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A nonparametric permutation approach to statistical shape analysis
Full text linkThe statistical community has shown an increased interest in shape analysis in the last decade, in particular with reference to the development of robust inferential statistical methods.
In this Ph.D. thesis we present an extension of NonParametric Combination (NPC) methodology (Pesarin, 2001) to shape analysis. At first we review inferential methods known in the shape analysis literature, highlighting some drawbacks of using Hotelling's T^2 test statistic. Then, focussing on the two independent sample case, through an exhaustive comparative simulation study, we evaluate the behaviour of traditional tests along with nonparametric permutation tests using also Multiple Aspect (MA) procedures and domain combinations.
The case of heterogeneous and dependent variation at each landmark is also investigated, along with the effects of superimposition on the power of NPC tests.
Permutation tests have been evaluated also in the particular case in which the number of variables is larger than the cardinality of permutation sample space. We have performed a simulation study to evaluate the power of multivariate NPC tests, showing that the power for the proposed tests increases when increasing the number of the processed variables provided that the noncentrality parameter increases, even when the number of covariates is larger than the permutation sample space.
These preliminary results allowed us to extend the notion of finite-sample consistency for permutation tests combination-based to the shape analysis field.
Sufficient conditions are given in order that the rejection rate converges to one, for fixed sample sizes at any attainable alpha-value, when the number of variables diverges, provided that the noncentrality induced by test statistics also diverges.
On the basis of these findings, we emphasize that the proposed tests provide efficient solutions to multivariate small sample problems, like those encountered in the shape analysis field.
Along with simulation studies, we present two applications to real data sets concerning Mediterranean monk seal skulls and aortic valve morphology.Nell'ultimo decennio la comunità statistica ha mostrato un crescente interesse per i problemi di shape analysis, con particolare riferimento allo sviluppo di tecniche inferenziali robuste. In questa tesi di dottorato presentiamo un'estensione della metodologia NPC per la combinazione non parametrica di test di permutazione dipendenti (Pesarin, 2001) nell'ambito della shape analysis.
Inizialmente si introduce una revisione dei metodi inferenziali noti in letteratura, evidenziando alcune problematiche legate all'uso della statistica test T^2 di Hotelling.
Focalizzandoci poi sul caso di due campioni indipendenti, tramite un esauriente studio di simulazione, abbiamo confrontato il comportamento, in termini di potenza, dei test parametrici tradizionali con quello dei test non parametrici proposti. Sono state utilizzate anche procedure di tipo multi aspetto (MA) e combinazioni per domini.
E’ stato anche esaminato il caso in cui i landmark sono correlati tra loro. Inoltre è stato valutato l'impatto della superimposizione sulla potenza dei test NPC.
I test di permutazione sono stati valutati in potenza e sotto H_0 nel caso in cui il numero di variabili processate è superiore alla cardinalità dello spazio di permutazione. Abbiamo inoltre effettuato uno studio di simulazione per valutare la potenza dei test multivariati NPC, evidenziando che la potenza di questi test cresce al crescere del numero di variabili processate, qualora apportino un aumento della non centralità, anche quando il numero di variabili è superiore alla cardinalità dello spazio di permutazione. Questi risultati preliminari ci hanno consentito di estendere la nozione di finite-sample consistency per i test NPC nell'ambito della shape analysis.
Vengono fornite condizioni sufficienti tali per cui la potenza del test converge a uno, per ampiezze campionarie fissate ad ogni livello raggiungibile alpha, quando il numero di variabili diverge, posto che diverga anche la non centralità indotta dall'aumento del numero di variabili.
