Calculate magnetic field at a given location and time according to the World Magnetic Model (WMM). Both the main field and secular variation components are returned. This functionality is useful for physicists and geophysicists who need orthogonal components from WMM. Currently, this package supports annualized time inputs between 2000 and 2025. If desired, users can specify which WMM version to use, e.g., the original WMM2015 release or the recent out-of-cycle WMM2015 release. Methods used to implement WMM, including the Gauss coefficients for each release, are described in the following publications: Chulliat et al (2020) <doi:10.25923/ytk1-yx35>, Chulliat et al (2019) <doi:10.25921/xhr3-0t19>, Chulliat et al (2015) <doi:10.7289/V5TB14V7>, Maus et al (2010) <https://www.ngdc.noaa.gov/geomag/WMM/data/WMMReports/WMM2010_Report.pdf>, McLean et al (2004) <https://www.ngdc.noaa.gov/geomag/WMM/data/WMMReports/TRWMM_2005.pdf>, and Macmillian et al (2000) <https://www.ngdc.noaa.gov/geomag/WMM/data/WMMReports/wmm2000.pdf>.

This package provides a toolbox to derive flexible cutoffs for fit indices in Covariance-based Structural Equation Modeling based on the paper by Niemand & Mai (2018) <doi:10.1007/s11747-018-0602-9>. Flexible cutoffs are an alternative to fixed cutoffs - rules-of-thumb - regarding an appropriate cutoff for fit indices such as CFI or SRMR'. It has been demonstrated that these flexible cutoffs perform better than fixed cutoffs in grey areas where misspecification is not easy to detect. The package provides an alternative to the tool at <https://flexiblecutoffs.org> as it allows to tailor flexible cutoffs to a given dataset and model, which is so far not available in the tool. The package simulates fit indices based on a given dataset and model and then estimates the flexible cutoffs. Some useful functions, e.g., to determine the GoF- or BoF-nature of a fit index, are provided. So far, additional options for a relative use (is a model better than another?) are provided in an exploratory manner.

This package provides tools implementing an automated version of the graphic double integration technique (GDI) for volume implementation, and some other related utilities for paleontological image-analysis. GDI was first employed by Jerison (1973) <ISBN:9780323141086> and Hurlburt (1999) <doi:10.1080/02724634.1999.10011145> and is primarily used for volume or mass estimation of (extinct) animals. The package gdi aims to make this technique as convenient and versatile as possible. The core functions of gdi provide utilities for automatically measuring diameters from digital silhouettes provided as image files and calculating volume via graphic double integration with simple elliptical, superelliptical (following Motani 2001 <doi:10.1666/0094-8373(2001)027%3C0735:EBMFST%3E2.0.CO;2>) or complex cross-sectional geometries (see also Zhao 2024 <doi:10.7717/peerj.17479>). Additionally, the package provides functions for estimating the center of mass position (COM), the moment of inertia (I) for 3D shapes and the second moment of area (Ix, Iy, Iz) of 2D cross-sections, as well as for the visualization of results.

This package provides efficient Markov chain Monte Carlo (MCMC) algorithms for dynamic shrinkage processes, which extend global-local shrinkage priors to the time series setting by allowing shrinkage to depend on its own past. These priors yield locally adaptive estimates, useful for time series and regression functions with irregular features. The package includes full MCMC implementations for trend filtering using dynamic shrinkage on signal differences, producing locally constant or linear fits with adaptive credible bands. Also included are models with static shrinkage and normal-inverse-Gamma priors for comparison. Additional tools cover dynamic regression with time-varying coefficients and B-spline models with shrinkage on basis differences, allowing for flexible curve-fitting with unequally spaced data. Some support for heteroscedastic errors, outlier detection, and change point estimation. Methods in this package are described in Kowal et al. (2019) <doi:10.1111/rssb.12325>, Wu et al. (2024) <doi:10.1080/07350015.2024.2362269>, Schafer and Matteson (2024) <doi:10.1080/00401706.2024.2407316>, and Cho and Matteson (2026) <doi:10.1080/07350015.2025.2602846>.

