Assists in the plotting and functional smoothing of traits measured over time and the extraction of features from these traits, implementing the SET (Smoothing and Extraction of Traits) method described in Brien et al. (2020) Plant Methods, 16. Smoothing of growth trends for individual plants using natural cubic smoothing splines or P-splines is available for removing transient effects and segmented smoothing is available to deal with discontinuities in growth trends. There are graphical tools for assessing the adequacy of trait smoothing, both when using this and other packages, such as those that fit nonlinear growth models. A range of per-unit (plant, pot, plot) growth traits or features can be extracted from the data, including single time points, interval growth rates and other growth statistics, such as maximum growth or days to maximum growth. The package also has tools adapted to inputting data from high-throughput phenotyping facilities, such from a Lemna-Tec Scananalyzer 3D (see <https://www.youtube.com/watch?v=MRAF_mAEa7E/> for more information). The package growthPheno can also be installed from <http://chris.brien.name/rpackages/>.

The differences in the RNA types being sequenced have an impact on the resulting sequencing profiles. mRNA-seq data is enriched with reads derived from exons, while GRO-, nucRNA- and chrRNA-seq demonstrate a substantial broader coverage of both exonic and intronic regions. The presence of intronic reads in GRO-seq type of data makes it possible to use it to computationally identify and quantify all de novo continuous regions of transcription distributed across the genome. This type of data, however, is more challenging to interpret and less common practice compared to mRNA-seq. One of the challenges for primary transcript detection concerns the simultaneous transcription of closely spaced genes, which needs to be properly divided into individually transcribed units. The R package transcriptR combines RNA-seq data with ChIP-seq data of histone modifications that mark active Transcription Start Sites (TSSs), such as, H3K4me3 or H3K9/14Ac to overcome this challenge. The advantage of this approach over the use of, for example, gene annotations is that this approach is data driven and therefore able to deal also with novel and case specific events.

Enhancing cross-language compatibility within the RStudio environment and supporting seamless language understanding, the deepRstudio package leverages the power of the DeepL API (see <https://www.deepl.com/docs-api>) to enable seamless, fast, accurate, and affordable translation of code comments, documents, and text. This package offers the ability to translate selected text into English (EN), as well as from English into various languages, namely Japanese (JA), Chinese (ZH), Spanish (ES), French (FR), Russian (RU), Portuguese (PT), and Indonesian (ID). With much of the text being written in English, the emphasis is on compatibility from English. It is also designed for developers working on multilingual projects and data analysts collaborating with international teams, simplifying the translation process and making code more accessible and comprehensible to people with diverse language backgrounds. This package uses the rstudioapi package and DeepL API, and is simply implemented, executed from addins or via shortcuts on RStudio'. With just a few steps, content can be translated between supported languages, promoting better collaboration and expanding the global reach of work. The functionality of this package works only on RStudio using rstudioapi'.

Conduct numerous exploratory analyses in an instant with a point-and-click interface. With one simple command, this tool launches a Shiny App on the local machine. Drag and drop variables in a data set to categorize them as possible independent, dependent, moderating, or mediating variables. Then run dozens (or hundreds) of analyses instantly to uncover any statistically significant relationships among variables. Any relationship thus uncovered should be tested in follow-up studies. This tool is designed only to facilitate exploratory analyses and should NEVER be used for p-hacking. Many of the functions used in this package are previous versions of functions in the R Packages kim and ezr'. Selected References: Chang et al. (2021) <https://CRAN.R-project.org/package=shiny>. Dowle et al. (2021) <https://CRAN.R-project.org/package=data.table>. Kim (2023) <https://jinkim.science/docs/kim.pdf>. Kim (2021) <doi:10.5281/zenodo.4619237>. Kim (2020) <https://CRAN.R-project.org/package=ezr>. Simmons et al. (2011) <doi:10.1177/0956797611417632> Tingley et al. (2019) <https://CRAN.R-project.org/package=mediation>. Wickham et al. (2020) <https://CRAN.R-project.org/package=ggplot2>.

