Predictive nonlinear biplots: maps and trajectories

When the difference between samples is measured using a Euclidean embeddable dissimilarity function, observations and the associated variables can be displayed on a nonlinear biplot. Furthermore, a nonlinear biplot is predictive if information on variables is added in such a way that it allows the values of the variables to be estimated for points in the biplot. In this paper an r dimensional biplot which maps the predicted value of a variable for every point in the plot, is introduced. Using such maps it is shown that even with continuous data, predicted values do not always vary continuously across the biplot plane. Prediction trajectories that appropriate for summarising such non-continuous prediction maps are also introduced. These prediction trajectories allow information about two or more variables to be estimated even when the underlying predicted values do not vary continuously

BiplotGUI: Interactive Biplots in R

Biplots simultaneously provide information on both the samples and the variables of a data matrix in two- or three-dimensional representations. The BiplotGUI package provides a graphical user interface for the construction of, interaction with, and manipulation of biplots in R. The samples are represented as points, with coordinates determined either by the choice of biplot, principal coordinate analysis or multidimensional scaling. Various transformations and dissimilarity metrics are available. Information on the original variables is incorporated by linear or non-linear calibrated axes. Goodness-of-fit measures are provided. Additional descriptors can be superimposed, including convex hulls, alpha-bags, point densities and classification regions. Amongst the interactive features are dynamic variable value prediction, zooming and point and axis drag-and-drop. Output can easily be exported to the R workspace for further manipulation. Three-dimensional biplots are incorporated via the rgl package. The user requires almost no knowledge of R syntax.

BiplotGUI: Interactive Biplots in R

Biplots simultaneously provide information on both the samples and the variables ofa data matrix in two- or three-dimensional representations. The BiplotGUI package provides a graphical user interface for the construction of, interaction with, and manipulation of biplots in R. The samples are represented as points, with coordinates determined either by the choice of biplot, principal coordinate analysis or multidimensional scaling. Various transformations and dissimilarity metrics are available. Information on the original variables is incorporated by linear or non-linear calibrated axes. Goodness-of-t measures are provided. Additional descriptors can be superimposed, including convex hulls, alpha-bags, point densities and classication regions. Amongst the interactive features are dynamic variable value prediction, zooming and point and axis drag-and-drop. Output can easily be exported to the R workspace for further manipulation. Three-dimensional biplots are incorporated via the rgl package. The user requires almost no knowledge of R syntax

More on Multidimensional Scaling and Unfolding in R: smacof Version 2

The smacof package offers a comprehensive implementation of multidimensional scaling (MDS) techniques in R. Since its first publication (De Leeuw and Mair 2009b) the functionality of the package has been enhanced, and several additional methods, features and utilities were added. Major updates include a complete re-implementation of multidimensional unfolding allowing for monotone dissimilarity transformations, including row-conditional, circular, and external unfolding. Additionally, the constrained MDS implementation was extended in terms of optimal scaling of the external variables. Further package additions include various tools and functions for goodness-of-fit assessment, unidimensional scaling, gravity MDS, asymmetric MDS, Procrustes, and MDS biplots. All these new package functionalities are illustrated using a variety of real-life applications

Optimal Scaling of Interaction Effects in Generalized Linear Models

Multiplicative interaction models, such as Goodman's RC(M) association models, can be a useful tool for analyzing the content of interaction effects. However, most models for interaction effects are only suitable for data sets with two or three predictor variables. Here, we discuss an optimal scaling model for analyzing the content of interaction effects in generalized linear models with any number of categorical predictor variables. This model, which we call the optimal scaling of interactions (OSI) model, is a parsimonious, one-dimensional multiplicative interaction model. We discuss how the model can be used to visually interpret the interaction effects. Two empirical data sets are used to show how the results of the model can be applied and interpreted. Finally, several multidimensional extensions of the one-dimensional model are explored.

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing

Effects of environmental factors on the historical time serie of blackspot seabream commercial landings (1983 to 2015) in the strait of Gibraltar: A shared marine resource between the Spanish and Moroccan fleets

In the Strait of Gibraltar, the Blackspot Seabream (Pagellus bogaraveo, Brünnich 1768) is an economic resource of great commercial importance for the Spanish and Moroccan artisanal and Moroccan longline fleets. Given the great interest of the species for the fleets, it is of vital importance to know the dynamics of landings and how this can be influenced by environmental variability. From this arises the hypothesis of the present study: environmental mechanisms cause forcings in the dynamics of landings. To this end, we analysed the average annual dynamics of the time series of commercial landings of the Blackspot Seabream from 1983 to 2015 from a multivariate perspective. We applied trend, principal component (PCA) and time series clustering analyses to determine patterns and relationships between the fishery series and different oceanographic variables and climatic indices. In addition, we determined the influence of this set of variables on landings from a linear approach based on multiple linear regressions (MLRs) and generalized linear models (GLMs) and non-linear determined by generalized additive models (GAMs). The results obtained indicated the presence of common temporal patterns and the existence of significant influence between landings and ocean temperature with the current velocity modulus in specific layers and heat flux, causing lower fishing yields as we get colder waters with less intense currents. Such studies are of vital importance for the application of an ecosystem approach to the management of this resource by understanding the effect and influence of the environment on the dynamics of landings from the fishery.The authors wish to express their gratitude to Dr. Juan Gil-Herrera (Oceanography Spanish Institute, Cádiz, Spain) and Dr. Said Benchoucha and Sana el Arraf (National Institute of Fisheries Research-INRHTangier, Morocco) for providing the data set of Blackspot Seabream landings in the Spanish and Moroccan ports. Víctor Sanz-Fernández is financed by the Spanish Ministry of Science, Innovation and Universities with a FPU fellowship (FPU17/04298). Funding for open access charge: Universidad de Huelva / CBUA

A Geneaology of Correspondence Analysis: Part 2 - The Variants

In 2012, a comprehensive historical and genealogical discussion of correspondence analysis was published in Australian and New Zealand Journal of Statistics. That genealogy consisted of more than 270 key books and articles and focused on an historical development of the correspondence analysis,a statistical tool which provides the analyst with a visual inspection of the association between two or more categorical variables. In this new genealogy, we provide a brief overview of over 30 variants of correspondence analysis that now exist outside of the traditional approaches used to analysethe association between two or more categorical variables. It comprises of a bibliography of a more than 300 books and articles that were not included in the 2012 bibliography and highlights the growth in the development ofcorrespondence analysis across all areas of research

Modeling realized measures of volatility

Although volatility is essential for many applications in finance, it is generally an unobservable process with no universal definition. Through association with integrated variance, a multitude of non-parametric volatility estimators collectively referred to as realized measures was proposed. The topic of this cumulative dissertation is modeling time series of realized measures with a special focus on forecasting. Currently, most popular univariate models are basically restricted linear regressions with some economic argumentation, whereas multivariate methods usually face complex unresolved numerical and theoretical issues. Chapters 2 and 3 propose alternative approaches to modeling univariate realized measures from two different perspectives, distributional with copulas and non-parametric with B-splines, respectively. Chapter 4 introduces a novel factor-based approach to modeling multivariate realized measures. All proposed methods are discussed theoretically and compared to respective benchmarks within corresponding extensive empirical studies