SIS#$#CLADAG#

Univeristà#degli#Studi##di#Cagliari#

Fondazione##Banco#di#Sardegna#

CLADAG#2015#10°#ScienBfic#MeeBng#of#the#ClassificaBon#and#Data#Analysis##Group#of#the#Italian#StaBsBcal#Society##Flamingo#Resort,#Santa#Margherita#di#Pula,##October#8$10,#2015###

BOOK#OF#ABSTRACTS#Editors:)#Francesco#Mola,#Claudio#Conversano#CUEC#Editrice,#Cagliari####ISBN:#978#88#8467#749#9#

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!CUEC EDITRICE by Sardegna Novamedia Soc. Coop. Via Basilicata n. 57/59 09127 Cagliari, ITALY Tel. & Fax +39 070 271573 www.cuec.eu info@cuec.eu ISBN: 978-88-8467-749-9 First Edition CUEC © 2015

Preface

CLADAG 2015, the 10th Scientific Meeting of the Classification and DataAnalysis Group of the Italian Statistical Society (SIS), will be held in SantaMargherita di Pula, Cagliari, Italy, from October 8th to October 10th 2015.The local organizer is the Department of Business and Economics of the Uni-versity of Cagliari.CLADAG 2015 will take place under the auspices of the International Feder-ation of Classification Societies (IFCS) and of the Italian Statistical Society(SIS). It promotes advanced methodological research in multivariate statisticswith a special vocation in Data Analysis and Classification. CLADAG supportsthe interchange of ideas in these fields of research, including the disseminationof concepts, numerical methods, algorithms, computational and applied results.It will also benefit of the support of Fondazione Banco di Sardegna.CLADAG is a member of the International Federation of Classification Societies(IFCS). Among its activities, CLADAG organizes a biennial scientific meeting,schools related to classification and data analysis, publishes a newsletter, andcooperates with other member societies of the IFCS to the organization of theirconferences.The scientific program comprises three Keynote Lectures, an Invited Session,10 Specialized Sessions, 15 Solicited Sessions and 15 Contributed Sessions. Allthe Specialized and Solicited Sessions have been promoted by the members ofthe Scientific Program Committee. The organizers wish to thank them for theircooperation in contributing to the success of CLADAG 2015.The Book of Abstracts contains short papers of all the presentations scheduledin the conference program. It is organized according to type of session/lecture:Keynote Lectures, Specialized Sessions, Solicited Sessions and Contributed Ses-sions.The editors would like to express their gratitude to the Rector of the Universityof Cagliari, the Director of the Department of Business and Economics and toall the statisticians working in the Department of Business and Economics fortheir enthusiasm in supporting the organization of this event from the very be-ginning, as well as to all people who worked hard to make it a success. Specialthanks go to Dr. Massimo Cannas, Dr. Luca Frigau and Dr. Farideh Tavazoeefor their editorial supportLast but not least, we thank all authors and participants, without whom theconference would not have been possible.

Cagliari, October 8 2015.

Francesco Mola,Claudio Conversano

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Conference Themes

The 10th Meeting is orientated towards all topics related to data analysis,classification, multivariate and computational statistics. Submission of papersaddressing these topics in both methodological and practical perspective hasbeen encouraged by the members of the Scientific Program Committee.

The list of topics includes, but is not limited to, the following:

A Classification TheoryBayesian Classification Biplots Clustering models Consensus of ClassificationsCorrespondence Analysis Discrimination and Classification Factor Analysisand Dimension Reduction Methods Fuzzy Methods Genetic Algorithms Hier-archical Classification Multidimensional Scaling Multiway Scaling MultiwayMethods Neural Networks for Classification Non Hierarchical ClassificationSimilarities and Dissimilarities Software algorithms for classification Unfoldingand Related Scaling Methods

B Data AnalysisBayesian data Analysis Big data analysis- Categorical Data Analysis Covari-ance Structure Analysis Data Mining Data Science Data Visualization DecisionTrees Functional data analysis Mixture and Latent Class Models Multileveldata Analysis Non Linear Data Analysis Nonparametric and SemiparametricRegression Partial Least Squares Pattern recognition Robustness and Data Di-agnostics Social networks- Software algorithms for multivariate analysis SpatialData Analysis Symbolic Data Analysis.