Calculates the chilling and heat accumulation for studies of the temperate fruit trees. The models in this package are: Utah (Richardson et al., 1974, ISSN:0018-5345), Positive Chill Units - PCU (Linsley-Noaks et al., 1995, ISSN:1017-0316), GDH-A - Growing Degree Hours by Anderson et al.(1986, ISSN:0567-7572), GDH-R - Growing Degree Hours by Richardson et al.(1975, ISSN:0018-5345), North Carolina (Shaltout e Unrath, 1983, ISSN:0003-1062), Landsberg Model (Landsberg, 1974, ISSN:0305-7364), Q10 Model (Bidabe, 1967, ISSN:0031-9368), Jones Model (Jones et al., 2013 <DOI:10.1111/j.1438-8677.2012.00590.x>), Low-Chill Model (Gilreath and Buchanan, 1981, ISSN:0003-1062), Model for Cherry "Sweetheart" (Guak and Nielsen, 2013 <DOI:10.1007/s13580-013-0140-9>), Model for apple "Gala" (Guak and Nielsen, 2013 <DOI:10.1007/s13580-013-0140-9>), Taiwan Model (Lu et al., 2012 <DOI:10.17660/ActaHortic.2012.962.35>), Dynamic Model (Fishman et al., 1987, ISSN:0022-5193) adapted from the function Dynamic_Model() of the chillR package (Luedeling, 2018), Unified Model (Chuine et al., 2016 <DOI:10.1111/gcb.13383>) and Heat Restriction model.

The heterogeneity of spatial data presenting a finite number of categories can be measured via computation of spatial entropy. Functions are available for the computation of the main entropy and spatial entropy measures in the literature. They include the traditional version of Shannon's entropy (Shannon, 1948 <doi:10.1002/j.1538-7305.1948.tb01338.x>), Batty's spatial entropy (Batty, 1974 <doi:10.1111/j.1538-4632.1974.tb01014.x>), O'Neill's entropy (O'Neill et al., 1998 <doi:10.1007/BF00162741>), Li and Reynolds contagion index (Li and Reynolds, 1993 <doi:10.1007/BF00125347>), Karlstrom and Ceccato's entropy (Karlstrom and Ceccato, 2002 <https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-61351>), Leibovici's entropy (Leibovici, 2009 <doi:10.1007/978-3-642-03832-7_24>), Parresol and Edwards entropy (Parresol and Edwards, 2014 <doi:10.3390/e16041842>) and Altieri's entropy (Altieri et al., 2018, <doi:10.1007/s10651-017-0383-1>). Full references for all measures can be found under the topic SpatEntropy'. The package is able to work with lattice and point data. The updated version works with the updated spatstat package (>= 3.0-2).

This package provides a random forest variant block forest ('BlockForest') tailored to the prediction of binary, survival and continuous outcomes using block-structured covariate data, for example, clinical covariates plus measurements of a certain omics data type or multi-omics data, that is, data for which measurements of different types of omics data and/or clinical data for each patient exist. Examples of different omics data types include gene expression measurements, mutation data and copy number variation measurements. Block forest are presented in Hornung & Wright (2019). The package includes four other random forest variants for multi-omics data: RandomBlock', BlockVarSel', VarProb', and SplitWeights'. These were also considered in Hornung & Wright (2019), but performed worse than block forest in their comparison study based on 20 real multi-omics data sets. Therefore, we recommend to use block forest ('BlockForest') in applications. The other random forest variants can, however, be consulted for academic purposes, for example, in the context of further methodological developments. Reference: Hornung, R. & Wright, M. N. (2019) Block Forests: random forests for blocks of clinical and omics covariate data. BMC Bioinformatics 20:358. <doi:10.1186/s12859-019-2942-y>.

When causal quantities are not identifiable from the observed data, it still may be possible to bound these quantities using the observed data. We outline a class of problems for which the derivation of tight bounds is always a linear programming problem and can therefore, at least theoretically, be solved using a symbolic linear optimizer. We extend and generalize the approach of Balke and Pearl (1994) <doi:10.1016/B978-1-55860-332-5.50011-0> and we provide a user friendly graphical interface for setting up such problems via directed acyclic graphs (DAG), which only allow for problems within this class to be depicted. The user can then define linear constraints to further refine their assumptions to meet their specific problem, and then specify a causal query using a text interface. The program converts this user defined DAG, query, and constraints, and returns tight bounds. The bounds can be converted to R functions to evaluate them for specific datasets, and to latex code for publication. The methods and proofs of tightness and validity of the bounds are described in a paper by Sachs, Jonzon, Gabriel, and Sjölander (2022) <doi:10.1080/10618600.2022.2071905>.

Computes various entropies of given time series. This is the initial version that includes ApEn() and SampEn() functions for calculating approximate entropy and sample entropy. Approximate entropy was proposed by S.M. Pincus in "Approximate entropy as a measure of system complexity", Proceedings of the National Academy of Sciences of the United States of America, 88, 2297-2301 (March 1991). Sample entropy was proposed by J. S. Richman and J. R. Moorman in "Physiological time-series analysis using approximate entropy and sample entropy", American Journal of Physiology, Heart and Circulatory Physiology, 278, 2039-2049 (June 2000). This package also contains FastApEn() and FastSampEn() functions for calculating fast approximate entropy and fast sample entropy. These are newly designed very fast algorithms, resulting from the modification of the original algorithms. The calculated values of these entropies are not the same as the original ones, but the entropy trend of the analyzed time series determines equally reliably. Their main advantage is their speed, which is up to a thousand times higher. A scientific article describing their properties has been submitted to The Journal of Supercomputing and in present time it is waiting for the acceptance.

