There is no ophthalmic researcher who has not had headaches from the handling of visual acuity entries. Different notations, untidy entries. This shall now be a matter of the past. Eye makes it as easy as pie to work with VA data - easy cleaning, easy conversion between Snellen, logMAR, ETDRS letters, and qualitative visual acuity shall never pester you again. The eye package automates the pesky task to count number of patients and eyes, and can help to clean data with easy re-coding for right and left eyes. It also contains functions to help reshaping eye side specific variables between wide and long format. Visual acuity conversion is based on Schulze-Bonsel et al. (2006) <doi:10.1167/iovs.05-0981>, Gregori et al. (2010) <doi:10.1097/iae.0b013e3181d87e04>, Beck et al. (2003) <doi:10.1016/s0002-9394(02)01825-1> and Bach (2007) <http:michaelbach.de/sci/acuity.html>.

Create and learn Chain Event Graph (CEG) models using a Bayesian framework. It provides us with a Hierarchical Agglomerative algorithm to search the CEG model space. The package also includes several facilities for visualisations of the objects associated with a CEG. The CEG class can represent a range of relational data types, and supports arbitrary vertex, edge and graph attributes. A Chain Event Graph is a tree-based graphical model that provides a powerful graphical interface through which domain experts can easily translate a process into sequences of observed events using plain language. CEGs have been a useful class of graphical model especially to capture context-specific conditional independences. References: Collazo R, Gorgen C, Smith J. Chain Event Graph. CRC Press, ISBN 9781498729604, 2018 (forthcoming); and Barday LM, Collazo RA, Smith JQ, Thwaites PA, Nicholson AE. The Dynamic Chain Event Graph. Electronic Journal of Statistics, 9 (2) 2130-2169 <doi:10.1214/15-EJS1068>.

The optimal linear regression olr(), runs all the possible combinations of linear regression equations. The olr() returns the equation which has the greatest adjusted R-squared term or the greatest R-squared term based on the user's discretion. Essentially, the olr() returns the best fit equation out of all the possible equations. R-squared increases with the addition of an explanatory variable whether it is significant or not, thus this was developed to eliminate that conundrum. Adjusted R-squared is preferred to overcome this phenomenon, but each combination will still produce different results and this will return the best one. Complimentary functions are included which list all of the equations, all of the equations in ascending order, a function to give the user a specific model's summary, and the list of adjusted R-squared terms & R-squared terms. A Python version is available at: <https://pypi.org/project/olr/>.

This package provides statistical methods for auditing as implemented in JASP for Audit (Derks et al., 2021 <doi:10.21105/joss.02733>). First, the package makes it easy for an auditor to plan a statistical sample, select the sample from the population, and evaluate the misstatement in the sample compliant with international auditing standards. Second, the package provides statistical methods for auditing data, including tests of digit distributions and repeated values. Finally, the package includes methods for auditing algorithms on the aspect of fairness and bias. Next to classical statistical methodology, the package implements Bayesian equivalents of these methods whose statistical underpinnings are described in Derks et al. (2021) <doi:10.1111/ijau.12240>, Derks et al. (2024) <doi:10.2308/AJPT-2021-086>, Derks et al. (2022) <doi:10.31234/osf.io/8nf3e> Derks et al. (2024) <doi:10.31234/osf.io/tgq5z>, and Derks et al. (2025) <doi:10.31234/osf.io/b8tu2>.

Algorithms for solving selective k-means problem, which is defined as finding k rows in an m x n matrix such that the sum of each column minimal is minimized. In the scenario when m == n and each cell value in matrix is a valid distance metric, this is equivalent to a k-means problem. The selective k-means extends the k-means problem in the sense that it is possible to have m != n, often the case m < n which implies the search is limited within a small subset of rows. Also, the selective k-means extends the k-means problem in the sense that the instance in row set can be instance not seen in the column set, e.g., select 2 from 3 internet service provider (row) for 5 houses (column) such that minimize the overall cost (cell value) - overall cost is the sum of the column minimal of the selected 2 service provider.

