This package provides functions for creating ensembles of optimal trees for regression, classification (Khan, Z., Gul, A., Perperoglou, A., Miftahuddin, M., Mahmoud, O., Adler, W., & Lausen, B. (2019). (2019) <doi:10.1007/s11634-019-00364-9>) and class membership probability estimation (Khan, Z, Gul, A, Mahmoud, O, Miftahuddin, M, Perperoglou, A, Adler, W & Lausen, B (2016) <doi:10.1007/978-3-319-25226-1_34>) are given. A few trees are selected from an initial set of trees grown by random forest for the ensemble on the basis of their individual and collective performance. Three different methods of tree selection for the case of classification are given. The prediction functions return estimates of the test responses and their class membership probabilities. Unexplained variations, error rates, confusion matrix, Brier scores, etc. are also returned for the test data.

Quantile-frequency analysis (QFA) of time series based on trigonometric quantile regression. Spline quantile regression (SQR) for regression coefficient estimation. References: [1] Li, T.-H. (2012) "Quantile periodograms," Journal 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. (2022) "Quantile Fourier transform, quantile series, and nonparametric estimation of quantile spectra," <doi:10.48550/arXiv.2211.05844>. [4] Li, T.-H. (2024) "Quantile crossing spectrum and spline autoregression estimation," <doi:10.48550/arXiv.2412.02513>. [5] Li, T.-H. (2024) "Spline autoregression method for estimation of quantile spectrum," <doi:10.48550/arXiv.2412.17163>. [6] Li, T.-H., and Megiddo, N. (2025) "Spline quantile regression," <doi:10.48550/arXiv.2501.03883>.

Support for fuzzy spatial objects, their operations, and fuzzy spatial inference models based on Spatial Plateau Algebra. It employs fuzzy set theory and fuzzy logic as foundation to deal with spatial fuzziness. It mainly implements underlying concepts defined in the following research papers: (i) "Spatial Plateau Algebra: An Executable Type System for Fuzzy Spatial Data Types" <doi:10.1109/FUZZ-IEEE.2018.8491565>; (ii) "A Systematic Approach to Creating Fuzzy Region Objects from Real Spatial Data Sets" <doi:10.1109/FUZZ-IEEE.2019.8858878>; (iii) "Spatial Data Types for Heterogeneously Structured Fuzzy Spatial Collections and Compositions" <doi:10.1109/FUZZ48607.2020.9177620>; (iv) "Fuzzy Inference on Fuzzy Spatial Objects (FIFUS) for Spatial Decision Support Systems" <doi:10.1109/FUZZ-IEEE.2017.8015707>; (v) "Evaluating Region Inference Methods by Using Fuzzy Spatial Inference Models" <doi:10.1109/FUZZ-IEEE55066.2022.9882658>.

Graph signals residing on the vertices of a graph have recently gained prominence in research in various fields. Many methodologies have been proposed to analyze graph signals by adapting classical signal processing tools. Recently, several notable graph signal decomposition methods have been proposed, which include graph Fourier decomposition based on graph Fourier transform, graph empirical mode decomposition, and statistical graph empirical mode decomposition. This package efficiently implements multiscale analysis applicable to various fields, and offers an effective tool for visualizing and decomposing graph signals. For the detailed methodology, see Ortega et al. (2018) <doi:10.1109/JPROC.2018.2820126>, Shuman et al. (2013) <doi:10.1109/MSP.2012.2235192>, Tremblay et al. (2014) <https://www.eurasip.org/Proceedings/Eusipco/Eusipco2014/HTML/papers/1569922141.pdf>, and Cho et al. (2024) "Statistical graph empirical mode decomposition by graph denoising and boundary treatment".

Tensor Composition Analysis (TCA) allows the deconvolution of two-dimensional data (features by observations) coming from a mixture of heterogeneous sources into a three-dimensional matrix of signals (features by observations by sources). The TCA framework further allows to test the features in the data for different statistical relations with an outcome of interest while modeling source-specific effects; particularly, it allows to look for statistical relations between source-specific signals and an outcome. For example, TCA can deconvolve bulk tissue-level DNA methylation data (methylation sites by individuals) into a three-dimensional tensor of cell-type-specific methylation levels for each individual (i.e. methylation sites by individuals by cell types) and it allows to detect cell-type-specific statistical relations (associations) with phenotypes. For more details see Rahmani et al. (2019) <DOI:10.1038/s41467-019-11052-9>.