Allows for building drug response models using screening data between bulk RNA-Seq and a drug response metric and two additional tools for biomarker discovery that have been developed by the Huang Laboratory at University of Minnesota. There are 3 main functions within this package. (1) calcPhenotype is used to build drug response models on RNA-Seq data and impute them on any other RNA-Seq dataset given to the model. (2) GLDS is used to calculate the general level of drug sensitivity, which can improve biomarker discovery. (3) IDWAS can take the results from calcPhenotype and link the imputed response back to available genomic (mutation and CNV alterations) to identify biomarkers. Each of these functions comes from a paper from the Huang research laboratory. Below gives the relevant paper for each function. calcPhenotype - Geeleher et al, Clinical drug response can be predicted using baseline gene expression levels and in vitro drug sensitivity in cell lines. GLDS - Geeleher et al, Cancer biomarker discovery is improved by accounting for variability in general levels of drug sensitivity in pre-clinical models. IDWAS - Geeleher et al, Discovering novel pharmacogenomic biomarkers by imputing drug response in cancer patients from large genomics studies.

Early generation breeding trials are to be conducted in multiple environments where it may not be possible to replicate all the lines in each environment due to scarcity of resources. For such situations, partially replicated (p-Rep) designs have wide application potential as only a proportion of the test lines are replicated at each environment. A collection of several utility functions related to p-Rep designs have been developed. Here, the package contains six functions for a complete stepwise analytical study of these designs. Five functions pRep1(), pRep2(), pRep3(), pRep4() and pRep5(), are used to generate five new series of p-Rep designs and also compute average variance factors and canonical efficiency factors of generated designs. A fourth function NCEV() is used to generate incidence matrix (N), information matrix (C), canonical efficiency factor (E) and average variance factor (V). This function is general in nature and can be used for studying the characterization properties of any block design. A construction procedure for p-Rep designs was given by Williams et al.(2011) <doi:10.1002/bimj.201000102> which was tedious and time consuming. Here, in this package, five different methods have been given to generate p-Rep designs easily.

Offers a convenient pipeline to test and compare various missing data imputation algorithms on simulated and real data. These include simpler methods, such as mean and median imputation and random replacement, but also include more sophisticated algorithms already implemented in popular R packages, such as mi', described by Su et al. (2011) <doi:10.18637/jss.v045.i02>; mice', described by van Buuren and Groothuis-Oudshoorn (2011) <doi:10.18637/jss.v045.i03>; missForest', described by Stekhoven and Buhlmann (2012) <doi:10.1093/bioinformatics/btr597>; missMDA', described by Josse and Husson (2016) <doi:10.18637/jss.v070.i01>; and pcaMethods', described by Stacklies et al. (2007) <doi:10.1093/bioinformatics/btm069>. The central assumption behind missCompare is that structurally different datasets (e.g. larger datasets with a large number of correlated variables vs. smaller datasets with non correlated variables) will benefit differently from different missing data imputation algorithms. missCompare takes measurements of your dataset and sets up a sandbox to try a curated list of standard and sophisticated missing data imputation algorithms and compares them assuming custom missingness patterns. missCompare will also impute your real-life dataset for you after the selection of the best performing algorithm in the simulations. The package also provides various post-imputation diagnostics and visualizations to help you assess imputation performance.

This package provides a function collection to extract metadata, sectioned text and study characteristics from scientific articles in NISO-JATS format. Articles in PDF format can be converted to NISO-JATS with the Content ExtRactor and MINEr ('CERMINE', <https://github.com/CeON/CERMINE>). For convenience, two functions bundle the extraction heuristics: JATSdecoder() converts NISO-JATS'-tagged XML files to a structured list with elements title, author, journal, history, DOI', abstract, sectioned text and reference list. study.character() extracts multiple study characteristics like number of included studies, statistical methods used, alpha error, power, statistical results, correction method for multiple testing, software used. The function get.stats() extracts all statistical results from text and recomputes p-values for many standard test statistics. It performs a consistency check of the reported with the recalculated p-values. An estimation of the involved sample size is performed based on textual reports within the abstract and the reported degrees of freedom within statistical results. In addition, the package contains some useful functions to process text (text2sentences(), text2num(), ngram(), strsplit2(), grep2()). See Böschen, I. (2021) <doi:10.1007/s11192-021-04162-z> Böschen, I. (2021) <doi:10.1038/s41598-021-98782-3>, Böschen, I. (2023) <doi:10.1038/s41598-022-27085-y>, and Böschen, I. (2024) <doi:10.48550/arXiv.2408.07948>.