Univariate and multivariate SQC tools that completes and increases the SQC techniques available in R. Apart from integrating different R packages devoted to SQC ('qcc','MSQC'), provides nonparametric tools that are highly useful when Gaussian assumption is not met. This package computes standard univariate control charts for individual measurements, X-bar', S', R', p', np', c', u', EWMA and CUSUM'. In addition, it includes functions to perform multivariate control charts such as Hotelling T2', MEWMA and MCUSUM'. As representative feature, multivariate nonparametric alternatives based on data depth are implemented in this package: r', Q and S control charts. In addition, Phase I and II control charts for functional data are included. This package also allows the estimation of the most complete set of capability indices from first to fourth generation, covering the nonparametric alternatives, and performing the corresponding capability analysis graphical outputs, including the process capability plots. See Flores et al. (2021) <doi:10.32614/RJ-2021-034>.

Introduction to some novel accurate hybrid methods of geostatistical and machine learning methods for spatial predictive modelling. It contains two commonly used geostatistical methods, two machine learning methods, four hybrid methods and two averaging methods. For each method, two functions are provided. One function is for assessing the predictive errors and accuracy of the method based on cross-validation. The other one is for generating spatial predictions using the method. For details please see: Li, J., Potter, A., Huang, Z., Daniell, J. J. and Heap, A. (2010) <https:www.ga.gov.au/metadata-gateway/metadata/record/gcat_71407> Li, J., Heap, A. D., Potter, A., Huang, Z. and Daniell, J. (2011) <doi:10.1016/j.csr.2011.05.015> Li, J., Heap, A. D., Potter, A. and Daniell, J. (2011) <doi:10.1016/j.envsoft.2011.07.004> Li, J., Potter, A., Huang, Z. and Heap, A. (2012) <https:www.ga.gov.au/metadata-gateway/metadata/record/74030>.

The standard Difference-in-Differences (DID) setup involves two periods and two groups -- a treated group and untreated group. Many applications of DID methods involve more than two periods and have individuals that are treated at different points in time. This package contains tools for computing average treatment effect parameters in Difference in Differences setups with more than two periods and with variation in treatment timing using the methods developed in Callaway and Sant'Anna (2021) <doi:10.1016/j.jeconom.2020.12.001>. The main parameters are group-time average treatment effects which are the average treatment effect for a particular group at a a particular time. These can be aggregated into a fewer number of treatment effect parameters, and the package deals with the cases where there is selective treatment timing, dynamic treatment effects, calendar time effects, or combinations of these. There are also functions for testing the Difference in Differences assumption, and plotting group-time average treatment effects.

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 models. 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 visualization of results.

We provide tools to estimate the individualized interval-valued dose rule (I2DR) that maximizes the expected beneficial clinical outcome for each individual and returns an optimal interval-valued dose, by using the jump Q-learning (JQL) method. The jump Q-learning method directly models the conditional mean of the response given the dose level and the baseline covariates via jump penalized least squares regression under the framework of Q learning. We develop a searching algorithm by dynamic programming in order to find the optimal I2DR with the time complexity O(n2) and spatial complexity O(n). To alleviate the effects of misspecification of the Q-function, a residual jump Q-learning is further proposed to estimate the optimal I2DR. The outcome of interest includes the best partition of the entire dosage of interest, the regression coefficients of each partition, and the value function under the estimated I2DR as well as the Wald-type confidence interval of value function constructed through the Bootstrap.

The main goal of this package is drawing the membership function of the fuzzy p-value which is defined as a fuzzy set on the unit interval for three following problems: (1) testing crisp hypotheses based on fuzzy data, see Filzmoser and Viertl (2004) <doi:10.1007/s001840300269>, (2) testing fuzzy hypotheses based on crisp data, see Parchami et al. (2010) <doi:10.1007/s00362-008-0133-4>, and (3) testing fuzzy hypotheses based on fuzzy data, see Parchami et al. (2012) <doi:10.1007/s00362-010-0353-2>. In all cases, the fuzziness of data or / and the fuzziness of the boundary of null fuzzy hypothesis transported via the p-value function and causes to produce the fuzzy p-value. If the p-value is fuzzy, it is more appropriate to consider a fuzzy significance level for the problem. Therefore, the comparison of the fuzzy p-value and the fuzzy significance level is evaluated by a fuzzy ranking method in this package.

This package provides methods and tools for (pre-)processing of metabolomics datasets (i.e. peak matrices), including filtering, normalisation, missing value imputation, scaling, and signal drift and batch effect correction methods. Filtering methods are based on: the fraction of missing values (across samples or features); Relative Standard Deviation (RSD) calculated from the Quality Control (QC) samples; the blank samples. Normalisation methods include Probabilistic Quotient Normalisation (PQN) and normalisation to total signal intensity. A unified user interface for several commonly used missing value imputation algorithms is also provided. Supported methods are: k-nearest neighbours (knn), random forests (rf), Bayesian PCA missing value estimator (bpca), mean or median value of the given feature and a constant small value. The generalised logarithm (glog) transformation algorithm is available to stabilise the variance across low and high intensity mass spectral features. Finally, this package provides an implementation of the Quality Control-Robust Spline Correction (QCRSC) algorithm for signal drift and batch effect correction of mass spectrometry-based datasets.

