1,721,113 research outputs found
Three-mode factor analysis with binary core and orthonormality constraints
No full textA constrained version of Three-mode Factor Analysis model is considered in order to make its interpretation easier. The constraints are obtained by fixing some elements of the core to zero and requiring orthonormal factor loadings. An algorithm to solve the related minimization problem and an example of core constraints with theoretically interesting features, are given
A general algorithm to fit constrained DEDICOM models
No full textThe DEDICOM model is a model to analyze square tables describing asymmetric relationships among n entities. Its importance in the asymmetric multidimensional scaling literature is due to the fact that several authors showed a large class of models to be simply a constrained version of DEDICOM.A typical example is the Generalized GIPSCAL proposed by Kiers & Takane. In this paper we present a new algorithm capable to fit, in the least squares sense, any DEDICOM constrained model
Scalar product and synthesis of s-matrices
No full textIn this paper we give an alternative view of the euclidean scalar product between symmetric positive semidefinite matrices, characterizing a matrix on the grounds of its spectral decomposition. Following this approach we reconsider the "compromise matrix" and "mean matrix" methods tacking into account the rank of the "compromise" or "mean" matrix
Mixture models for mixed-type data through a composite likelihood approach
No full textA mixture model is considered to classify continuous and/or ordinal variables. Under this model, both the continuous and the ordinal variables are assumed to follow a heteroscedastic Gaussian mixture model, where, as regards the ordinal variables, it is only partially observed. More specifically, the ordinal variables are assumed to be a discretization of some mixture variables. From a computational point of view, this creates some problems for the maximum likelihood estimation of model parameters. Indeed, the likelihood function involves multidimensional integrals, whose evaluation is computationally demanding as the number of ordinal variables increases. The proposal is to replace this cumbersome likelihood with a surrogate objective function that is easier to maximize. A composite approach is used, in particular the original joint distribution is replaced by the product of three blocks: the marginal distribution of continuous variables, all bivariate marginal distributions of ordinal variables and the marginal distributions given by all continuous variables and only one ordinal variable. This leads to a surrogate function that is the sum of the log contributions for each block. The estimation of model parameters is carried out maximizing the surrogate function within an EM-like algorithm. The effectiveness of the proposal is investigated through a simulation study and two applications to real data
A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption
No full textHidden Markov models (HMMs) are frequently used to analyse longitudinal data, where the same set of subjects is repeatedly observed over time. In this context, several sources of heterogeneity may arise at individual and/or time level, which affect the hidden process, that is, the transition probabilities between the hidden states. In this paper, we propose the use of a finite mixture of non-homogeneous HMMs (NH-HMMs) to face the heterogeneity problem. The non-homogeneity of the model allows us to take into account observed sources of heterogeneity by means of a proper set of covariates, time and/or individual dependent, explaining the variations in the transition probabilities. Moreover, we handle the unobserved sources of heterogeneity at the individual level, due to, for example, omitted covariates, by introducing a random term with a discrete distribution. The resulting model is a finite mixture of NH-HMM that can be used to classify individuals according to their dynamic behaviour or to estimate a mixed NH-HMM without any assumption regarding the distribution of the random term following the non-parametric maximum likelihood approach. We test the effectiveness of the proposal through a simulation study and an application to real data on alcohol abuse
L’approccio fattoriale per l’integrazione delle dimensioni micro e macro
No full textLa spiegazione dei fenomeni individuali. attraverso le sole caratteristiche dell'individuo, porta in molti casi a risultati insoddisfacenti anche quando sono state prese in considerazione tutte le informazioni rilevanti. Il problema non risiede nella carenza di informazione a livello individuale, ma piuttosto nell'ipotizzare gli individui come completamente indipendenti dal contesto in cui vivono e. agiscono. Nelle situazioni reali, almeno per quanto riguarda i fenomeni umani, il quadro è ben più articolato poiché l'ambiente definito mediante norme. strutture, servizi. tessuto economico, sociale c culturale. intcragisce con l'azione individuale creando delle similitudini tra individui appartenenti al medesimo contesto. Siamo perciò in presenza di due diverse dimensioni, quella micro c quella macro. che intcragiscono tra loro instaurando relazioni di dipendenza o interdipendcnza tra le variabili a loro corrispondenti. Non volendo limitare la problematica dell'integrazione del micro con il macro al solo rapporto individuoambiente_ possiamo riferirei più in generale ad una situazione osservazionalc in cui è presente una struttura di tipo gerarchico. dove si possono individuare unità statistiche di primo livello, o micro, contenute in unità di secondo livello. o macro. ..
Composite likelihood methods for parsimonious model-based clustering of mixed-type data
No full textIn this paper, we propose twelve parsimonious models for clustering mixed-type (ordinal and continuous) data. The dependence among the different types of variables is modeled by assuming that ordinal and continuous data follow a multivariate finite mixture of Gaussians, where the ordinal variables are a discretization of some continuous variates of the mixture. The general class of parsimonious models is based on a factor decomposition of the component-specific covariance matrices. Parameter estimation is carried out using a EM-type algorithm based on composite likelihood. The proposal is evaluated through a simulation study and an application to real data
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