This package provides a set of estimators for models and (robust) covariance matrices, and tests for panel data econometrics, including within/fixed effects, random effects, between, first-difference, nested random effects as well as instrumental-variable (IV) and Hausman-Taylor-style models, panel generalized method of moments (GMM) and general FGLS models, mean groups (MG), demeaned MG, and common correlated effects (CCEMG) and pooled (CCEP) estimators with common factors, variable coefficients and limited dependent variables models. Test functions include model specification, serial correlation, cross-sectional dependence, panel unit root and panel Granger (non-)causality. Typical references are general econometrics text books such as Baltagi (2021), Econometric Analysis of Panel Data (<doi:10.1007/978-3-030-53953-5>), Hsiao (2014), Analysis of Panel Data (<doi:10.1017/CBO9781139839327>), and Croissant and Millo (2018), Panel Data Econometrics with R (<doi:10.1002/9781119504641>).

Applies Beta Control Charts to defined values. The Beta Chart presents control limits based on the Beta probability distribution, making it suitable for monitoring fraction data from a Binomial distribution as a replacement for p-Charts. The Beta Chart has been applied in three real studies and compared with control limits from three different schemes. The comparative analysis showed that: (i) the Beta approximation to the Binomial distribution is more appropriate for values confined within the [0, 1] interval; and (ii) the proposed charts are more sensitive to the average run length (ARL) in both in-control and out-of-control process monitoring. Overall, the Beta Charts outperform the Shewhart control charts in monitoring fraction data. For more details, see à ngelo Márcio Oliveira Santâ Anna and Carla Schwengber ten Caten (2012) <doi:10.1016/j.eswa.2012.02.146>.

ANOVA and REML estimation of linear mixed models is implemented, once following Searle et al. (1991, ANOVA for unbalanced data), once making use of the lme4 package. The primary objective of this package is to perform a variance component analysis (VCA) according to CLSI EP05-A3 guideline "Evaluation of Precision of Quantitative Measurement Procedures" (2014). There are plotting methods for visualization of an experimental design, plotting random effects and residuals. For ANOVA type estimation two methods for computing ANOVA mean squares are implemented (SWEEP and quadratic forms). The covariance matrix of variance components can be derived, which is used in estimating confidence intervals. Linear hypotheses of fixed effects and LS means can be computed. LS means can be computed at specific values of covariables and with custom weighting schemes for factor variables. See ?VCA for a more comprehensive description of the features.

Implementation of the Dual Feature Reduction (DFR) approach for the Sparse Group Lasso (SGL) and the Adaptive Sparse Group Lasso (aSGL) (Feser and Evangelou (2024) <doi:10.48550/arXiv.2405.17094>). The DFR approach is a feature reduction approach that applies strong screening to reduce the feature space before optimisation, leading to speed-up improvements for fitting SGL (Simon et al. (2013) <doi:10.1080/10618600.2012.681250>) and aSGL (Mendez-Civieta et al. (2020) <doi:10.1007/s11634-020-00413-8> and Poignard (2020) <doi:10.1007/s10463-018-0692-7>) models. DFR is implemented using the Adaptive Three Operator Splitting (ATOS) (Pedregosa and Gidel (2018) <doi:10.48550/arXiv.1804.02339>) algorithm, with linear and logistic SGL models supported, both of which can be fit using k-fold cross-validation. Dense and sparse input matrices are supported.

This package provides a comprehensive set of tools for working with order statistics, including functions for simulating order statistics, censored samples (Type I and Type II), and record values from various continuous distributions. Additionally, it offers functions to compute moments (mean, variance, skewness, kurtosis) of order statistics for several continuous distributions. These tools assist researchers and statisticians in understanding and analyzing the properties of order statistics and related data. The methods and algorithms implemented in this package are based on several published works, including Ahsanullah et al (2013, ISBN:9789491216831), Arnold and Balakrishnan (2012, ISBN:1461236444), Harter and Balakrishnan (1996, ISBN:9780849394522), Balakrishnan and Sandhu (1995) <doi:10.1080/00031305.1995.10476150>, Genç (2012) <doi:10.1007/s00362-010-0320-y>, Makouei et al (2021) <doi:10.1016/j.cam.2021.113386> and Nagaraja (2013) <doi:10.1016/j.spl.2013.06.028>.

Network meta-analysis tools based on contrast-based approach using the multivariate meta-analysis and meta-regression models (Noma et al. (2025) <doi:10.1101/2025.09.15.25335823>). Comprehensive analysis tools for network meta-analysis and meta-regression (e.g., synthesis analysis, ranking analysis, and creating league table) are available through simple commands. For inconsistency assessment, the local and global inconsistency tests based on the Higgins design-by-treatment interaction model are available. In addition, the side-splitting methods and Jackson's random inconsistency model can be applied. Standard graphical tools for network meta-analysis, including network plots, ranked forest plots, and transitivity analyses, are also provided. For the synthesis analyses, the Noma-Hamura's improved REML (restricted maximum likelihood)-based methods (Noma et al. (2023) <doi:10.1002/jrsm.1652> <doi:10.1002/jrsm.1651>) are adopted as the default methods.

