A Universal Non-Uniform Random Number Generator

A universal non-uniform random number generator for quite arbitrary distributions with piecewise twice differentiable densities.

Functions for Optimal Non-Bipartite Matching

Perform non-bipartite matching and matched randomization. A "bipartite" matching utilizes two separate groups, e.g. smokers being matched to nonsmokers or cases being matched to controls. A "non-bipartite" matching creates mates from one big group, e.g. 100 hospitals being randomized for a two-arm cluster randomized trial or 5000 children who have been exposed to various levels of secondhand smoke and are being paired to form a greater exposure vs. lesser exposure comparison. At the core of a non-bipartite matching is a N x N distance matrix for N potential mates. The distance between two units expresses a measure of similarity or quality as mates (the lower the better). The 'gendistance()' and 'distancematrix()' functions assist in creating this. The 'nonbimatch()' function creates the matching that minimizes the total sum of distances between mates; hence, it is referred to as an "optimal" matching. The 'assign.grp()' function aids in performing a matched randomization. Note bipartite matching can be performed using the prevent option in 'gendistance()'.

Random Orthonormal Matrix Generation and Optimization on the Stiefel Manifold

Simulation of random orthonormal matrices from linear and quadratic exponential family distributions on the Stiefel manifold. The most general type of distribution covered is the matrix-variate Bingham-von Mises-Fisher distribution. Most of the simulation methods are presented in Hoff(2009) "Simulation of the Matrix Bingham-von Mises-Fisher Distribution, With Applications to Multivariate and Relational Data" . The package also includes functions for optimization on the Stiefel manifold based on algorithms described in Wen and Yin (2013) "A feasible method for optimization with orthogonality constraints" .

A Diceware Passphrase Implementation

The Diceware method can be used to generate strong passphrases. In short, you roll a 6-faced dice 5 times in a row, the number obtained is matched against a dictionary of easily remembered words. By combining together 7 words thus generated, you obtain a password that is relatively easy to remember, but would take several millions years (on average) for a powerful computer to guess.

Flexible Procedures for Clustering

Various methods for clustering and cluster validation. Fixed point clustering. Linear regression clustering. Clustering by merging Gaussian mixture components. Symmetric and asymmetric discriminant projections for visualisation of the separation of groupings. Cluster validation statistics for distance based clustering including corrected Rand index. Standardisation of cluster validation statistics by random clusterings and comparison between many clustering methods and numbers of clusters based on this. Cluster-wise cluster stability assessment. Methods for estimation of the number of clusters: Calinski-Harabasz, Tibshirani and Walther's prediction strength, Fang and Wang's bootstrap stability. Gaussian/multinomial mixture fitting for mixed continuous/categorical variables. Variable-wise statistics for cluster interpretation. DBSCAN clustering. Interface functions for many clustering methods implemented in R, including estimating the number of clusters with kmeans, pam and clara. Modality diagnosis for Gaussian mixtures. For an overview see package?fpc.

A Laboratory for Recursive Partytioning

A computational toolbox for recursive partitioning. The core of the package is ctree(), an implementation of conditional inference trees which embed tree-structured regression models into a well defined theory of conditional inference procedures. This non-parametric class of regression trees is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. Based on conditional inference trees, cforest() provides an implementation of Breiman's random forests. The function mob() implements an algorithm for recursive partitioning based on parametric models (e.g. linear models, GLMs or survival regression) employing parameter instability tests for split selection. Extensible functionality for visualizing tree-structured regression models is available. The methods are described in Hothorn et al. (2006) , Zeileis et al. (2008) and Strobl et al. (2007) .

Temporal Exponential Random Graph Models by Bootstrapped Pseudolikelihood

Temporal Exponential Random Graph Models (TERGM) estimated by maximum pseudolikelihood with bootstrapped confidence intervals or Markov Chain Monte Carlo maximum likelihood. Goodness of fit assessment for ERGMs, TERGMs, and SAOMs. Micro-level interpretation of ERGMs and TERGMs. The methods are described in Leifeld, Cranmer and Desmarais (2018), JStatSoft .

Wrapper Algorithm for All Relevant Feature Selection

An all relevant feature selection wrapper algorithm. It finds relevant features by comparing original attributes' importance with importance achievable at random, estimated using their permuted copies (shadows).

Tools for Analyzing Finite Mixture Models

Analyzes finite mixture models for various parametric and semiparametric settings. This includes mixtures of parametric distributions (normal, multivariate normal, multinomial, gamma), various Reliability Mixture Models (RMMs), mixtures-of-regressions settings (linear regression, logistic regression, Poisson regression, linear regression with changepoints, predictor-dependent mixing proportions, random effects regressions, hierarchical mixtures-of-experts), and tools for selecting the number of components (bootstrapping the likelihood ratio test statistic, mixturegrams, and model selection criteria). Bayesian estimation of mixtures-of-linear-regressions models is available as well as a novel data depth method for obtaining credible bands. This package is based upon work supported by the National Science Foundation under Grant No. SES-0518772 and the Chan Zuckerberg Initiative: Essential Open Source Software for Science (Grant No. 2020-255193).

Distances and Routes on Geographical Grids

Provides classes and functions to calculate various distance measures and routes in heterogeneous geographic spaces represented as grids. The package implements measures to model dispersal histories first presented by van Etten and Hijmans (2010) . Least-cost distances as well as more complex distances based on (constrained) random walks can be calculated. The distances implemented in the package are used in geographical genetics, accessibility indicators, and may also have applications in other fields of geospatial analysis.