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).

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.

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 .

Generation of Random Vectors with User-Defined Density

Random vectors with arbitrary Lipschitz density are generated using acceptance/ rejection. The method is based on G. Beliakov (2005) .

Gradient Projection Factor Rotation

Gradient projection algorithms for orthogonal and oblique rotation of factor loadings matrices in factor analysis. Implements a comprehensive set of rotation criteria including quartimax, quartimin, oblimin, geomin, simplimax, the Crawford-Ferguson family, and target rotation, among others. Supports multiple random starts. For details see Bernaards and Jennrich (2005) .

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.

Randomization Inference Tools

Tools for randomization-based inference. Current focus is on the d^2 omnibus test of differences of means following Hansen and Bowers (2008) . This test is useful for assessing balance in matched observational studies or for analysis of outcomes in block-randomized experiments.

Testing Randomness in R

Provides several non parametric randomness tests for numeric sequences.

Bayesian Random-Effects Meta-Analysis and Meta-Regression

A collection of functions allowing to derive the posterior distribution of the model parameters in random-effects meta-analysis or meta-regression, and providing functionality to evaluate joint and marginal posterior probability distributions, predictive distributions, shrinkage effects, posterior predictive p-values, etc.; For more details, see also Roever C (2020) , or Roever C and Friede T (2022) .

Core Functionality of the 'spatstat' Family

Functionality for data analysis and modelling of spatial data, mainly spatial point patterns, in the 'spatstat' family of packages. (Excludes analysis of spatial data on a linear network, which is covered by the separate package 'spatstat.linnet'.) Exploratory methods include quadrat counts, K-functions and their simulation envelopes, nearest neighbour distance and empty space statistics, Fry plots, pair correlation function, kernel smoothed intensity, relative risk estimation with cross-validated bandwidth selection, mark correlation functions, segregation indices, mark dependence diagnostics, and kernel estimates of covariate effects. Formal hypothesis tests of random pattern (chi-squared, Kolmogorov-Smirnov, Monte Carlo, Diggle-Cressie-Loosmore-Ford, Dao-Genton, two-stage Monte Carlo) and tests for covariate effects (Cox-Berman-Waller-Lawson, Kolmogorov-Smirnov, ANOVA) are also supported. Parametric models can be fitted to point pattern data using the functions ppm(), kppm(), slrm(), dppm() similar to glm(). Types of models include Poisson, Gibbs and Cox point processes, Neyman-Scott cluster processes, and determinantal point processes. Models may involve dependence on covariates, inter-point interaction, cluster formation and dependence on marks. Models are fitted by maximum likelihood, logistic regression, minimum contrast, and composite likelihood methods. A model can be fitted to a list of point patterns (replicated point pattern data) using the function mppm(). The model can include random effects and fixed effects depending on the experimental design, in addition to all the features listed above. Fitted point process models can be simulated, automatically. Formal hypothesis tests of a fitted model are supported (likelihood ratio test, analysis of deviance, Monte Carlo tests) along with basic tools for model selection (stepwise(), AIC()) and variable selection (sdr). Tools for validating the fitted model include simulation envelopes, residuals, residual plots and Q-Q plots, leverage and influence diagnostics, partial residuals, and added variable plots.