This package provides propensity score weighting methods to control for confounding in causal inference with dichotomous treatments and continuous/binary outcomes. It includes the following functional modules: (1) visualization of the propensity score distribution in both treatment groups with mirror histogram, (2) covariate balance diagnosis, (3) propensity score model specification test, (4) weighted estimation of treatment effect, and (5) augmented estimation of treatment effect with outcome regression. The weighting methods include the inverse probability weight (IPW) for estimating the average treatment effect (ATE), the IPW for average treatment effect of the treated (ATT), the IPW for the average treatment effect of the controls (ATC), the matching weight (MW), the overlap weight (OVERLAP), and the trapezoidal weight (TRAPEZOIDAL). Sandwich variance estimation is provided to adjust for the sampling variability of the estimated propensity score. These methods are discussed by Hirano et al (2003) <DOI:10.1111/1468-0262.00442>, Lunceford and Davidian (2004) <DOI:10.1002/sim.1903>, Li and Greene (2013) <DOI:10.1515/ijb-2012-0030>, and Li et al (2016) <DOI:10.1080/01621459.2016.1260466>.

This package performs hypergraph-based setwise variable selection with false discovery rate control (Organ, Kenney & Gu, 2026, <doi:10.48550/arXiv.2606.20514>). The idea is, in addition to selecting individual predictors when there is sufficient evidence, to also test all pairs of predictors, and when there is insufficient evidence to be sure which is the true predictor, it will select possibly overlapping pairs, for which there is strong evidence that at least one is a true predictor. The method is designed to control a generalised false discovery rate, where discoveries are counted based on the number of independent sets. The function of this package is similar to the hypergraph.sizing package, but this package is optimised for faster computation in the case where we test all pairs of predictors. The package also includes functions for counting independent sets in a graph or hypergraph, either exactly or approximately. There is also a very limited function for isotonic regression, which is designed for fast computation in the specific case needed for hypergraph variable selection, rather than for general use.

Bayes factors represent the ratio of probabilities assigned to data by competing scientific hypotheses. However, one drawback of Bayes factors is their dependence on prior specifications that define null and alternative hypotheses. Additionally, there are challenges in their computation. To address these issues, we define Bayes factor functions (BFFs) directly from common test statistics. BFFs express Bayes factors as a function of the prior densities used to define the alternative hypotheses. These prior densities are centered on standardized effects, which serve as indices for the BFF. Therefore, BFFs offer a summary of evidence in favor of alternative hypotheses that correspond to a range of scientifically interesting effect sizes. Such summaries remove the need for arbitrary thresholds to determine "statistical significance." BFFs are available in closed form and can be easily computed from z, t, chi-squared, and F statistics. They depend on hyperparameters "r" and "tau^2", which determine the shape and scale of the prior distributions defining the alternative hypotheses. Plots of BFFs versus effect size provide informative summaries of hypothesis tests that can be easily aggregated across studies.

Artificial selection through selective breeding is an efficient way to induce changes in traits of interest in experimental populations. This package (sra) provides a set of tools to analyse artificial-selection response datasets. The data typically feature for several generations the average value of a trait in a population, the variance of the trait, the population size and the average value of the parents that were chosen to breed. Sra implements two families of models aiming at describing the dynamics of the genetic architecture of the trait during the selection response. The first family relies on purely descriptive (phenomenological) models, based on an autoregressive framework. The second family provides different mechanistic models, accounting e.g. for inbreeding, mutations, genetic and environmental canalization, or epistasis. The parameters underlying the dynamics of the time series are estimated by maximum likelihood. The sra package thus provides (i) a wrapper for the R functions mle() and optim() aiming at fitting in a convenient way a predetermined set of models, and (ii) some functions to plot and analyze the output of the models.

Fits the Bayesian multinomial probit model via Markov chain Monte Carlo. The multinomial probit model is often used to analyze the discrete choices made by individuals recorded in survey data. Examples where the multinomial probit model may be useful include the analysis of product choice by consumers in market research and the analysis of candidate or party choice by voters in electoral studies. The MNP package can also fit the model with different choice sets for each individual, and complete or partial individual choice orderings of the available alternatives from the choice set. The estimation is based on the efficient marginal data augmentation algorithm that is developed by Imai and van Dyk (2005). "A Bayesian Analysis of the Multinomial Probit Model Using the Data Augmentation." Journal of Econometrics, Vol. 124, No. 2 (February), pp. 311-334. <doi:10.1016/j.jeconom.2004.02.002> Detailed examples are given in Imai and van Dyk (2005). "MNP: R Package for Fitting the Multinomial Probit Model." Journal of Statistical Software, Vol. 14, No. 3 (May), pp. 1-32. <doi:10.18637/jss.v014.i03>.