Incorporating node-level covariates for community detection has gained increasing attention these years. This package provides the function for implementing the novel community detection algorithm known as Network-Adjusted Covariates for Community Detection (NAC), which is designed to detect latent community structure in graphs with node-level information, i.e., covariates. This algorithm can handle models such as the degree-corrected stochastic block model (DCSBM) with covariates. NAC specifically addresses the discrepancy between the community structure inferred from the adjacency information and the community structure inferred from the covariates information. For more detailed information, please refer to the reference paper: Yaofang Hu and Wanjie Wang (2023) <arXiv:2306.15616>. In addition to NAC, this package includes several other existing community detection algorithms that are compared to NAC in the reference paper. These algorithms are Spectral Clustering On Ratios-of Eigenvectors (SCORE), network-based regularized spectral clustering (Net-based), covariate-based spectral clustering (Cov-based), covariate-assisted spectral clustering (CAclustering) and semidefinite programming (SDP).

Mortality rates are typically provided in an abridged format, i.e., by age groups 0, [1, 5], [5, 10]', [10, 15]', and so on. Some applications necessitate a detailed (single) age description. Despite the large number of proposed approaches in the literature, only a few methods ensure great performance at both younger and higher ages. For example, the 6-term Lagrange interpolation function is well suited to mortality interpolation at younger ages (with irregular intervals), but not at older ages. The Karup-King method, on the other hand, performs well at older ages but is not suitable for younger ones. Interested readers can find a full discussion of the two stated methods in the book Shryock, Siegel, and Associates (1993).The Q2q package combines the two methods to allow for the interpolation of mortality rates across all age groups. It begins by implementing each method independently, and then the resulting curves are linked using a 5-age averaged error between the two partial curves.

Calculate the optimal sample size allocation that produces the highest statistical power for experimental studies under a budget constraint, and perform power analyses with and without accommodating cost structures of sampling. The designs cover single-level and multilevel experiments detecting main, mediation, and moderation effects (and some combinations). The references for the proposed methods include: (1) Shen, Z., & Kelcey, B. (2020). Optimal sample allocation under unequal costs in cluster-randomized trials. Journal of Educational and Behavioral Statistics, 45(4): 446-474. <doi:10.3102/1076998620912418>. (2) Shen, Z., & Kelcey, B. (2022b). Optimal sample allocation for three-level multisite cluster-randomized trials. Journal of Research on Educational Effectiveness, 15 (1), 130-150. <doi:10.1080/19345747.2021.1953200>. (3) Shen, Z., & Kelcey, B. (2022a). Optimal sample allocation in multisite randomized trials. The Journal of Experimental Education. <doi:10.1080/00220973.2020.1830361>. (4) Champely, S. (2020). pwr: Basic functions for power analysis (Version 1.3-0) [Software]. Available from <https://CRAN.R-project.org/package=pwr>.

Implementations of the kernel measure of multi-sample dissimilarity (KMD) between several samples using K-nearest neighbor graphs and minimum spanning trees. The KMD measures the dissimilarity between multiple samples, based on the observations from them. It converges to the population quantity (depending on the kernel) which is between 0 and 1. A small value indicates the multiple samples are from the same distribution, and a large value indicates the corresponding distributions are different. The population quantity is 0 if and only if all distributions are the same, and 1 if and only if all distributions are mutually singular. The package also implements the tests based on KMD for H0: the M distributions are equal against H1: not all the distributions are equal. Both permutation test and asymptotic test are available. These tests are consistent against all alternatives where at least two samples have different distributions. For more details on KMD and the associated tests, see Huang, Z. and B. Sen (2022) <arXiv:2210.00634>.