Estimate the abundance of cell clones from the distribution of lengths of DNA fragments (as created by sonication, whence `sonicLength'). The algorithm in "Estimating abundances of retroviral insertion sites from DNA fragment length data" by Berry CC, Gillet NA, Melamed A, Gormley N, Bangham CR, Bushman FD. Bioinformatics; 2012 Mar 15;28(6):755-62 is implemented. The experimental setting and estimation details are described in detail there. Briefly, integration of new DNA in a host genome (due to retroviral infection or gene therapy) can be tracked using DNA sequencing, potentially allowing characterization of the abundance of individual cell clones bearing distinct integration sites. The locations of integration sites can be determined by fragmenting the host DNA (via sonication or fragmentase), breaking the newly integrated DNA at a known sequence, amplifying the fragments containing both host and integrated DNA, sequencing those amplicons, then mapping the host sequences to positions on the reference genome. The relative number of fragments containing a given position in the host genome estimates the relative abundance of cells hosting the corresponding integration site, but that number is not available and the count of amplicons per fragment varies widely. However, the expected number of distinct fragment lengths is a function of the abundance of cells hosting an integration site at a given position and a certain nuisance parameter. The algorithm implicitly estimates that function to estimate the relative abundance.

Application of the Partitioning-Around-Medoids (PAM) clustering algorithm described in Schubert, E. and Rousseeuw, P.J.: "Fast and eager k-medoids clustering: O(k) runtime improvement of the PAM, CLARA, and CLARANS algorithms." Information Systems, vol. 101, p. 101804, (2021). <doi:10.1016/j.is.2021.101804>. It uses a binary format for storing and retrieval of matrices developed for the jmatrix package but the functionality of jmatrix is included here, so you do not need to install it. Also, it is used by package scellpam', so if you have installed it, you do not need to install this package. PAM can be applied to sets of data whose dissimilarity matrix can be very big. It has been tested with up to 100.000 points. It does this with the help of the code developed for other package, jmatrix', which allows the matrix not to be loaded in R memory (which would force it to be of double type) but it gets from disk, which allows using float (or even smaller data types). Moreover, the dissimilarity matrix is calculated in parallel if the computer has several cores so it can open many threads. The initial part of the PAM algorithm can be done with the BUILD or LAB algorithms; the BUILD algorithm has been implemented in parallel. The optimization phase implements the FastPAM1 algorithm, also in parallel. Finally, calculation of silhouette is available and also implemented in parallel.

Data on multiple individuals through time are often sampled at times that differ between persons. Irregular observation times can severely complicate the statistical analysis of the data. The broken stick model approximates each subjectâ s trajectory by one or more connected line segments. The times at which segments connect (breakpoints) are identical for all subjects and under control of the user. A well-fitting broken stick model effectively transforms individual measurements made at irregular times into regular trajectories with common observation times. Specification of the model requires three variables: time, measurement and subject. The model is a special case of the linear mixed model, with time as a linear B-spline and subject as the grouping factor. The main assumptions are: subjects are exchangeable, trajectories between consecutive breakpoints are straight, random effects follow a multivariate normal distribution, and unobserved data are missing at random. The package contains functions for fitting the broken stick model to data, for predicting curves in new data and for plotting broken stick estimates. The package supports two optimization methods, and includes options to structure the variance-covariance matrix of the random effects. The analyst may use the software to smooth growth curves by a series of connected straight lines, to align irregularly observed curves to a common time grid, to create synthetic curves at a user-specified set of breakpoints, to estimate the time-to-time correlation matrix and to predict future observations. See <doi:10.18637/jss.v106.i07> for additional documentation on background, methodology and applications.