This package implements Meta Fuzzy Functions (MFFs) for regression Tak and Ucan (2026) <doi:10.1016/j.asoc.2026.114592> by aggregating predictions from multiple base learners using membership weights learned in the prediction space of validation set. The package supports fuzzy and crisp meta-ensemble structures via Fuzzy C-Means (FCM) Tak (2018) <doi:10.1016/j.asoc.2018.08.009>, Possibilistic FCM (PFCM) Tak (2021) <doi:10.1016/j.ins.2021.01.024>, Gustafsonâ Kessel (GK) clustering, and k-means, and provides a workflow to (i) generate validation/test prediction matrices from common regression learners (linear and penalized regression via glmnet', random forests, gradient boosting with xgboost and lightgbm'), (ii) fit cluster-wise meta fuzzy functions and compute membership-based weights, (iii) tune clustering-related hyperparameters (number of clusters/functions, fuzziness exponent, possibilistic regularization) via grid search on validation loss, and (iv) predict on new/test prediction matrices and evaluate performance using standard regression metrics (MAE, RMSE, MAPE, SMAPE, MSE, MedAE). This enables flexible, interpretable ensemble regression where different base models contribute to different meta components according to learned memberships.

Forecasting of univariate time series using feature extraction with variable prediction methods is provided. Feature extraction is done with a redundant Haar wavelet transform with filter h = (0.5, 0.5). The advantage of the approach compared to typical Fourier based methods is an dynamic adaptation to varying seasonalities. Currently implemented prediction methods based on the selected wavelets levels and scales are a regression and a multi-layer perceptron. Forecasts can be computed for horizon 1 or higher. Model selection is performed with an evolutionary optimization. Selection criteria are currently the AIC criterion, the Mean Absolute Error or the Mean Root Error. The data is split into three parts for model selection: Training, test, and evaluation dataset. The training data is for computing the weights of a parameter set. The test data is for choosing the best parameter set. The evaluation data is for assessing the forecast performance of the best parameter set on new data unknown to the model. This work is published in Stier, Q.; Gehlert, T.; Thrun, M.C. Multiresolution Forecasting for Industrial Applications. Processes 2021, 9, 1697. <doi:10.3390/pr9101697>.

Stochastic Newton Sampler (SNS) is a Metropolis-Hastings-based, Markov Chain Monte Carlo sampler for twice differentiable, log-concave probability density functions (PDFs) where the proposal density function is a multivariate Gaussian resulting from a second-order Taylor-series expansion of log-density around the current point. The mean of the Gaussian proposal is the full Newton-Raphson step from the current point. A Boolean flag allows for switching from SNS to Newton-Raphson optimization (by choosing the mean of proposal function as next point). This can be used during burn-in to get close to the mode of the PDF (which is unique due to concavity). For high-dimensional densities, mixing can be improved via state space partitioning strategy, in which SNS is applied to disjoint subsets of state space, wrapped in a Gibbs cycle. Numerical differentiation is available when analytical expressions for gradient and Hessian are not available. Facilities for validation and numerical differentiation of log-density are provided. Note: Formerly available versions of the MfUSampler can be obtained from the archive <https://cran.r-project.org/src/contrib/Archive/MfUSampler/>.

Computes various geospatial indices of socioeconomic deprivation and disparity in the United States. Some indices are considered "spatial" because they consider the values of neighboring (i.e., adjacent) census geographies in their computation, while other indices are "aspatial" because they only consider the value within each census geography. Two types of aspatial neighborhood deprivation indices (NDI) are available, including: (1) based on Messer et al. (2006) <doi:10.1007/s11524-006-9094-x> and (2) based on Andrews et al. (2020) <doi:10.1080/17445647.2020.1750066> and Slotman et al. (2022) <doi:10.1016/j.dib.2022.108002> who use variables chosen by Roux and Mair (2010) <doi:10.1111/j.1749-6632.2009.05333.x>. Both are a decomposition of multiple demographic characteristics from the U.S. Census Bureau American Community Survey 5-year estimates (ACS-5; 2006-2010 onward). Using data from the ACS-5 (2005-2009 onward), the package can also compute indices of racial or ethnic residential segregation, including but limited to those discussed in Massey & Denton (1988) <doi:10.1093/sf/67.2.281>, and additional indices of socioeconomic disparity.