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Committees

Scientific Program Committee

Chair: Paolo Giudici (University of Pavia)

MembersGiuseppe Bove (University of Roma Tre)Daniela Calo (University of Bologna)Agostino Di Ciaccio (University of Roma La Sapienza)Vincenzo Esposito Vinzi (ESSEC, France)Francesca Greselin (University of Milano Bicocca)Francesco Mola (University of Cagliari)Francesco Palumbo (University of Naples Federico II)Carla Rampichini (University of Firenze)Giancarlo Ragozini (University of Naples Federico II)Fabrizio Ruggeri (CNR IMATI, Milan)Silvia Salini (University of Milan)Adalbert F.X. Wilhelm (Jacobs University Bremen, Germany)

Local Organizing Committee

Chair: Francesco Mola (University of Cagliari, Italy).

Members: Stefano Cabras, Massimo Cannas, Claudio Conversano, Luca Frigau,Monica Musio, Mariano Porcu, Luisa Salaris, Isabella Sulis, Nicola Tedesco.

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PARTICIPATING ORGANIZATIONS !!!

!International Federation of Classifican Societies (IFCS) !!

!SIS - CLADAG (Classification and Data Analysis Group of the Italian Statistical Society)!!

!Fondazione Banco di Sardegna!!!!!!!!!!!

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!! Società Italiana di Statistica (SIS)!!

!! Università degli Studi di Cagliari!!!!

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Table of Contents

Keynote Lectures

Mining key networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21David BanksVariable selection for model-based clustering of categorical data 22Brendan MurphyEigenvalues in mixture modeling: geometric, robustness and compu-tational issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23Salvatore Ingrassia

Specialized sessions

Robust methods for the analysis of Economic (Big) dataOrganizer and Chair: Silvia SaliniFast and robust seemingly unrelated regression . . . . . . . . . . . . . 25Mia Hubert, Tim Verdonck and Ozlem YorulmazApplication to the detection of customs fraud of the goodness-of-fit testing for the newcomb-benford law . . . . . . . . . . . . . . . . . . 30Lucio Barabesi, Andrea Cerasa, Andrea Cerioli and Domenico PerrottaMonitoring the robust analysis of a single multivariate sample . . . 34Marco Riani, Anthony C. Atkinson and Andrea Cerioli

Bayesian nonparametric clusteringOrganizer: Fabrizio Ruggeri; Chair: Renata RotondiA baysian nonparametric approach to model association betweenclusters of snps and disease responses . . . . . . . . . . . . . . . . . . . . 39Raffaele Argiento, Alessandra Guglielmi, Chuhsing Kate Hsiao, Fabrizio Ruggeriand Charlotte WangA bayesian nonparametric model for clustering and borrowing in-formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43Antonio Lijoi, Bernardo Nipoti and Igor PrünsterSequential clustering based on dirichlet process priors . . . . . . . . 47Roberto Casarin, Andrea Pastore and Stefano F. Tonellato

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Causal Inference with Complex Data StructuresOrganizer and Chair: Alessandra MatteiShort term impact of pm10 exposure on mortality: a propensityscore approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52Michela Baccini, Alessandra Mattei and Fabrizia MealliIdentification and estimation of causal mechanisms in clustered en-couragement designs: disentangling bed nets using bayesian princi-pal stratification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Laura Forastiere, Fabrizia Mealli and Tyler VanderWeeleThe effects of a dropout prevention program on secondary stu-dents' outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Enrico Conti , Silvia Duranti, Alessandra Mattei, Fabrizia Mealli and Nicola Sci-clone

Clustering in Time SeriesOrganizer and Chair: Michele La RoccaProbabilistic boosted-oriented clustering of time series . . . . . . . 61Antonio D'Ambrosio, Gianluca Frasso, Carmela Iorio and Roberta SicilianoCopula-based fuzzy clustering of time series . . . . . . . . . . . . . . . 65Pierpaolo D'Urso, Marta Disegna and Fabrizio DuranteComparing multi-step ahead forecasting functions for time seriesclustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69Marcella Corduas and Giancarlo Ragozini

Multiway AnalysisOrganizer and Chair: Giuseppe Bove(Interactive) visualisation of threeway data . . . . . . . . . . . . . . . 74Casper J. Albers and John C. GowerRobust fuzzy clustering of multivariate time trajectories . . . . . . 78Pierpaolo D'Urso and Riccardo MassariEstimation procedures for avoiding degenerate solutions in cande-comp/parafac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82Paolo Giordani