The kernelSmoothing() function allows you to square and smooth geolocated data. It calculates a classical kernel smoothing (conservative) or a geographically weighted median. There are four major call modes of the function. The first call mode is kernelSmoothing(obs, epsg, cellsize, bandwidth) for a classical kernel smoothing and automatic grid. The second call mode is kernelSmoothing(obs, epsg, cellsize, bandwidth, quantiles) for a geographically weighted median and automatic grid. The third call mode is kernelSmoothing(obs, epsg, cellsize, bandwidth, centroids) for a classical kernel smoothing and user grid. The fourth call mode is kernelSmoothing(obs, epsg, cellsize, bandwidth, quantiles, centroids) for a geographically weighted median and user grid. Geographically weighted summary statistics : a framework for localised exploratory data analysis, C.Brunsdon & al., in Computers, Environment and Urban Systems C.Brunsdon & al. (2002) <doi:10.1016/S0198-9715(01)00009-6>, Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, Third Edition, Diggle, pp. 83-86, (2003) <doi:10.1080/13658816.2014.937718>.

Developed for computing the probability density function, computing the cumulative distribution function, computing the quantile function, random generation, drawing q-q plot, and estimating the parameters of 24 G-family of statistical distributions via the maximum product spacing approach introduced in <https://www.jstor.org/stable/2345411>. The set of families contains: beta G distribution, beta exponential G distribution, beta extended G distribution, exponentiated G distribution, exponentiated exponential Poisson G distribution, exponentiated generalized G distribution, exponentiated Kumaraswamy G distribution, gamma type I G distribution, gamma type II G distribution, gamma uniform G distribution, gamma-X generated of log-logistic family of G distribution, gamma-X family of modified beta exponential G distribution, geometric exponential Poisson G distribution, generalized beta G distribution, generalized transmuted G distribution, Kumaraswamy G distribution, log gamma type I G distribution, log gamma type II G distribution, Marshall Olkin G distribution, Marshall Olkin Kumaraswamy G distribution, modified beta G distribution, odd log-logistic G distribution, truncated-exponential skew-symmetric G distribution, and Weibull G distribution.

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>.

An implementation of the Similarity-First Search algorithm (SFS), a combinatorial algorithm which can be used to solve the seriation problem and to recognize some structured weighted graphs. The SFS algorithm represents a generalization to weighted graphs of the graph search algorithm Lexicographic Breadth-First Search (Lex-BFS), a variant of Breadth-First Search. The SFS algorithm reduces to Lex-BFS when applied to binary matrices (or, equivalently, unweighted graphs). Hence this library can be also considered for Lex-BFS applications such as recognition of graph classes like chordal or unit interval graphs. In fact, the SFS seriation algorithm implemented in this package is a multisweep algorithm, which consists in repeating a finite number of SFS iterations (at most n sweeps for a matrix of size n). If the data matrix has a Robinsonian structure, then the ranking returned by the multistep SFS algorithm is a Robinson ordering of the input matrix. Otherwise the algorithm can be used as a heuristic to return a ranking partially satisfying the Robinson property.

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 a framework for analysing state sequences with probabilistic suffix trees (PST), the construction that stores variable length Markov chains (VLMC). Besides functions for learning and optimizing VLMC models, the PST library includes many additional tools to analyse sequence data with these models: visualization tools, functions for sequence prediction and artificial sequences generation, as well as for context and pattern mining. The package is specifically adapted to the field of social sciences by allowing to learn VLMC models from sets of individual sequences possibly containing missing values, and by accounting for case weights. The library also allows to compute probabilistic divergence between two models, and to fit segmented VLMC, where sub-models fitted to distinct strata of the learning sample are stored in a single PST. This software results from research work executed within the framework of the Swiss National Centre of Competence in Research LIVES, which is financed by the Swiss National Science Foundation. The authors are grateful to the Swiss National Science Foundation for its financial support.

Basic infrastructure and several algorithms for 1d-4d bin packing problem. This package provides a set of c-level classes and solvers for 1d-4d bin packing problem, and an r-level solver for 4d bin packing problem, which is a wrapper over the c-level 4d bin packing problem solver. The 4d bin packing problem solver aims to solve bin packing problem, a.k.a container loading problem, with an additional constraint on weight. Given a set of rectangular-shaped items, and a set of rectangular-shaped bins with weight limit, the solver looks for an orthogonal packing solution such that minimizes the number of bins and maximize volume utilization. Each rectangular-shaped item i = 1, .. , n is characterized by length l_i, depth d_i, height h_i, and weight w_i, and each rectangular-shaped bin j = 1, .. , m is specified similarly by length l_j, depth d_j, height h_j, and weight limit w_j. The item can be rotated into any orthogonal direction, and no further restrictions implied.

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>.