Estimation, inference, and quantities of interest for ordered probit and ordered logit models whose outcome contains an inflated category: a single ordered category (bottom, middle, top, or any other) that mixes observations generated by the ordered process with observations generated by a distinct split-population process. Fits the zero-inflated ordered probit of Harris and Zhao (2007) <doi:10.1016/j.jeconom.2007.01.002> and its middle- and top-inflated extensions (Bagozzi and Mukherjee 2012 <doi:10.1093/pan/mps020>; Bagozzi, Hill, Moore and Mukherjee 2015 <doi:10.1177/0022002713520530>; Bagozzi, Joo and Mukherjee 2024 <doi:10.1093/fpa/orae006>), generalized to an arbitrary inflated category and to the logit link, with optional correlated errors for the probit form, plus the standard ordered probit and logit and their partial proportional-odds (non-parallel) variants on the same footing. Provides analytic, robust, and cluster-robust standard errors, survey weights and offsets, model comparison (Vuong, likelihood-ratio, information criteria), regime-specific predicted probabilities and first differences, simulation for residual diagnostics, and tidy/table-package integration. The likelihood, its gradient, and the bivariate-normal probabilities are implemented in C++.

Outcome-dependent sampling (ODS) schemes are cost-effective ways to enhance study efficiency. In ODS designs, one observes the exposure/covariates with a probability that depends on the outcome variable. Popular ODS designs include case-control for binary outcome, case-cohort for time-to-event outcome, and continuous outcome ODS design (Zhou et al. 2002) <doi: 10.1111/j.0006-341X.2002.00413.x>. Because ODS data has biased sampling nature, standard statistical analysis such as linear regression will lead to biases estimates of the population parameters. This package implements four statistical methods related to ODS designs: (1) An empirical likelihood method analyzing the primary continuous outcome with respect to exposure variables in continuous ODS design (Zhou et al., 2002). (2) A partial linear model analyzing the primary outcome in continuous ODS design (Zhou, Qin and Longnecker, 2011) <doi: 10.1111/j.1541-0420.2010.01500.x>. (3) Analyze a secondary outcome in continuous ODS design (Pan et al. 2018) <doi: 10.1002/sim.7672>. (4) An estimated likelihood method analyzing a secondary outcome in case-cohort data (Pan et al. 2017) <doi: 10.1111/biom.12838>.

This package implements a comprehensive suite of experimental designs, both fixed (e.g., block, stratified, matched-pair, cluster, factorial, and mixed-integer-programming-based optimal designs) and sequential (including matching-on-the-fly designs, biased coin designs, and covariate-adaptive urn designs that assign treatment one subject at a time while maintaining covariate balance), for continuous, incidence, count, proportion, survival, and ordinal response types. For each design and response type combination, provides the corresponding inference procedures, including exact, asymptotic, distribution-free, and resampling-based (bootstrap, jackknife, and randomization) methods, so that estimation and testing are always matched to how the data were generated. An InferenceSuite facility runs all applicable inference procedures for a given design and response type at once and reports a single Cauchy-combined p-value summarizing their evidence. A built-in simulation framework supports power analysis and operating-characteristic studies across designs, response types, and inference procedures, with optional parallelization via mirai'. Missing covariate data is handled automatically via built-in imputation. Core numerical routines are implemented in C++ via Rcpp for speed on large designs and simulation studies. Machine-specific tuning for optimization is included.

Function that implements the Quantum Genetic Algorithm, first proposed by Han and Kim in 2000. This is an R implementation of the python application developed by Lahoz-Beltra (<https://github.com/ResearchCodesHub/QuantumGeneticAlgorithms>). Each optimization problem is represented as a maximization one, where each solution is a sequence of (qu)bits. Following the quantum paradigm, these qubits are in a superposition state: when measuring them, they collapse in a 0 or 1 state. After measurement, the fitness of the solution is calculated as in usual genetic algorithms. The evolution at each iteration is oriented by the application of two quantum gates to the amplitudes of the qubits: (1) a rotation gate (always); (2) a Pauli-X gate (optionally). The rotation is based on the theta angle values: higher values allow a quicker evolution, and lower values avoid local maxima. The Pauli-X gate is equivalent to the classical mutation operator and determines the swap between alfa and beta amplitudes of a given qubit. The package has been developed in such a way as to permit a complete separation between the engine, and the particular problem subject to combinatorial optimization.

