126 research outputs found
Covariance pattern mixture models for the analysis of multivariate heterogeneous longitudinal data
We propose a novel approach for modeling multivariate longitudinal data in
the presence of unobserved heterogeneity for the analysis of the Health and
Retirement Study (HRS) data. Our proposal can be cast within the framework of
linear mixed models with discrete individual random intercepts; however,
differently from the standard formulation, the proposed Covariance Pattern
Mixture Model (CPMM) does not require the usual local independence assumption.
The model is thus able to simultaneously model the heterogeneity, the
association among the responses and the temporal dependence structure. We focus
on the investigation of temporal patterns related to the cognitive functioning
in retired American respondents. In particular, we aim to understand whether it
can be affected by some individual socio-economical characteristics and whether
it is possible to identify some homogenous groups of respondents that share a
similar cognitive profile. An accurate description of the detected groups
allows government policy interventions to be opportunely addressed. Results
identify three homogenous clusters of individuals with specific cognitive
functioning, consistent with the class conditional distribution of the
covariates. The flexibility of CPMM allows for a different contribution of each
regressor on the responses according to group membership. In so doing, the
identified groups receive a global and accurate phenomenological
characterization.Comment: Published at http://dx.doi.org/10.1214/15-AOAS816 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Deep Gaussian Mixture Models
Deep learning is a hierarchical inference method formed by subsequent
multiple layers of learning able to more efficiently describe complex
relationships. In this work, Deep Gaussian Mixture Models are introduced and
discussed. A Deep Gaussian Mixture model (DGMM) is a network of multiple layers
of latent variables, where, at each layer, the variables follow a mixture of
Gaussian distributions. Thus, the deep mixture model consists of a set of
nested mixtures of linear models, which globally provide a nonlinear model able
to describe the data in a very flexible way. In order to avoid
overparameterized solutions, dimension reduction by factor models can be
applied at each layer of the architecture thus resulting in deep mixtures of
factor analysers.Comment: 19 pages, 4 figure
The Importance of Being Clustered: Uncluttering the Trends of Statistics from 1970 to 2015
In this paper we retrace the recent history of statistics by analyzing all
the papers published in five prestigious statistical journals since 1970,
namely: Annals of Statistics, Biometrika, Journal of the American Statistical
Association, Journal of the Royal Statistical Society, series B and Statistical
Science. The aim is to construct a kind of "taxonomy" of the statistical papers
by organizing and by clustering them in main themes. In this sense being
identified in a cluster means being important enough to be uncluttered in the
vast and interconnected world of the statistical research. Since the main
statistical research topics naturally born, evolve or die during time, we will
also develop a dynamic clustering strategy, where a group in a time period is
allowed to migrate or to merge into different groups in the following one.
Results show that statistics is a very dynamic and evolving science, stimulated
by the rise of new research questions and types of data
A dimensionally reduced finite mixture model for multilevel data
AbstractRecently, different mixture models have been proposed for multilevel data, generally requiring the local independence assumption. In this work, this assumption is relaxed by allowing each mixture component at the lower level of the hierarchical structure to be modeled according to a multivariate Gaussian distribution with a non-diagonal covariance matrix. For high-dimensional problems, this solution can lead to highly parameterized models. In this proposal, the trade-off between model parsimony and flexibility is governed by assuming a latent factor generative model
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