Computing package for Multidimensional Poverty Index (MPI) using Alkire-Foster method. Given N individuals, each person has D indicators of deprivation, the package compute MPI value to represent the degree of poverty in a population. The inputs are 1) an N by D matrix, which has the element (i,j) represents whether an individual i is deprived in an indicator j (1 is deprived and 0 is not deprived), and 2) the deprivation threshold. The main output is the MPI value, which has the range between zero and one. MPI value is approaching one if almost all people are deprived in all indicators, and it is approaching zero if almost no people are deprived in any indicator. Please see Alkire S., Chatterjee, M., Conconi, A., Seth, S. and Ana Vaz (2014) <doi:10.35648/20.500.12413/11781/ii039> for The Alkire-Foster methodology.

This package performs parametric and non-parametric estimation and simulation for multi-state discrete-time semi-Markov processes. For the parametric estimation, several discrete distributions are considered for the sojourn times: Uniform, Geometric, Poisson, Discrete Weibull and Negative Binomial. The non-parametric estimation concerns the sojourn time distributions, where no assumptions are done on the shape of distributions. Moreover, the estimation can be done on the basis of one or several sample paths, with or without censoring at the beginning or/and at the end of the sample paths. The implemented methods are described in Barbu, V.S., Limnios, N. (2008) <doi:10.1007/978-0-387-73173-5>, Barbu, V.S., Limnios, N. (2008) <doi:10.1080/10485250701261913> and Trevezas, S., Limnios, N. (2011) <doi:10.1080/10485252.2011.555543>. Estimation and simulation of discrete-time k-th order Markov chains are also considered.

This package provides an integrated analysis workflow for robust and reproducible analysis of mass spectrometry proteomics data for differential protein expression or differential enrichment. It requires tabular input (e.g. txt files) as generated by quantitative analysis softwares of raw mass spectrometry data, such as MaxQuant or IsobarQuant. Functions are provided for data preparation, filtering, variance normalization and imputation of missing values, as well as statistical testing of differentially enriched / expressed proteins. It also includes tools to check intermediate steps in the workflow, such as normalization and missing values imputation. Finally, visualization tools are provided to explore the results, including heatmap, volcano plot and barplot representations. For scientists with limited experience in R, the package also contains wrapper functions that entail the complete analysis workflow and generate a report. Even easier to use are the interactive Shiny apps that are provided by the package.

Paired mass distance (PMD) analysis proposed in Yu, Olkowicz and Pawliszyn (2018) <doi:10.1016/j.aca.2018.10.062> and PMD based reactomics analysis proposed in Yu and Petrick (2020) <doi:10.1038/s42004-020-00403-z> for gas/liquid chromatographyâ mass spectrometry (GC/LC-MS) based non-targeted analysis. PMD analysis including GlobalStd algorithm and structure/reaction directed analysis. GlobalStd algorithm could found independent peaks in m/z-retention time profiles based on retention time hierarchical cluster analysis and frequency analysis of paired mass distances within retention time groups. Structure directed analysis could be used to find potential relationship among those independent peaks in different retention time groups based on frequency of paired mass distances. Reactomics analysis could also be performed to build PMD network, assign sources and make biomarker reaction discovery. GUIs for PMD analysis is also included as shiny applications.

This package performs linear regression with respect to a data-driven convex loss function that is chosen to minimize the asymptotic covariance of the resulting M-estimator. The convex loss function is estimated in 5 steps: (1) form an initial OLS (ordinary least squares) or LAD (least absolute deviation) estimate of the regression coefficients; (2) use the resulting residuals to obtain a kernel estimator of the error density; (3) estimate the score function of the errors by differentiating the logarithm of the kernel density estimate; (4) compute the L2 projection of the estimated score function onto the set of decreasing functions; (5) take a negative antiderivative of the projected score function estimate. Newton's method (with Hessian modification) is then used to minimize the convex empirical risk function. Further details of the method are given in Feng et al. (2024) <doi:10.48550/arXiv.2403.16688>.

This package provides a likelihood-based hypothesis testing approach is implemented for assessing causal mediation. Described in Millstein, Chen, and Breton (2016), <DOI:10.1093/bioinformatics/btw135>, it could be used to test for mediation of a known causal association between a DNA variant, the instrumental variable', and a clinical outcome or phenotype by gene expression or DNA methylation, the potential mediator. Another example would be testing mediation of the effect of a drug on a clinical outcome by the molecular target. The hypothesis test generates a p-value or permutation-based FDR value with confidence intervals to quantify uncertainty in the causal inference. The outcome can be represented by either a continuous or binary variable, the potential mediator is continuous, and the instrumental variable can be continuous or binary and is not limited to a single variable but may be a design matrix representing multiple variables.

