On a class of time-Fractional continuous-State branching processes

We propose a class of non-Markov population models with continuous or discrete state space via a limiting procedure involving sequences of rescaled and randomly time-changed Galton – Watson processes. The class includes as specific cases the classical continuous-state branching processes and Markov branching processes. Several results such as the expressions of moments and the branching inequality governing the evolution of the process are presented and commented. The generalized Feller branching diffusion and the fractional Yule process are analyzed in detail as special cases of the general model

Strong existence and uniqueness of the stationary distribution for a stochastic inviscid dyadic model

We consider an inviscid stochastically forced dyadic model, where the additive noise acts only on the first component. We prove that a strong solution for this problem exists and is unique by means of uniform energy estimates. Moreover, we exploit these results to establish strong existence and uniqueness of the stationary distribution

A proposal for the multidimensional extension of CUB models

Particular emphasis has been put, lately, on the analysis of categorical data and many proposals have appeared, ranging from pure methodological contributions to more applicative ones. Among such proposals, the CUB class of distributions, a mixture model for the analysis of ordinal data that has been successfully employed in various fields, seems of particular interest. CUB are univariate models that do not possess, at present, a multivariate version: aim of the present work is to investigate the feasibility of building a higher-dimensional version of such models and its possible applications. In order to achieve such results, we propose to employ techniques typical of the framework of copula models, that have proven to be valid tools for multivariate models construction and data analysi

Multidimensional item response theory models for dichotomous data in customer satisfaction evaluation

In this paper, multidimensional item response theory models for dichotomous data, developed in the fields of psychometrics and ability assessment, are discussed in connection with the problem of evaluating customer satisfaction. These models allow us to take into account latent constructs at various degrees of complexity and provide interesting new perspectives for services quality assessment. Markov chain Monte Carlo techniques are considered for estimation. An application to a real data set is also presente

Missing data and parameters estimates in multidimensional item response models

Statistical analyses of data based on surveys usually face the problem of missing data. However, some statistical methods require a complete data matrix to be applicable, hence the need to cope with such missingness. Literature on imputation abounds with contributions concerning quantitative responses, but seems to be poor with respect to the handling of categorical data. The present work aims at evaluating the impact of different imputation methods on multidimensional IRT models estimation for dichotomous data

Multidimensional extensions of IRT models and their application to customer satisfaction evaluation

Multidimensional IRT models (MIRTM), developed in the fields of psychometrics and ability assessment, are here considered in connection with the problem of evaluating customer satisfaction. Different models, that allow us to take into account more complex and, possibly, more realistic latent constructs than those usually assumed, are presented and discussed. Eventually, these models are applied to a real dataset, MCMC techniques for the estimation are implemented and analogies and differences with results from previous analyses on the same survey in the literature are discussed