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Big Data AnalysisOrganizer and Chair: Donato MalerbaTowards a statistical framework for attribute comparison in verylarge relational databases . . . . . . . . . . . . . . . . . . . . . . . . . . . 83Cesare Alippi, Elisa Quintarelli, Manuel Roveri and Letizia TancaMining big data with high performance computing solutions . . . . . 91Fabrizio Angiulli, Stefano Basta, Stefano Lodi,Gianluca Moro and Claudio SartoriEnhancing big data exploration with faceted browsing . . . . . . . . 95Sonia Bergamaschi, Giovanni Simonini and Song Zhu

New Methodologies for Composite IndicatorsOrganizer and Chair: Agostino Di CiaccioAdvances in composite-based path modeling for synthetic indicators 100Vincenzo Esposito Vinzi, Laura Trinchera and Giorgio RussolilloComposite indicators modeling . . . . . . . . . . . . . . . . . . . . . . . . . 102Maurizio VichiMeasuring the importance of variables in composite indicators . . . 104William Becker, Michaela Saisana, Paolo Paruolo and Andrea Saltelli

Cluster analysis software and validationOrganizer and Chair: Christian HennigAdaptive choice of input parameters in robust clustering . . . . . . 109Luis A. García-Escudero and Augustin Mayo-IscarRobust model-based clustering with covariance matrix constraints 113Pietro Coretto and Christian HennigFlexible implementation of resampling schemes for cluster validation117Friedrich Leisch

Selecting a mixture model with a clustering focusOrganizer and Chair: Gilles CeleuxClustering in finite mixtures using an integrated completed likeli-hood criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122Marco Bertoletti, Nial Friel and Riccardo RastelliEstimation and model selection for model-based clustering with theconditional classification likelihood . . . . . . . . . . . . . . . . . . . . 126Jean-Patrick Baudry

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On the different ways to compute the integrated completed likeli-hood criterion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Gilles Celeux

Exploring relationships between blocks of variablesOrganizer and Chair: Giorgio RussolilloWeighted multiblock clustering . . . . . . . . . . . . . . . . . . . . . . . . 135Ndéye Niang and Mory OuattaraThematic model exploration through multiple co-structure maximi-sation: method and software . . . . . . . . . . . . . . . . . . . . . . . . . . 139Xavier Bry and Thomas VerronA new component-based approach of regularisation for multivariategeneralised linear regression . . . . . . . . . . . . . . . . . . . . . . . . . 144Catherine Trottier, Xavier Bry, Frederic Mortier and Guillaume Cornu

Solicited Sessions

Advances in Density-based clusteringOrganizer and Chair: Francesca GreselinA nonparametric clustering method for image segmentation . . . . . 150Giovanna MenardiRobust clustering for heterogenous skew data . . . . . . . . . . . . . 154Luis A. García-Escudero, Francesca Greselin and Agustin Mayo-IscarRegularizing finite mixtures of gaussian distributions . . . . . . . . . 154Bettina Grün and Gertraud Malsiner-Walli

Latent variable models for longitudinal data - Part IOrganizer and Chair: Silvia BacciA joint model for longitudinal and survival data based on an ar(1)latent process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Silvia Bacci, Francesco Bartolucci and Silvia PandolfiFinite mixture models for mixed data: em algorithms and parafacrepresentations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167Marco Alfó and Paolo GiordaniOn the use of the contaminated gaussian distribution in hidden markovmodels for longitudinal data . . . . . . . . . . . . . . . . . . . . . . . . . . 171Antonio Punzo and Antonello Maruotti

Latent variable models for longitudinal data - Part IIOrganizer and Chair: Francesco BartolucciA hidden markov approach to the analysis of incomplete multivari-ate longitudinal data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Francesco LagonaLatent markov and growth mixture models: a comparison . . . . . . 181

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Fulvia Pennoni and Isabella RomeoLatent worths and longitudinal paired comparisons - a markov modelof dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Brian Francis, Alexandra Grand and Regina Dittrich

Multivariate data analysis in environmental sciencesOrganizer: Fabrizio Ruggeri; Chair: Raffaele ArgientoMultivariate downscaling for non-gaussian data . . . . . . . . . . . . . 191Daniela Cocchi, Lucia Paci and Carlo TrivisanoPreliminary results on tapering multivariate spatio temporal mod-els for exposure to airborne multipollutants in europe . . . . . . . . 195Alessandro Fassó, Francesco Finazzi and Ferdinand NdongoClustering macroseismic fields by statistical data depth functions 199Claudio Agostinelli, Renata Rotondi and Elisa Varini