An implementation of a collection of tools for exact Bayesian inference with discrete times series. This package contains functions that can be used for prediction, model selection, estimation, segmentation/change-point detection and other statistical tasks. Specifically, the functions provided can be used for the exact computation of the prior predictive likelihood of the data, for the identification of the a posteriori most likely (MAP) variable-memory Markov models, for calculating the exact posterior probabilities and the AIC and BIC scores of these models, for prediction with respect to log-loss and 0-1 loss and segmentation/change-point detection. Example data sets from finance, genetics, animal communication and meteorology are also provided. Detailed descriptions of the underlying theory and algorithms can be found in [Kontoyiannis et al. Bayesian Context Trees: Modelling and exact inference for discrete time series. Journal of the Royal Statistical Society: Series B (Statistical Methodology), April 2022. Available at: <doi:10.48550/arXiv.2007.14900> [stat.ME], July 2020] and [Lungu et al. Change-point Detection and Segmentation of Discrete Data using Bayesian Context Trees <doi:10.48550/arXiv.2203.04341> [stat.ME], March 2022].

This package provides statistical tests and algorithms for the detection of change points in time series and point processes - particularly for changes in the mean in time series and for changes in the rate and in the variance in point processes. References - Michael Messer, Marietta Kirchner, Julia Schiemann, Jochen Roeper, Ralph Neininger and Gaby Schneider (2014), A multiple filter test for the detection of rate changes in renewal processes with varying variance <doi:10.1214/14-AOAS782>. Stefan Albert, Michael Messer, Julia Schiemann, Jochen Roeper, Gaby Schneider (2017), Multi-scale detection of variance changes in renewal processes in the presence of rate change points <doi:10.1111/jtsa.12254>. Michael Messer, Kaue M. Costa, Jochen Roeper and Gaby Schneider (2017), Multi-scale detection of rate changes in spike trains with weak dependencies <doi:10.1007/s10827-016-0635-3>. Michael Messer, Stefan Albert and Gaby Schneider (2018), The multiple filter test for change point detection in time series <doi:10.1007/s00184-018-0672-1>. Michael Messer, Hendrik Backhaus, Albrecht Stroh and Gaby Schneider (2020) A multi-scale approach for testing and detecting peaks in time series <doi:10.1080/02331888.2020.1823980>.

Piecewise constant hazard functions are used to flexibly model survival distributions with non-proportional hazards and to simulate data from the specified distributions. A function to calculate weighted log-rank tests for the comparison of two hazard functions is included. Also, a function to calculate a test using the maximum of a set of test statistics from weighted log-rank tests (MaxCombo test) is provided. This test utilizes the asymptotic multivariate normal joint distribution of the separate test statistics. The correlation is estimated from the data. These methods are described in Ristl et al. (2021) <doi:10.1002/pst.2062>. Finally, a function is provided for the estimation and inferential statistics of various parameters that quantify the difference between two survival curves. Eligible parameters are differences in survival probabilities, log survival probabilities, complementary log log (cloglog) transformed survival probabilities, quantiles of the survival functions, log transformed quantiles, restricted mean survival times, as well as an average hazard ratio, the Cox model score statistic (logrank statistic), and the Cox-model hazard ratio. Adjustments for multiple testing and simultaneous confidence intervals are calculated using a multivariate normal approximation to the set of selected parameters.

