11,161 research outputs found
Multivariate Spatiotemporal Hawkes Processes and Network Reconstruction
There is often latent network structure in spatial and temporal data and the
tools of network analysis can yield fascinating insights into such data. In
this paper, we develop a nonparametric method for network reconstruction from
spatiotemporal data sets using multivariate Hawkes processes. In contrast to
prior work on network reconstruction with point-process models, which has often
focused on exclusively temporal information, our approach uses both temporal
and spatial information and does not assume a specific parametric form of
network dynamics. This leads to an effective way of recovering an underlying
network. We illustrate our approach using both synthetic networks and networks
constructed from real-world data sets (a location-based social media network, a
narrative of crime events, and violent gang crimes). Our results demonstrate
that, in comparison to using only temporal data, our spatiotemporal approach
yields improved network reconstruction, providing a basis for meaningful
subsequent analysis --- such as community structure and motif analysis --- of
the reconstructed networks
Item selection by Latent Class-based methods
The evaluation of nursing homes is usually based on the administration of
questionnaires made of a large number of polytomous items. In such a context,
the Latent Class (LC) model represents a useful tool for clustering subjects in
homogenous groups corresponding to different degrees of impairment of the
health conditions. It is known that the performance of model-based clustering
and the accuracy of the choice of the number of latent classes may be affected
by the presence of irrelevant or noise variables. In this paper, we show the
application of an item selection algorithm to real data collected within a
project, named ULISSE, on the quality-of-life of elderly patients hosted in
italian nursing homes. This algorithm, which is closely related to that
proposed by Dean and Raftery in 2010, is aimed at finding the subset of items
which provides the best clustering according to the Bayesian Information
Criterion. At the same time, it allows us to select the optimal number of
latent classes. Given the complexity of the ULISSE study, we perform a
validation of the results by means of a sensitivity analysis to different
specifications of the initial subset of items and of a resampling procedure
On the "Poisson Trick" and its Extensions for Fitting Multinomial Regression Models
This article is concerned with the fitting of multinomial regression models
using the so-called "Poisson Trick". The work is motivated by Chen & Kuo (2001)
and Malchow-M{\o}ller & Svarer (2003) which have been criticized for being
computationally inefficient and sometimes producing nonsense results. We first
discuss the case of independent data and offer a parsimonious fitting strategy
when all covariates are categorical. We then propose a new approach for
modelling correlated responses based on an extension of the Gamma-Poisson
model, where the likelihood can be expressed in closed-form. The parameters are
estimated via an Expectation/Conditional Maximization (ECM) algorithm, which
can be implemented using functions for fitting generalized linear models
readily available in standard statistical software packages. Compared to
existing methods, our approach avoids the need to approximate the intractable
integrals and thus the inference is exact with respect to the approximating
Gamma-Poisson model. The proposed method is illustrated via a reanalysis of the
yogurt data discussed by Chen & Kuo (2001)
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