Advanced models for tourism analysisOrganizer and Chair: Stefania MignaniAnalysing territorial heterogeneity in tourists’satisfaction towardsitalian destinations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204Cristina Bernini, Augusto Cerqua and Guido PellegriniMicro-economic determinants of tourist expenditure: a quantileregression approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208Emanuela Marrocu, Raffaele Paci and Andrea ZaraInequalities and tourism consumption behaviour: a mixture modelanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212Cristina Bernini, Maria Francesca Cracolici and Cinzia Viroli

Bayesian Networks and Graphical Models in Socio-Economic SciencesOrganizer and Chair: Paola VicardBayesian networks for firm performance evaluation . . . . . . . . . . 217Maria E. De Giuli, Pietro Gottardo, Anna M. Moisello and Claudia TarantolaGraphical model using copulas for measurement error modeling . . 221Daniela Marella and Paola Vicard

Time Series in ClusteringOrganizer and Chair: Michele La RoccaParsimonious clustering of time series . . . . . . . . . . . . . . . . . . . 226Carmela Iorio, Antonio D’Ambrosio, Gianluca Frasso and Roberta SicilianoDynamic time warping-based fuzzy clustering for spatial time series 230Pierpaolo D’Urso, Marta Disegna and Riccardo MassariPeriodical feature based time series clustering . . . . . . . . . . . . . 234Francesco Giordano, Michele La Rocca and Maria Lucia Parrella

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Big Data AnalysisOrganizer and Chair: Donato MalerbaInteractive machine learning with r . . . . . . . . . . . . . . . . . . . . . 239Giorgio Maria Di NunzioWorkload estimation for a call center . . . . . . . . . . . . . . . . . . . 243Pierluigi Riva and Ruggiero ScommegnaPrediction in olive oil trade using regression models on temporaldata network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245Corrado Loglisci , Umberto Medicamento and Arturo Casieri

Advances in Ordinal and Preference DataOrganizer and Chair: Antonio D’AmbrosioMeasuring consensus in the setting of non-uniform qualitative scales250José L. García-Lapresta and David Pérez-RománAccurate algorithms for consensus ranking detection . . . . . . . . . 255Giulio Mazzeo, Antonio D’Ambrosio and Roberta SicilianoLogistic regression trees for ordinal and preference data . . . . . . 259Thomas Rusch, Achim Zeileis and Kurt Hornik

Case studies in data science from Ligurian companiesOrganizer and Chair: Delio PanaroStatistical methods for the analysis of ostreopsis ovata bloom eventsfrom meteo-marine data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262Ennio Ottaviani, Valentina Asnaghi, Mariachiara Chiantore, Andrea Pedronciniand Rosella BertolottoData mining for optimal gambling . . . . . . . . . . . . . . . . . . . . . . . 266Gabriele Torre and Fabrizio MalfantiA fraud detection algorithm for online banking . . . . . . . . . . . . . 271Delio Panaro, Eva Riccomagno and Fabrizio MalfantiDoes directors’ background matter? firm performance, board fea-tures and financial reporting reliability . . . . . . . . . . . . . . . . . . 275Delio Panaro, Silvia Ferramosca and Sara Trucco

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Modeling ordinal dataOrganizer and Chair: Maurizio CarpitaPosterior predictive model checks for assessing the goodness of fitof bayesian multidimensional irt models . . . . . . . . . . . . . . . . . . . 280Mariagiulia Matteucci and Stefania MignaniInternational tourism in italy: a bayesian network approach . . . . 284Federica Cugnata and Giovanni PeruccaClustering upper level units in multilevel models for ordinal data 288Leonardo Grilli, Agnese Panzera and Carla Rampichini

Functional data analysis for environmental dataOrganizer and Chair: Tonio Di BattistaClustering spatially dependent functional data: a method based onthe concept of spatial dispersion function of a curve . . . . . . . . . 292Elvira Romano, Antonio Balzanella and Rosanna VerdeTwo case studies on object oriented spatial statistics . . . . . . . . . 296Piercesare Secchi, Simone Vantini and Valeria VitelliInference on functional biodiversity tools . . . . . . . . . . . . . . . . 298Tonio Di Battista, Francesca Fortuna and Fabrizio Maturo

