Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

Identificazione di un profilo molecolare di rischio nei pazienti pediatrici affetti da Linfoma di Hodgkin

Obiettivi: nonostante i miglioramenti nel trattamento, circa il 30% dei pazienti pediatrici affetti da Linfoma di Hodgkin (LH) in stadio avanzato recidiva o muore per progressione di malattia e i correnti metodi predittivi biologico-clinici non consentono di individuare tali pazienti. L’obiettivo dello studio è stato quello di definire un profilo molecolare di rischio che correli con l’outcome in questi pazienti. Materiali e metodi: studio retrospettico condotto su pazienti pediatrici affetti da LH omogeneamente trattati dal 2004 in poi. Su tali pazienti è stato intrapreso uno studio di validazione di marcatori molecolari già identificati in studi esplorativi precedenti. 27 geni sono stati analizzati in RT PCR su campioni di tessuto istologico prelevato alla diagnosi fissato in formalina e processato in paraffina relativi a una coorte di 37 pazienti, 12 ad outcome sfavorevole e 25 ad outcome favorevole. Risultati: dall’analisi univariata è emerso che solo l’espressione di CASP3 e CYCS, appartenenti al pathway apoptotico, è in grado di influenzare l’EFS in modo significativo nella nostra coorte di pazienti. Lo studio delle possibili combinazioni di questi geni ha mostrato l’esistenza di 3 gruppi di rischio che correlano con l’EFS: alto rischio (down regolazione di entrambi i geni), rischio intermedio (down regolazione di uno solo dei 2 geni), basso rischio (up regolazione di entrambi i geni). Dall’analisi multivariata è emerso che CASP3 è l’unica variabile che mantiene la sua indipendenza nell’influenzare la prognosi con un rischio di eventi di oltre il doppio di chi ha un’espressione bassa di questo gene. Conclusioni: i risultati ottenuti sulla nostra coorte di pazienti pediatrici affetti da LH confermano l’impatto sulla prognosi di due marcatori molecolari CASP3 e CYCS coinvolti nel patwhay apoptotico. La valutazione del profilo di espressione di tali geni, potrebbe pertanto essere utilizzata in corso di stadiazione, come criterio di predittività.