normally distributed random effects is often inappropriate and unnecessarily restrictive. The proposed approximate Dirichlet process mixture assumes a hierarchical Gaussian mixture that is based on the truncated version of the stick breaking presentation of the Dirichlet process. In addition to the weakening of distributional assumptions, the specification allows to identify clusters of observations with a similar random effects structure. An Expectation-Maximization algorithm is given that solves the estimation problem and that, in certain respects, may exhibit advantages over Markov chain Monte Carlo approaches when modelling with Dirichlet processes. The method is evaluated in a simulation study and applied to the dynamics of unemployment in Germany as well as lung function growth data.

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Feb 01, 2013

Variable selection has been suggested for Random Forests to improve their efficiency of data prediction and interpretation. However, its basic element, i.e. variable importance measures, can not be computed straightforward when there is missing data. Therefore an extensive simulation study has been conducted to explore possible solutions, i.e. multiple imputation, complete case analysis and a newly suggested importance measure for several missing data generating processes. The ability to distinguish relevant from non-relevant variables has been investigated for these procedures in combination with two popular variable selection methods. Findings and recommendations: Complete case analysis should not be applied as it lead to inaccurate variable selection and models with the worst prediction accuracy. Multiple imputation is a good means to select variables that would be of relevance in fully observed data. It produced the best prediction accuracy. By contrast, the application of the new importance measure causes a selection of variables that reflects the actual data situation, i.e. that takes the occurrence of missing values into account. It's error was only negligible worse compared to imputation.

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Jan 15, 2013

This short note contains an explicit proof of the Dirichlet distribution being the conjugate prior to the Multinomial sample distribution as resulting from the general construction method described, e.g., in Bernardo and Smith (2000). The well-known Dirichlet-Multinomial model is thus shown to fit into the framework of canonical conjugate analysis (Bernardo and Smith 2000, Prop.~5.6, p.~273), where the update step for the prior parameters to their posterior counterparts has an especially simple structure. This structure is used, e.g., in the Imprecise Dirichlet Model (IDM) by Walley (1996), a simple yet powerful model for imprecise Bayesian inference using sets of Dirichlet priors to model vague prior knowledge, and furthermore in other imprecise probability models for inference in exponential families where sets of priors are considered.

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Oct 04, 2012

The use of the multinomial logit model is typically restricted to applications with few predictors, because in high-dimensional settings maximum likelihood estimates tend to deteriorate. In this paper we are proposing a sparsity-inducing penalty that accounts for the special structure of multinomial models. In contrast to existing methods, it penalizes the parameters that are linked to one variable in a grouped way and thus yields variable selection instead of parameter selection. We develop a proximal gradient method that is able to efficiently compute stable estimates. In addition, the penalization is extended to the important case of predictors that vary across response categories. We apply our estimator to the modeling of party choice of voters in Germany including voter-specific variables like age and gender but also party-specific features like stance on nuclear energy and immigration.

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Jun 21, 2012

The use of the multinomial logit model is typically restricted to applications with few predictors, because in high-dimensional settings maximum likelihood estimates tend to deteriorate. In this paper we are proposing a sparsity-inducing penalty that accounts for the special structure of multinomial models. In contrast to existing methods, it penalizes the parameters that are linked to one variable in a grouped way and thus yields variable selection instead of parameter selection. We develop a proximal gradient method that is able to efficiently compute stable estimates. In addition, the penalization is extended to the important case of predictors that vary across response categories. We apply our estimator to the modeling of party choice of voters in Germany including voter-specific variables like age and gender but also party-specific features like stance on nuclear energy and immigration.

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Jun 21, 2012

A method is proposed that aims at identifying clusters of individuals that show similar patterns when observed repeatedly. We consider linear mixed models which are widely used for the modeling of longitudinal data. In contrast to the classical assumption of a normal distribution for the random effects a finite mixture of normal distributions is assumed. Typically, the number of mixture components is unknown and has to be chosen, ideally by data driven tools. For this purpose an EM algorithm-based approach is considered that uses a penalized normal mixture as random effects distribution. The penalty term shrinks the pairwise distances of cluster centers based on the group lasso and the fused lasso method. The effect is that individuals with similar time trends are merged into the same cluster. The strength of regularization is determined by one penalization parameter. For finding the optimal penalization parameter a new model choice criterion is proposed.

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Jun 12, 2012

A novel point process model continuous in space-time is proposed for quantifying the transmission dynamics of the two most common meningococcal antigenic sequence types observed in Germany 2002-2008. Modelling is based on the conditional intensity function (CIF) which is described by a superposition of additive and multiplicative components. As an epidemiological interesting finding, spread behaviour was shown to depend on type in addition to age: basic reproduction numbers were 0.25 (95% CI 0.19-0.34) and 0.11 (95% CI 0.07-0.17) for types B:P1.7-2,4:F1-5 and C:P1.5,2:F3-3, respectively. Altogether, the proposed methodology represents a comprehensive and universal regression framework for the modelling, simulation and inference of self-exciting spatio-temporal point processes based on the CIF. Usability of the modelling in biometric practice is promoted by an implementation in the R package surveillance.

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Jun 01, 2012

A novel point process model continuous in space-time is proposed for quantifying the transmission dynamics of the two most common meningococcal antigenic sequence types observed in Germany 2002-2008. Modelling is based on the conditional intensity function (CIF) which is described by a superposition of additive and multiplicative components. As an epidemiological interesting finding, spread behaviour was shown to depend on type in addition to age: basic reproduction numbers were 0.25 (95% CI 0.19-0.34) and 0.11 (95% CI 0.07-0.17) for types B:P1.7-2,4:F1-5 and C:P1.5,2:F3-3, respectively. Altogether, the proposed methodology represents a comprehensive and universal regression framework for the modelling, simulation and inference of self-exciting spatio-temporal point processes based on the CIF. Usability of the modelling in biometric practice is promoted by an implementation in the R package surveillance.