Advances in quantile regressionOrganizer and Chair: Cristina DavinoM-quantile regression: diagnostics and parametric representationof the model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303Annamaria Bianchi, Enrico Fabrizi, Nicola Salvati and Nikos TzavidisQuantile regression: a bayesian robust approach . . . . . . . . . . . . 307Marco Bottone, Mauro Bernardi and Lea PetrellaA comparison among estimators for linear regression methods . . . 311Marilena Furno and Domenico VistoccoHandling heterogeneity among units in quantile regression . . . . . 315Cristina Davino and Domenico Vistocco

Directional DataOrganizer and Chair: Giovanni C. PorzioSmall biased circular density estimation . . . . . . . . . . . . . . . . . . 320Marco Di Marzio, Stefania Fensore, Agnese Panzera, and Charles C. TaylorA depth-based classifier for circular data . . . . . . . . . . . . . . . . . 324

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Giuseppe PandolfoNonparametric estimates of the mode for directional data . . . . . . 328Thomas Kirschstein, Steffen Liebscher, Giovanni C. Porzio and Giancarlo Ragozini

Recent developments in statistical analysis of network dataOrganizer and Chair: Domenico De StefanoGame theory and network models for the reconstruction of ar-chaeological networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331Viviana Amati and Ulrik BrandesA model for clustering a spatial network with application to locallabour system identification . . . . . . . . . . . . . . . . . . . . . . . . . . 335Francesco Pauli, Nicola Torelli and Susanna ZaccarinOn the sampling distributions of the ml estimators in network ef-fect models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339Michele La Rocca, Giovanni C. Porzio, Maria Prosperina Vitale and Patrick Dor-eianCorrespondence analysis with doubling for two-mode valued net-works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343Giancarlo Ragozini, Domenico De Stefano and Daniela D’Ambrosio

Current challenges in clustering and classification of biomedical dataOrganizer and Chair: Adalbert F.X. WilhelmSemantic multi classifier systems for the detection of aging relatedprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348Hans A. Kestler, Ludwig Lausser, Lyn-Rouven Schirra, Florian SchmidEmotion recognition in human computer interaction using multipleclassifier systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349Friedhelm SchwenkerEnsemble of selected classifiers . . . . . . . . . . . . . . . . . . . . . . . 352Berthold Lausen, Asma Gul, Zardad Khan and Osama Mahmoud

Contributed papers

A generalized distance for inference in functional data . . . . . . . 354Andrea Ghiglietti and Anna M. PaganoniLong gaps in multivariate spatio-temporal data: an approach basedon functional data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 359Mariantonietta Ruggieri, Antonella Plaia and Francesca Di SalvoEffects on curve clustering of different transformations of chrono-logical textual data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363Matilde Trevisani and Arjuna TuzziA note on the reliability of a classifier . . . . . . . . . . . . . . . . . . 366Luca Frigau

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366Robustified classification of multivariate functional data . . . . . . 370Francesca Ieva and Anna M. PaganoniSize control of robust regression estimators . . . . . . . . . . . . . . . 374Silvia Salini, Andrea Cerioli, Fabrizio Laurini and Marco RianiThe movements of emotions: an exploratory classification on af-fective movement data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378Pasquale Dente, Arvid Kappas and Adalbert F. X. WilhelmElectre tri-machine learning approach to the record linkage problem382Valentina Minnetti and Renato De LeoneQuality of classification approaches for the quantitative analysisof international conflict . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387Adalbert F.X. WilhelmThe rtclust procedure for robust clustering . . . . . . . . . . . . . . . 391Francesco Dotto, Alessio Farcomeni, Luis Angel García-Escudero and Agustín Mayo-IscarWhat are the true clusters? . . . . . . . . . . . . . . . . . . . . . . . . . . 396Christian HennigA novel model-based clustering approach for massive datasets ofspatially registered time series. with application to sea surfacetemperature remote sensing data . . . . . . . . . . . . . . . . . . . . . . . 399Francesco Finazzi and Marian ScottBig data classification: simulations in the many features case . . . . 403Claus WeihsFrom big data to information: statistical issues through examples . 407Silvia Biffignandi and Serena SignorelliBig data meet pharmaceutical industry: an application on socialmedia data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411Caterina Liberati and Paolo MarianiDefining the subjects distance in hierarchical cluster analysis bycopula approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416Andrea Bonanomi, Marta Nai Ruscone and Silvia Angela Osmetti

