Joint modelling of multiple network wiews

Latent space models (LSM) for network data were introduced by Hoff et al. (2002) under the basic assumption that each node of the network has an unknown position in a D-dimensional Euclidean latent space: generally the smaller the distance between two nodes in the latent space, the greater their probability of being connected. In this paper we propose a variational inference approach to estimate the intractable posterior of the LSM. In many cases, different network views on the same set of nodes are available. It can therefore be useful to build a model able to jointly summarise the information given by all the network views. For this purpose, we introduce the latent space joint model (LSJM) that merges the information given by multiple network views assuming that the probability of a node being connected with other nodes in each network view is explained by a unique latent variable. This model is demonstrated on the analysis of two datasets: an excerpt of 50 girls from 'Teenage Friends and Lifestyle Study' data at three time points and the Saccharomyces cerevisiae genetic and physical protein-protein interactions

GWmodel

In GWmodel, we introduce techniques from a particular branch of spatial statistics,termed geographically-weighted (GW) models. GW models suit situations when data are not described well by some global model, but where there are spatial regions where a suitably localised calibration provides a better description. GWmodel includes functions to calibrate: GW summary statistics, GW principal components analysis,GW discriminant analysis and various forms of GW regression; some of which are provided in basic and robust (outlier resistant) forms

Analyzing regional economic development patterns in a fast developing province of China through geographically weighted principal component analysis

Understanding the spatial structure of regional economic development is of importance for regional planning and provincial development strategy making. Taking Jiangsu Province in the economically richest Yangtze Delta as a case study, this paper aims to explore regional economic development level on a provincial scale. Using the data sets from provincial statistical yearbook of 2010, eleven variables are selected for statistical and spatial analyses at a county level. Both the traditional principal component analysis (PCA) and its local version—geographically weighted PCA (GWPCA)—are employed to these analyses for the purpose of comparison. The results have confirmed that GWPCA is an effective means of analyzing regional economic development level through mapping its local principal components. It is also concluded that the regional economic development in Jiangsu Province demonstrates spatial inequality between the North and South

Geographically weighted elastic net logistic regression

This paper develops a localized approach to elastic net logistic regression, extending previous research describing a localized elastic net as an extension to a localized ridge regression or a localized lasso. All such models have the objective to capture data relationships that vary across space. Geographically weighted elastic net logistic regression is first evaluated through a simulation experiment and shown to provide a robust approach for local model selection and alleviating local collinearity, before application to two case studies: county-level voting patterns in the 2016 USA presidential election, examining the spatial structure of socio-economic factors associated with voting for Trump, and a species presence–absence data set linked to explanatory environmental and climatic factors at gridded locations covering mainland USA. The approach is compared with other logistic regressions. It improves prediction for the election case study only which exhibits much greater spatial heterogeneity in the binary response than the species case study. Model comparisons show that standard geographically weighted logistic regression over-estimated relationship non-stationarity because it fails to adequately deal with collinearity and model selection. Results are discussed in the context of predictor variable collinearity and selection and the heterogeneities that were observed. Ongoing work is investigating locally derived elastic net parameters

An overview on the URV model-based approach to cluster mixed-type data

In this paper, we provide an overview on the underlying response variable (URV) model-based approach to cluster and, optionally, simultaneously reduce ordinal and, optionally, continuous variables. We summarize and compare its main features discussing some key issues. An example of application to real data is illustrated comparing and discussing clustering performances