The Algorithms for Quantitative Pedology (AQP) project was started in 2009 to organize a loosely-related set of concepts and source code on the topic of soil profile visualization, aggregation, and classification into this package (aqp). Over the past 8 years, the project has grown into a suite of related R packages that enhance and simplify the quantitative analysis of soil profile data. Central to the AQP project is a new vocabulary of specialized functions and data structures that can accommodate the inherent complexity of soil profile information; freeing the scientist to focus on ideas rather than boilerplate data processing tasks <doi:10.1016/j.cageo.2012.10.020>. These functions and data structures have been extensively tested and documented, applied to projects involving hundreds of thousands of soil profiles, and deeply integrated into widely used tools such as SoilWeb <https://casoilresource.lawr.ucdavis.edu/soilweb-apps>. Components of the AQP project (aqp, soilDB, sharpshootR, soilReports packages) serve an important role in routine data analysis within the USDA-NRCS Soil Science Division. The AQP suite of R packages offer a convenient platform for bridging the gap between pedometric theory and practice.

This package performs adjusted inferences based on model objects fitted, using maximum likelihood estimation, by the extreme value analysis packages eva <https://cran.r-project.org/package=eva>, evd <https://cran.r-project.org/package=evd>, evir <https://cran.r-project.org/package=evir>, extRemes <https://cran.r-project.org/package=extRemes>, fExtremes <https://cran.r-project.org/package=fExtremes>, ismev <https://cran.r-project.org/package=ismev>, mev <https://cran.r-project.org/package=mev>, POT <https://cran.r-project.org/package=POT> and texmex <https://cran.r-project.org/package=texmex>. Adjusted standard errors and an adjusted loglikelihood are provided, using the chandwich package <https://cran.r-project.org/package=chandwich> and the object-oriented features of the sandwich package <https://cran.r-project.org/package=sandwich>. The adjustment is based on a robust sandwich estimator of the parameter covariance matrix, based on the methodology in Chandler and Bate (2007) <doi:10.1093/biomet/asm015>. This can be used for cluster correlated data when interest lies in the parameters of the marginal distributions, or for performing inferences that are robust to certain types of model misspecification. Univariate extreme value models, including regression models, are supported.

The purpose of Early Warning Systems (EWS) is to detect accurately the occurrence of a crisis, which is represented by a binary variable which takes the value of one when the event occurs, and the value of zero otherwise. EWS are a toolbox for policymakers to prevent or attenuate the impact of economic downturns. Modern EWS are based on the econometric framework of Kauppi and Saikkonen (2008) <doi:10.1162/rest.90.4.777>. Specifically, this framework includes four dichotomous models, relying on a logit approach to model the relationship between yield spreads and future recessions, controlling for recession risk factors. These models can be estimated in a univariate or a balanced panel framework as in Candelon, Dumitrescu and Hurlin (2014) <doi:10.1016/j.ijforecast.2014.03.015>. This package provides both methods for estimating these models and a dataset covering 13 OECD countries over a period of 45 years. In addition, this package also provides methods for the analysis of the propagation mechanisms of an exogenous shock, as well as robust confidence intervals for these response functions using a block-bootstrap method as in Lajaunie (2021). This package constitutes a useful toolbox (data and functions) for scholars as well as policymakers.

Implementation of quantile frequency analysis (QFA) for time series based on trigonometric quantile regression and of spline quantile regression (SQR) for estimating the coefficients in linear quantile regression models as smooth functions of the quantile level. References: [1] Li, T.-H. (2012). Quantile periodograms, J. of the American Statistical Association, 107, 765â 776. <doi:10.1080/01621459.2012.682815> [2] Li, T.-H. (2014). Time Series with Mixed Spectra, CRC Press. <doi:10.1201/b15154> [3] Li, T.-H. (2025). Quantile Fourier transform, quantile series, and nonparametric estimation of quantile spectra, Communications in Statistics: Simulation and Computation, 1â 22. <doi:10.1080/03610918.2025.2509820> [4] Li, T.-H. (2025). Quantile-crossing spectrum and spline autoregression estimation, Statistical Inference for Stochastic Processes, 28, 20. <doi:10.1007/s11203-025-09336-7> [5] Li, T.-H. (2025). Spline autoregression method for estimation of quantile spectrum, J. of Computational and Graphical Statistics, 1-15. <doi:10.1080/10618600.2025.2549452> [6] Li, T.-H., and Megiddo, N. (2026). Spline quantile regression, J. of Statistical Theory and Practice, 20, 30. <doi:10.1007/s42519-026-00545-8> [7] Li, T.-H. (2026). Spline quantile regression with cubic and linear smoothing splines, <doi:10.48550/arXiv.2603.22408>.