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416Supervised classification of defective crankshafts by image analysis 420Beatriz Remeseiro, Javier Tarrío-Saavedra, Mario Francisco-Fernández, Manuel G.Penedo, Salvador Naya and Ricardo CaoArchetypal analysis for data-driven prototype identification . . . . 424Giancarlo Ragozini, Francesco Palumbo and Maria R. D’EspositoPrincipal component analysis of complex data and application toclimatology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428Sergio Camiz and Silvia CretaSparse exploratory multidimensional irt models . . . . . . . . . . . . . 432Lara Fontanella, Sara Fontanella, Pasquale Valentini, Nickolay TrendafilovIterative factor clustering for categorical data reconsidered . . . 437Alfonso Iodice D’Enza, Angelos Markos and Francesco PalumboTesting antipodal symmetry of circular data . . . . . . . . . . . . . . . 442Giovanni Casale, Giuseppe Pandolfo and Giovanni C. PorzioHow to define deviance residuals in multinomial regression . . . . . 446Giovanni Romeo, Mariangela Sciandra and Marcello ChiodiDiagnostic tools for gamlss fitted objects . . . . . . . . . . . . . . . . 451Andrea Marletta and Mariangela SciandraBayesian regression analysis with linked and duplicated data . . . . 455Andrea Tancredi, Rebecca Steorts and Brunero LiseoA semi-parametric fay-herriot-type model with unknown samplingvariances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460Silvia PolettiniPosterior distributions from optimally b-robust estimating func-tions and approximate bayesian computation . . . . . . . . . . . . . . . . 464Ivan Luciano Danesi, Fabio Piacenza, Erlis Ruli and Laura VenturaMca based community detection . . . . . . . . . . . . . . . . . . . . . . . . 468Carlo DragoClassifying social roles by network structures . . . . . . . . . . . . . 472Simona Gozzo and Venera TomaselliA multilevel heckman model to investigate financial assets amongold people in europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 476Omar Paccagnella and Chiara Dal BiancoOptimal pricing using bayesian semiparametric price response models 480Winfried J. Steiner, Anett Weber, Stefan Lang and Peter Wechselberger

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Monetary transmission models for banking interest rates . . . . . . 484Laura Parisi, Paolo Giudici, Igor Gianfrancesco and Camillo GilibertoEstimating the effect of prenatal care on birth outcomes . . . . . . 490Emiliano Sironi and Massimo CannasRecursive partitioning: an approach based on the weighted kemenydistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494Mariangela Sciandra, Antonella Plaia and Veronica PiconeWhy to study abroad? an example of clustering . . . . . . . . . . . . . 498Valeria Caviezel and Anna M. FalzoniA graphical copula-based tool for detecting tail dependence . . . . 502Roberta Pappadà, Fabrizio Durante and Nicola TorelliClassification models as tools of bankruptcy prediction - polish ex-perience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506Józef Pociecha, Barbara Pawełek, Mateusz Baryła and Sabina AugustynThe relationship between individual price response of beer con-sumers and their demographic/psychographic characteristics . . . . 510Friederike PaetzThe ensemble conceptual clustering of symbolic data for customerloyalty analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514Marcin PełkaInsert here consumers’ perceptions of corporate social responsibil-ities and willingness to pay: a partial least squares . . . . . . . . . . 519Karsten Lübke, Christian Hose and Thomas ObermeierInspecting the quality of italian wine through causal reasoning . . 521Eugenio Brentari, Maurizio Carpita and Silvia GoliaExploring socio-economic factors associated with adherence to themediterranean diet: a multilevel approach . . . . . . . . . . . . . . . . 525Tiziana Laureti and Luca SecondiBig data and ’social’ reputation: a financial example . . . . . . . . . . 529Paola CerchielloBayesian networks for stock picking . . . . . . . . . . . . . . . . . . . . . 533Alessandro Greppi, Maria Elena De Giuli and Claudia TarantolaPortfolio selection with lasso algorithm . . . . . . . . . . . . . . . . . 537Riccardo Bramante, Silvia Facchinetti and Diego ZappaSunspot in economic models with externalities . . . . . . . . . . . . . . 540Beatrice Venturi and Alessandro Pirisinu

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ROBUST CLUSTERINGFOR HETEROGENOUS SKEW DATA

Luis Angel Garcıa-Escudero,1 Francesca Greselin2and Agustin Mayo-Iscar1

1 Department of Statistics and Operations Research and IMUVA, University of Val-ladolid (e-mail: lagarcia@eio.uva.es, agustinm@eio.uva.es)2 Department of Statistics and Quantitative Methods, Milano-Bicocca University (e-mail: francesca.greselin@unimib.it)

ABSTRACT: The existing robust methods for model-based classification and cluster-ing deal with elliptically contoured components. Here we introduce robust estimationfor mixtures of skew-normal, by the joint usage of trimming and constraints. Themodel allows to fit heterogeneous skew data with great flexibility.