Collective matrix factorization (CMF) finds joint low-rank representations for a collection of matrices with shared row or column entities. This code learns a variational Bayesian approximation for CMF, supporting multiple likelihood potentials and missing data, while identifying both factors shared by multiple matrices and factors private for each matrix. For further details on the method see Klami et al. (2014) <arXiv:1312.5921>. The package can also be used to learn Bayesian canonical correlation analysis (CCA) and group factor analysis (GFA) models, both of which are special cases of CMF. This is likely to be useful for people looking for CCA and GFA solutions supporting missing data and non-Gaussian likelihoods. See Klami et al. (2013) <https://research.cs.aalto.fi/pml/online-papers/klami13a.pdf> and Virtanen et al. (2012) <http://proceedings.mlr.press/v22/virtanen12.html> for details on Bayesian CCA and GFA, respectively.

General P-splines are non-uniform B-splines penalized by a general difference penalty, proposed by Li and Cao (2022) <arXiv:2201.06808>. Constructible on arbitrary knots, they extend the standard P-splines of Eilers and Marx (1996) <doi:10.1214/ss/1038425655>. They are also related to the O-splines of O'Sullivan (1986) <doi:10.1214/ss/1177013525> via a sandwich formula that links a general difference penalty to a derivative penalty. The package includes routines for setting up and handling difference and derivative penalties. It also fits P-splines and O-splines to (x, y) data (optionally weighted) for a grid of smoothing parameter values in the automatic search intervals of Li and Cao (2023) <doi:10.1007/s11222-022-10178-z>. It aims to facilitate other packages to implement P-splines or O-splines as a smoothing tool in their model estimation framework.

This package implements the doubly robust distribution balancing weighting proposed by Katsumata (2024) <doi:10.1017/psrm.2024.23>, which improves the augmented inverse probability weighting (AIPW) by estimating propensity scores with estimating equations suitable for the pre-specified parameter of interest (e.g., the average treatment effects or the average treatment effects on the treated) and estimating outcome models with the estimated inverse probability weights. It also implements the covariate balancing propensity score proposed by Imai and Ratkovic (2014) <doi:10.1111/rssb.12027> and the entropy balancing weighting proposed by Hainmueller (2012) <doi:10.1093/pan/mpr025>, both of which use covariate balancing conditions in propensity score estimation. The point estimate of the parameter of interest and its uncertainty as well as coefficients for propensity score estimation and outcome regression are produced using the M-estimation. The same functions can be used to estimate average outcomes in missing outcome cases.

Index of Multiple Deprivation for UK nations at various geographical levels. In England, deprivation data is for Lower Layer Super Output Areas, Middle Layer Super Output Areas, Wards, and Local Authorities based on data from <https://www.gov.uk/government/statistics/english-indices-of-deprivation-2019>. In Wales, deprivation data is for Lower Layer Super Output Areas, Middle Layer Super Output Areas, Wards, and Local Authorities based on data from <https://gov.wales/welsh-index-multiple-deprivation-full-index-update-ranks-2019>. In Scotland, deprivation data is for Data Zones, Intermediate Zones, and Council Areas based on data from <https://simd.scot>. In Northern Ireland, deprivation data is for Super Output Areas and Local Government Districts based on data from <https://www.nisra.gov.uk/statistics/deprivation/northern-ireland-multiple-deprivation-measure-2017-nimdm2017>. The IMD package also provides the composite UK index developed by <https://github.com/mysociety/composite_uk_imd>.

Accumulated Local Effects (ALE) were initially developed as a model-agnostic approach for global explanations of the results of black-box machine learning algorithms. ALE has a key advantage over other approaches like partial dependency plots (PDP) and SHapley Additive exPlanations (SHAP): its values represent a clean functional decomposition of the model. As such, ALE values are not affected by the presence or absence of interactions among variables in a mode. Moreover, its computation is relatively rapid. This package reimplements the algorithms for calculating ALE data and develops highly interpretable visualizations for plotting these ALE values. It also extends the original ALE concept to add bootstrap-based confidence intervals and ALE-based statistics that can be used for statistical inference. For more details, see Okoli, Chitu. 2023. â Statistical Inference Using Machine Learning and Classical Techniques Based on Accumulated Local Effects (ALE).â arXiv. <doi:10.48550/arXiv.2310.09877>.

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) <https://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>.