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Jun 01, 2012

The partial area under the receiver operating characteristic curve (PAUC) is a well-established performance measure to evaluate biomarker combinations for disease classification. Because the PAUC is defined as the area under the ROC curve within a restricted interval of false positive rates, it enables practitioners to quantify sensitivity rates within pre-specified specificity ranges. This issue is of considerable importance for the development of medical screening tests. Although many authors have highlighted the importance of PAUC, there exist only few methods that use the PAUC as an objective function for finding optimal combinations of biomarkers. In this paper, we introduce a boosting method for deriving marker combinations that is explicitly based on the PAUC criterion. The proposed method can be applied in high-dimensional settings where the number of biomarkers exceeds the number of observations. Additionally, the proposed method incorporates a recently proposed variable selection technique (stability selection) that results in sparse prediction rules incorporating only those biomarkers that make relevant contributions to predicting the outcome of interest. Using both simulated data and real data, we demonstrate that our method performs well with respect to both variable selection and prediction accuracy. Specifically, if the focus is on a limited range of specificity values, the new method results in better predictions than other established techniques for disease classification.

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Jan 01, 2012

Security-Frameworks sind baukastenähnliche, zunächst abstrakte Konzepte, die aufeinander abgestimmte technische und organisatorische Maßnahmen zur Prävention, Detektion und Bearbeitung von Informationssicherheitsvorfällen bündeln. Anders als bei der Zusammenstellung eigener Sicherheitskonzepte aus einer Vielzahl punktueller Einzelmaßnahmen wird bei der Anwendung von Security-Frameworks das Ziel verfolgt, mit einem relativ geringen Aufwand auf bewährte Lösungsansätze zur Absicherung von komplexen IT-Diensten und IT-Architekturen zurückgreifen zu können. Die praktische Umsetzung eines Security-Frameworks erfordert seine szenarienspezifische Adaption und Implementierung, durch die insbesondere eine nahtlose Integration in die vorhandene Infrastruktur sichergestellt und die Basis für den nachhaltigen, effizienten Betrieb geschaffen werden müssen. Die vorliegende Arbeit behandelt das integrierte Management von Security-Frameworks. Im Kern ihrer Betrachtungen liegen folglich nicht individuelle Frameworkkonzepte, sondern Managementmethoden, -prozesse und -werkzeuge für den parallelen Einsatz mehrerer Frameworkinstanzen in komplexen organisationsweiten und -übergreifenden Szenarien. Ihre Schwerpunkte werden zum einen durch die derzeit sehr technische Ausprägung vieler Security-Frameworks und zum anderen durch die fehlende Betrachtung ihres Lebenszyklus über die szenarienspezifische Anpassung hinaus motiviert. Beide Aspekte wirken sich bislang inhibitorisch auf den praktischen Einsatz aus, da zur Umsetzung von Security-Frameworks immer noch ein erheblicher szenarienspezifischer konzeptioneller Aufwand erbracht werden muss. Nach der Diskussion der relevanten Grundlagen des Sicherheitsmanagements und der Einordnung von Security-Frameworks in Informationssicherheitsmanagementsysteme werden auf Basis ausgewählter konkreter Szenarien mehr als 50 Anforderungen an Security-Frameworks aus der Perspektive ihres Managements abgeleitet und begründet gewichtet. Die anschließende Anwendung dieses Anforderungskatalogs auf mehr als 75 aktuelle Security-Frameworks zeigt typische Stärken sowie Schwächen auf und motiviert neben konkreten Verbesserungsvorschlägen für Frameworkkonzepte die nachfolgend erarbeiteten, für Security-Frameworks spezifischen Managementmethoden. Als Bezugsbasis für alle eigenen Konzepte dient eine detaillierte Analyse des gesamten Lebenszyklus von Security-Frameworks, der zur grundlegenden Spezifikation von Managementaufgaben, Verantwortlichkeiten und Schnittstellen zu anderen Managementprozessen herangezogen wird. Darauf aufbauend werden an den Einsatz von Security-Frameworks angepasste Methoden und Prozesse u. a. für das Risikomanagement und ausgewählte Disziplinen des operativen Sicherheitsmanagements spezifiziert, eine Sicherheitsmanagementarchitektur für Security-Frameworks konzipiert, die prozessualen Schnittstellen am Beispiel von ISO/IEC 27001 und ITIL v3 umfassend ausgearbeitet und der Einsatz von IT-Sicherheitskennzahlen zur Beurteilung von Security-Frameworks demonstriert. Die praktische Anwendung dieser innovativen Methoden erfordert dedizierte Managementwerkzeuge, die im Anschluss im Detail konzipiert und in Form von Prototypen bzw. Simulationen umgesetzt, exemplifiziert und bewertet werden. Ein umfassendes Anwendungsbeispiel demonstriert die praktische, parallele Anwendung mehrerer Security-Frameworks und der spezifizierten Konzepte und Werkzeuge. Abschließend werden alle erreichten Ergebnisse kritisch beurteilt und ein Ausblick auf mögliche Weiterentwicklungen und offene Forschungsfragestellungen in verwandten Bereichen gegeben.

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Jan 01, 2012