KEYWORDS: Clustering, robust estimation, skew data.

1 Introduction

In recent years, empirical evidences of asymmetric departures from normal-ity in some real subpopulations suggested the introduction of skewed compo-nents in the classical mixture model approach. Therefore, increasing atten-tion has been devoted to mixtures of multivariate skew normal and skew t, aswell as to mixtures of normal-inverse-Gaussian distributions, shifted asymmet-ric Laplace distributions, generalized hyperbolic distributions and hierarchicalmixtures (mixtures of mixtures), to capture asymmetric shapes in components.Most of these parametric families of skew distributions are clearly related, asit has been described in a careful review by Lee & McLachlan (2013a). Inthis paper we address robust estimation of mixtures of skew normal distribu-tions. Our interest for the Finite Mixtures of Canonical Fundamental SkewNormal (FM CFUSN) has been motivated by the aim of adapting to the Gaus-sian case the methodology developed for Finite Mixtures of Canonical Fun-damental Skew t (FM CFUST) in Lee & McLachlan (2014), based on skewdistributions originated in Arellano-Valle & Genton (2005). By mimicking theCFUST properties, CFUSN has the special appealing of including as particu-lar cases the restricted and unrestricted Skew Normal, respectively rMSN anduMSN. The great flexibility of CFUSN is due to its parameters, which allowto separately govern location, scale, correlation, and skewness. We will show,

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herein, that the FM CFUSN offers a very tractable model for many situationsof departures from symmetry, being analytically and computationally easierthan the FM CFUST. Taking advantage of its robust estimation, the model be-comes even more adaptable to real phenomena. Indeed, robustness is oftenrequired by many datasets available nowadays, where populations are noisy,have some non-symmetric features, and could contain outliers asymmetricallydisposed around the data clusters.

The first step to achieve robustness and obtain good breakdown propertiesfor the estimators, is based on a trimming procedure incorporated along theiterations of the EM algorithm. The key idea is that a small portion of ob-servations, which are highly unlikely to occur under the current fitted modelassumption, is discarded from contributing to the parameter estimates. Thesame methodology has been proven to be very effective when addressing ro-bust clustering for Gaussian and t mixtures models (see Neykov et al. , 2007;Gallegos & Ritter, 2009; Garcıa-Escudero et al. , 2014). Furthermore - andthis is the second step - we implement a constrained ML estimation for thecomponent covariances, aiming at reducing spurious solutions and preventingsingularities of the likelihood, along the lines of Ingrassia & Rocci (2007).

Monte Carlo experiments show that bias and MSE of the estimator in sev-eral cases of contaminated data are dramatically inflated, while they return tobe comparable to results obtained on skew data without noise, when the com-bined effect of trimming and constrained estimation is applied. Further, it canbe shown that the estimator resists the influence of all classes of contaminat-ing observations, as far as the outliers appear in a proportion lower than thetrimming level α. As a final remark, we want to stress that the joint usage oftrimming and constrained estimation allow to set the underlying mathematicaland statistical problems as well posed ones.

2 Methodology

We consider the ML estimation for a g-component mixture model in which arandom sample (Y1, . . . ,Yn) follows a mixture of CFUSNs. The probabilitydensity function can be written as

Y j g

∑i=1

πi f (y j|µi,Σi,∆i), πi 0,g

∑i=1

πi = 1,

where f (·) denotes a CFUSN density, Θ= (θ1, . . . ,θg) with θi = (πi,µi,Σi,∆i)are the unknown parameters of component i, and πi are the weights of thegroups.

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To define the location-scale variant of the CFUSN distribution, let (Y0,Y1)be a p+q multivariate normal r.v., such that

Y0Y1

N q+p

00

,

Iq 00 Σ

(1)

where Σ is a positive definite scale matrix and 0 is a vector of zeros with ap-propriate dimension. Then, given a p q matrix ∆, we obtain the stochasticrepresentation for Y, i.e. Y = µ+∆|Y0|+Y1, that follows the CFUSN distri-bution with density given by

f (y;µ,Σ,∆) = 2qφp(y;µ,Ω)Φq

∆TΩ1(yµ);0,Λ)

where Ω = Σ+∆∆T , Λ = Ip ∆TΩ1∆, and as usual φp(y;µ,Σ) denotes thep-dimensional density of the multivariate Gaussian with mean µ and scale Σevaluated at y, while Φq(·) denotes the cumulative distribution function.