Sulla base dei risultati ottenuti, possiamo affermare che i test NPC forniscono soluzioni efficienti per i problemi multivariati di shape analysis in presenza di bassa numerosità campionarie, problemi del resto frequenti nell'ambito della shape analysis. Oltre agli studi di simulazione, vengono presentati due casi studio, uno relativo allo studio della forma del cranio della foca monaca del Mediterraneo e l'altro relativo alla morfologia della valvola aortica
Evaluating treatment effect within a multivariate stochastic ordering framework: NPC methodology applied to a study on Multiple Sclerosis
No full textEvaluating treatment e effect within a multivariate stochastic ordering framework: NPC methodology applied to a study on Multiple Sclerosis
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Bayesian methods for joint modeling of longitudinal and survival data to assess validity of biomarkers in AIDS data
No full textPowerful Nonparametric Tests in Shape Analysis for Large Number of Variables and Few Subjects
No full textAnalisi multivariata per osservazioni appaiate con dati mancanti: un caso studio
Full text linkAll parametric approaches require that analysis should be done on complete data sets and so, in presence of missing data, parametric solutions are based either on the so-called deletion principle or imputation methods. But when we delete incomplete vectors we also remove all information they contain, which may be valuable and useful for analysis. And when we replace missing data by suitable functions of actually observed data, that is imputing method, we may introduce biased information which may negatively infuence the analysis. On the other hand, non-parametric solutions in a permutation framework consider data as they are, and units with missing data participate in the permutation mechanism as well as all other units, without deletion or imputing.
In this paper we provide a comparison between a parametric solution, represented by ITT principle, and a non parametric one, in a testing problem with multivariate paired observations
Overview of NonParametric Combination-based permutation tests for Multivariate multi-sample problems
No full textIn this work we present a review on nonparametric combination-based permutation tests along with SAS macros allowing to deal with two-sample and one-way MANOVA design problems, within NonParametric Combination methodology framework. Applications to real case studies are also presented
Nonparametric combination-based tests in dynamic shape analysis
No full textLandmark-based geometric morphometric methods are probably the most widely used approaches for shape analysis. Much work has been done for static or cross-sectional shape analysis while considerably less research has focused on dynamic or longitudinal shapes. The question of analysing shape changes over time is a fundamental issue in many research fields. In this paper, as a motivating example, we consider the problem of describing the dynamics of facial expressions for which medical and sociological studies call for a proper differential analysis to distinguish their different characteristics. We address the problem from an inferential point of view testing whether landmark positions change over time, within each facial expression, and whether these changes are different between different expressions. As the shape changes over time completely depend on geometrical landmarks, part of the problem becomes finding the subset of landmarks which best describes the dynamics of the expressions. In this paper, we show by means of a motivating example related to the analysis of the FG-NET (Face and Gesture Recognition Research Network) database with facial expressions and emotions from the Technical University Munich [Wallhoff, F. (2006), Database with Facial Expressions and Emotions from Technical University of Munich (FEEDTUM)'], that NonParametric Combination (NPC) tests can be effective tools when testing whether there is a difference between dynamics of facial expressions or testing which of the landmarks are more informative in explaining their dynamics. In particular, we start analysing data by means of bivariate linear mixed-effects models and then we improve inferential results using the NPC methodology
Well-being therapy in school settings: A pilot study
No full textBackground: There is increasing interest in the psychobiological mechanisms of resilience and psychological well-being. It is conceivable that activation of such mechanisms in the school setting may entail long-term benefits, both in terms of the developmental process and of prevention of distress. This study wants to apply and test the efficacy of a school-based intervention protocol derived from well-being therapy (WBT) compared to cognitive-behavioral strategies. Methods:School interventions were performed in a population of 111 students randomly assigned to: (a) a protocol using theories and techniques derived from cognitive-behavioral therapy; (b) a protocol derived from WBT. Assessment before and after interventions was performed using two self-rating scales: Kellner's Symptom Questionnaire and Ryff's Psychological Well-Being Scales. Results: Both school-based interventions resulted in a comparable improvement in symptoms and psychological well-being. Conclusions: This new well-being-enhancing strategy could play an important role in the prevention of psychological distress in school settings and in promoting optimal human functioning among children. Copyright (c) 2006 S. Karger AG, Base
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