Abstract: R package krippendorffsalpha provides tools for measuring agreement using Krippendorff's Alpha coefficient, a well-known nonparametric measure of agreement (also called inter-rater reliability and various other names). This article first develops Krippendorff's Alpha in a natural way, and situates Alpha among statistical procedures. Then the usage of package krippendorffsalpha is illustrated via analyses of two datasets, the latter of which was collected during an imaging study of hip cartilage. The package permits users to apply the Alpha methodology using built-in distance functions for the nominal, ordinal, interval, or ratio levels of measurement. User-defined distance functions are also supported. The fitting function can accommodate any number of units, any number of coders, and missingness. Bootstrap inference is supported, and the bootstrap computation can be carried out in parallel.

Abstract: Recurrence quantification analysis is a widely used method for characterizing patterns in time series. This article presents a comprehensive survey for conducting a wide range of recurrence based analyses to quantify the dynamical structure of single and multivariate time series and capture coupling properties underlying leader-follower relationships. The basics of recurrence quantification analysis (RQA) and all its variants are formally introduced step-by-step from the simplest auto recurrence to the most advanced multivariate case. Importantly, we show how such RQA methods can be deployed under a single computational framework in R using a substantially renewed version of our crqa 2.0 package. This package includes implementations of several recent advances in recurrence based analysis, among them applications to multivariate data and improved entropy calculations for categorical data. We show concrete applications of our package to example data, together with a detailed description of its functions and some guidelines on their usage.

Abstract: Several persistent homology software libraries have been implemented in R. Specifically, the Dionysus, GUDHI, and Ripser libraries have been wrapped by the TDA and TDAstats CRAN packages. These software represent powerful analysis tools that are computationally expensive and, to our knowledge, have not been formally benchmarked. Here, we analyze runtime and memory growth for the 2 R packages and the 3 underlying libraries. We find that datasets with less than 3 dimensions can be evaluated with persistent homology fastest by the GUDHI library in the TDA package. For higher-dimensional datasets, the Ripser library in the TDAstats package is the fastest. Ripser and TDAstats are also the most memory-efficient tools to calculate persistent homology.

Abstract: Last decades show an increased interest in modeling various types of data through copulae. Different copula models have been developed, which lead to the challenge of finding the best fitting model for a particular dataset. From the other side, a strand of literature developed a list of different Goodness-of-Fit (GoF) tests with different powers under different conditions. Usual practice is the selection of the best copula via the p-value of the GoF test. Although this method is not purely correct due to the fact that non-rejection does not imply acception, this strategy is favoured by practitioners. Unfortunately, different GoF tests often provide contradicting outputs. The proposed R-package brings under one umbrella 13 most used copulae - plus their rotated variants - together with 16 GoF tests and a hybrid one. The package offers flexible margin modeling, automatized parallelization, parameter estimation as well as a user friendly interface and pleasant visualizations of the results. To illustrate the functionality of the package, two exemplary applications are provided.

Abstract: Chaos theory has been hailed as a revolution of thoughts and attracting ever-increasing attention of many scientists from diverse disciplines. Chaotic systems are non-linear deterministic dynamic systems which can behave like an erratic and apparently random motion. A relevant field inside chaos theory is the detection of chaotic behavior from empirical time-series data. One of the main features of chaos is the well-known initial-value sensitivity property. Methods and techniques related to testing the hypothesis of chaos try to quantify the initial-value sensitive property estimating the so-called Lyapunov exponents. This paper describes the main estimation methods of the Lyapunov exponent from time series data. At the same time, we present the DChaos library. R users may compute the delayed-coordinate embedding vector from time series data, estimates the best-fitted neural net model from the delayed-coordinate embedding vectors, calculates analytically the partial derivatives from the chosen neural nets model. They can also obtain the neural net estimator of the Lyapunov exponent from the partial derivatives computed previously by two different procedures and four ways of subsampling by blocks. To sum up, the DChaos package allows the R users to test robustly the hypothesis of chaos in order to know if the data-generating process behind time series behaves chaotically or not. The package’s functionality is illustrated by examples.

Abstract: This paper introduces a new flexible distribution for discrete data. Approximate moment estimators of the parameters of the distribution, to be used as starting values for numerical optimization procedures, are discussed. “Exact” moment estimation, effected via a numerical procedure, and maximum likelihood estimation, are considered. The quality of the results produced by these estimators is assessed via simulation experiments. Several examples are given of fitting instances of the new distribution to real and simulated data. It is noted that the new distribution is a member of the exponential family. Expressions for the gradient and Hessian of the log-likelihood of the new distribution are derived. The former facilitates the numerical maximization of the likelihood with optim(); the latter provides means of calculating or estimating the covariance matrix of of the parameter estimates. A discrepancy between estimates of the covariance matrix obtained by inverting the Hessian and those obtained by Monte Carlo methods is discussed.

Abstract: In network analysis, many community detection algorithms have been developed, however, their implementation leaves unaddressed the question of the statistical validation of the results. Here we present robin(ROBustness In Network), an R package to assess the robustness of the community structure of a network found by one or more methods to give indications about their reliability. The procedure initially detects if the community structure found by a set of algorithms is statistically significant and then compares two selected detection algorithms on the same graph to choose the one that better fits the network of interest. We demonstrate the use of our package on the American College Football benchmark dataset.