In the ML approach, we consider the following trimmed log-likelihoodfunction (see Neykov et al. , 2007; Gallegos & Ritter, 2009; Garcıa-Escuderoet al. , 2014)

L trim =n

∑i=1

z(yi) log"

G

∑g=1

φp(yi;µg,Ωg)Φq(∆TgΩ

1g (yiµg);0,Λg)πg

#

. (2)

By z(·) we denote a 0-1 trimming indicator function that indicates whetherobservation yi is trimmed off: z(yi)=0, or not: z(yi)=1. A fixed fraction αof observations, whose contributions to the likelihood are lower than their α-quantile, can be unassigned by setting ∑n

i=1 z(yi) = [n(1α)] at each E-step,hence they do not contribute to the parameter estimation.

Further, we want to deal with the unboundedness of the target functionL trim when no constraints are imposed on the scatter parameters. In this case,the defining problem is ill-posed because the log-likelihood tends to ∞ wheneither µg = yi and |Σg| ! 0. As a trivial consequence, the EM algorithm canbe trapped into non-interesting local maximizers, called “spurious” solutions,and the result of the EM algorithm strongly depends on its initialization. Forthis reason, we set a constraint on the maximization in (2), concerning theeigenvalues λl(Σg)l=1,...,d of the scatter matrices Σg, by imposing

λl1(Σg1) c λl2(Σg2) for every 1 l1 6= l2 d and 1 g1 6= g2 G.

as in Ingrassia & Rocci (2007); Garcıa-Escudero et al. (2008); Gallegos &Ritter (2009). It is important to remark that the parameters related with location

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and skewness are not affected by the constrained maximization applied to thecovariance matrices.

As usual, among many runs of the EM algorithm, we select the parametersgiven by the best final likelihood. To complete a synthetic description of thealgorithm, our proposal for the initialization of the EM is to take a small ran-dom subsample for each component and to draw, for each observation in it, arandom variate Y0 from N p (0,Ip). By applying multivariate regression on theselected observations in each component, and using the corresponding vectors|Y0|, we get an estimation of the model parameters (i.e. µg, Σg and ∆g) for theg-th component. Finally, initial estimations for the group weights are drawnfrom a multinomial random variable.

References

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FRITZ, H., GARCIA-ESCUDERO, L.A., & MAYO-ISCAR, A. 2012. tclust: An RPackage for a Trimming Approach to Cluster Analysis. Journal of Statistical Soft-ware, 47(12).

GALLEGOS, M.T., & RITTER, G. 2009. Trimmed ML estimation of contaminatedmixtures. Sankhya (Ser. A), 164–220.

GARCIA-ESCUDERO, L.A, GORDALIZA, A., MATRAN, C., & MAYO-ISCAR, A.2008. A general trimming approach to robust cluster analysis. The Annals of Statis-tics, 1324–1345.

GARCIA-ESCUDERO, L.A., GORDALIZA, A., & MAYO-ISCAR, A. 2014. A con-strained robust proposal for mixture modeling avoiding spurious solutions. Ad-vances in Data Analysis and Classification, 8(1), 27–43.

INGRASSIA, S., & ROCCI, R. 2007. Constrained monotone EM algorithms for finitemixture of multivariate Gaussians. Computational Statistics & Data Analysis, 51,5339–5351.

LEE, S., & MCLACHLAN, G. 2013a. Model-based clustering and classification withnon-normal mixture distributions. Statistical Methods & Applications, 22(4), 427–454.

LEE, S., & MCLACHLAN, G. 2013b. On mixtures of skew normal and skew t-distributions. Advances in Data Analysis and Classification, 7(3), 241–266.

LEE, S., & MCLACHLAN, G. 2014. Finite Mixtures of Canonical Fundamental Skewt-Distributions. arXiv preprint arXiv:1405.0685.

NEYKOV, N., FILZMOSER, P., DIMOVA, R., & NEYTCHEV, P. 2007. Robust Fittingof Mixtures Using the Trimmed Likelihood Estimator. Computational Statistics &Data Analysis, 52(1), 299–308.

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