Now showing 1 - 9 of 9
  • Publication
    Model-based clustering of longitudinal data
    A new family of mixture models for the model-based clustering of longitudinal data is introduced. The covariance structures of eight members of this new family of models are given and the associated maximum likelihood estimates for the parameters are derived via expectation-maximization (EM) algorithms. The Bayesian information criterion is used for model selection and a convergence criterion based on Aitken’s acceleration is used to determine convergence of these EM algorithms. This new family of models is applied to yeast sporulation time course data, where the models give good clustering performance. Further constraints are then imposed on the decomposition to allow a deeper investigation of correlation structure of the yeast data. These constraints greatly extend this new family of models, with the addition of many parsimonious models.
    Scopus© Citations 79  1393
  • Publication
    A Mixture of Experts Latent Position Cluster Model for Social Network Data
    Social network data represent the interactions between a group of social actors. Interactions between colleagues and friendship networks are typical examples of such data. The latent space model for social network data locates each actor in a network in a latent (social) space and models the probability of an interaction between two actors as a function of their locations. The latent position cluster model extends the latent space model to deal with network data in which clusters of actors exist — actor locations are drawn from a finite mixture model, each component of which represents a cluster of actors. A mixture of experts model builds on the structure of a mixture model by taking account of both observations and associated covariates when modeling a heterogeneous population. Herein, a mixture of experts extension of the latent position cluster model is developed. The mixture of experts framework allows covariates to enter the latent position cluster model in a number of ways, yielding different model interpretations. Estimates of the model parameters are derived in a Bayesian framework using a Markov Chain Monte Carlo algorithm. The algorithm is generally computationally expensive — surrogate proposal distributions which shadow the target distributions are derived, reducing the computational burden. The methodology is demonstrated through an illustrative example detailing relationships between a group of lawyers in the USA.
      610Scopus© Citations 29
  • Publication
    Exploring Voting Blocs Within the Irish Electorate: A Mixture Modeling Approach
    (Taylor and Francis, 2008-09) ;
    Irish elections use a voting system called proportion representation by means of a single transferable vote(PR-STV). Under this system, voters express their vote by ranking some (or all) of the candidates in order of preference. Which candidates are elected is determined through a series of counts where candidates are eliminated and surplus votes are distributed.The electorate in any election forms a heterogeneous population: that is voters with different political and ideological persuasions would be expected to have different preferences for the candidates. The purpose of this article is to establish the presence of voting bloes in the Irish electorate, to characterize these blocs and to estimate their size.A mixture modeling approach is used to explore the heterogenecity of the Irish electorate and to establish the existence of clearly defined voting blocs. The voting blocs are characterized by thier voting preferences which are described using a ranking data model. In addition the care with which voters choose lower tier preferences is estimated in the model.The methodology is used to explore data from two Irish election. Data from eight opinion polls taken during the six weeks prior to the 1997 Irish presidential election are analyzed. These data reveal the evolution of the structure of the electorate during the election campaign. In addition data that record the votes from the Dublin West constituency of the 2002 Irish general election are analyzed to reveal distinct voting blocs within the electoate these blocs are characterized by party politics, candidate profile and political ideology.
    Scopus© Citations 72  545
  • Publication
    Analysis of Irish third-level college applications data
    The Irish college admissions system involves prospective students listing up to 10 courses in order of preference on their application. Places in third-level educational institutions are subsequently offered to the applicants on the basis of both their preferences and their final second-level examination results. The college applications system is a large area of public debate in Ireland. Detractors suggest that the process creates artificial demand for 'high profile' courses, causing applicants to ignore their vocational callings. Supporters argue that the system is impartial and transparent. The Irish college degree applications data from the year 2000 are analysed by using mixture models based on ranked data models to investigate the types of application behaviour that are exhibited by college applicants. The results of this analysis show that applicants form groups according to both the discipline and the geographical location of their course choices. In addition, there is evidence of the suggested 'points race' for high profile courses. Finally, gender emerges as an influential factor when studying course choice behaviour.
    Scopus© Citations 47  599
  • Publication
    Model-Based clustering of microarray expression data via latent Gaussian mixture models
    (Oxford University Press, 2010-11-01) ;
    In recent years, work has been carried out on clustering gene expression microarray data. Some approaches are developed from an algorithmic viewpoint whereas others are developed via the application of mixture models. In this article, a family of eight mixture models which utilizes the factor analysis covariance structure is extended to 12 models and applied to gene expression microarray data. This modelling approach builds on previous work by introducing a modified factor analysis covariance structure, leading to a family of 12 mixture models, including parsimonious models. This family of models allows for the modelling of the correlation between gene expression levels even when the number of samples is small. Parameter estimation is carried out using a variant of the expectation–maximization algorithm and model selection is achieved using the Bayesian information criterion. This expanded family of Gaussian mixture models, known as the expanded parsimonious Gaussian mixture model (EPGMM) family, is then applied to two well-known gene expression data sets.
    Scopus© Citations 117  426
  • Publication
    Exponential family mixed membership models for soft clustering of multivariate data
    For several years, model-based clustering methods have successfully tackled many of the challenges presented by data-analysts. However, as the scope of data analysis has evolved, some problems may be beyond the standard mixture model framework. One such problem is when observations in a dataset come from overlapping clusters, whereby different clusters will possess similar parameters for multiple variables. In this setting, mixed membership models, a soft clustering approach whereby observations are not restricted to single cluster membership, have proved to be an effective tool. In this paper, a method for fitting mixed membership models to data generated by a member of an exponential family is outlined. The method is applied to count data obtained from an ultra running competition, and compared with a standard mixture model approach.
      245Scopus© Citations 2
  • Publication
    A mixture of experts model for rank data with applications in election studies
    (Institute of Mathematical Statistics, 2008-12) ;
    A voting bloc is defined to be a group of voters who have similar voting preferences. The cleavage of the Irish electorate into voting blocs is of interest. Irish elections employ a 'single transferable vote' electoral system; under this system voters rank some or all of the electoral candidates in order of preference. These rank votes provide a rich source of preference information from which inferences about the composition of the electorate may be drawn. Additionally, the influence of social factors or covariates on the electorate composition is of interest. A mixture of experts model is a mixture model in which the model parameters are functions of covariates. A mixture of experts model for rank data is developed to provide a model-based method to cluster Irish voters into voting blocs, to examine the influence of social factors on this clustering and to examine the characteristic preferences of the voting blocs. The Benter model for rank data is employed as the family of component densities within the mixture of experts model; generalized linear model theory is employed to model the influence of covariates on the mixing proportions. Model fitting is achieved via a hybrid of the EM and MM algorithms. An example of the methodology is illustrated by examining an Irish presidential election. The existence of voting blocs in the electorate is established and it is determined that age and government satisfaction levels are important factors in influencing voting in this election.
      336Scopus© Citations 82
  • Publication
    Bayesian Nonparametric Plackett-Luce Models for the Analysis of Preferences for College Degree Programmes
    (Institute of Mathematical Statistics, 2014) ; ;
    In this paper we propose a Bayesian nonparametric model for clustering partial ranking data.We start by developing a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with prior specified by a completely random measure. We characterise the posterior distribution given data, and derive a simple and effective Gibbs sampler for posterior simulation. We then develop a Dirichlet process mixture extension of our model and apply it to investigate the clustering of preferences for college degree programmes amongst Irish secondary school graduates. The existence of clusters of applicants who have similar preferences for degree programmes is established and we determine that subject matter and geographical location of the third level institution characterise these clusters.
    Scopus© Citations 38  312
  • Publication
    Variable Selection for Latent Class Analysis with Application to Low Back Pain Diagnosis
    (The Institute of Mathematical Statistics, 2017-12-28) ; ;
    The identification of most relevant clinical criteria related to low back pain disordersis a crucial task for a quick and correct diagnosis of the nature of pain and its treatment.Data concerning low back pain can be of categorical nature, in form of check-list in whicheach item denotes presence or absence of a clinical condition. Latent class analysis is amodel-based clustering method for multivariate categorical responses which can be appliedto such data for a preliminary diagnosis of the type of pain. In this work we propose avariable selection method for latent class analysis applied to the selection of the mostuseful variables in detecting the group structure in the data. The method is based onthe comparison of two different models and allows the discarding of those variables withno group information and those variables carrying the same information as the alreadyselected ones. We consider a swap-stepwise algorithm where at each step the models arecompared through and approximation to their Bayes factor. The method is applied tothe selection of the clinical criteria most useful for the clustering of patients in differentclasses of pain. It is shown to perform a parsimonious variable selection and to give agood clustering performance. The quality of the approach is also assessed on simulateddata
    Scopus© Citations 33  540