Especially when cross-sectional data are observational, effects of treatment selection bias and confounding are best revealed by using Nonparametric and Unsupervised methods to "Design" the analysis of the given data ...rather than the collection of "designed data". Specifically, the "effect-size distribution" that best quantifies a potentially causal relationship between a numeric y-Outcome variable and either a binary t-Treatment or continuous e-Exposure variable needs to consist of BLOCKS of relatively well-matched experimental units (e.g. patients) that have the most similar X-confounder characteristics. Since our NU Learning approach will form BLOCKS by "clustering" experimental units in confounder X-space, the implicit statistical model for learning is One-Way ANOVA. Within Block measures of effect-size are then either [a] LOCAL Treatment Differences (LTDs) between Within-Cluster y-Outcome Means ("new" minus "control") when treatment choice is Binary or else [b] LOCAL Rank Correlations (LRCs) when the e-Exposure variable is numeric with (hopefully many) more than two levels. An Instrumental Variable (IV) method is also provided so that Local Average y-Outcomes (LAOs) within BLOCKS may also contribute information for effect-size inferences when X-Covariates are assumed to influence Treatment choice or Exposure level but otherwise have no direct effects on y-Outcomes. Finally, a "Most-Like-Me" function provides histograms of effect-size distributions to aid Doctor-Patient (or Researcher-Society) communications about Heterogeneous Outcomes. Obenchain and Young (2013) <doi:10.1080/15598608.2013.772821>; Obenchain, Young and Krstic (2019) <doi:10.1016/j.yrtph.2019.104418>.

Function gmcmtx0() computes a more reliable (general) correlation matrix. Since causal paths from data are important for all sciences, the package provides many sophisticated functions. causeSummBlk() and causeSum2Blk() give easy-to-interpret causal paths. Let Z denote control variables and compare two flipped kernel regressions: X=f(Y, Z)+e1 and Y=g(X, Z)+e2. Our criterion Cr1 says that if |e1*Y|>|e2*X| then variation in X is more "exogenous or independent" than in Y, and the causal path is X to Y. Criterion Cr2 requires |e2|<|e1|. These inequalities between many absolute values are quantified by four orders of stochastic dominance. Our third criterion Cr3, for the causal path X to Y, requires new generalized partial correlations to satisfy |r*(x|y,z)|< |r*(y|x,z)|. The function parcorVec() reports generalized partials between the first variable and all others. The package provides several R functions including get0outliers() for outlier detection, bigfp() for numerical integration by the trapezoidal rule, stochdom2() for stochastic dominance, pillar3D() for 3D charts, canonRho() for generalized canonical correlations, depMeas() measures nonlinear dependence, and causeSummary(mtx) reports summary of causal paths among matrix columns. Portfolio selection: decileVote(), momentVote(), dif4mtx(), exactSdMtx() can rank several stocks. Functions whose names begin with boot provide bootstrap statistical inference, including a new bootGcRsq() test for "Granger-causality" allowing nonlinear relations. A new tool for evaluation of out-of-sample portfolio performance is outOFsamp(). Panel data implementation is now included. See eight vignettes of the package for theory, examples, and usage tips. See Vinod (2019) \doi10.1080/03610918.2015.1122048.

This package provides a collection of functions for directional data (including massive data, with millions of observations) analysis. Hypothesis testing, discriminant and regression analysis, MLE of distributions and more are included. The standard textbook for such data is the "Directional Statistics" by Mardia, K. V. and Jupp, P. E. (2000). Other references include: a) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (2018). "An elliptically symmetric angular Gaussian distribution". Statistics and Computing 28(3): 689-697. <doi:10.1007/s11222-017-9756-4>. b) Tsagris M. and Alenazi A. (2019). "Comparison of discriminant analysis methods on the sphere". Communications in Statistics: Case Studies, Data Analysis and Applications 5(4):467--491. <doi:10.1080/23737484.2019.1684854>. c) Paine J.P., Preston S.P., Tsagris M. and Wood A.T.A. (2020). "Spherical regression models with general covariates and anisotropic errors". Statistics and Computing 30(1): 153--165. <doi:10.1007/s11222-019-09872-2>. d) Tsagris M. and Alenazi A. (2024). "An investigation of hypothesis testing procedures for circular and spherical mean vectors". Communications in Statistics-Simulation and Computation, 53(3): 1387--1408. <doi:10.1080/03610918.2022.2045499>. e) Yu Z. and Huang X. (2024). A new parameterization for elliptically symmetric angular Gaussian distributions of arbitrary dimension. Electronic Journal of Statistics, 18(1): 301--334. <doi:10.1214/23-EJS2210>. f) Tsagris M. and Alzeley O. (2024). "Circular and spherical projected Cauchy distributions: A Novel Framework for Circular and Directional Data Modeling". Australian & New Zealand Journal of Statistics (Accepted for publication). <doi:10.1111/anzs.12434>. g) Tsagris M., Papastamoulis P. and Kato S. (2024). "Directional data analysis: spherical Cauchy or Poisson kernel-based distribution". Statistics and Computing (Accepted for publication). <doi:10.48550/arXiv.2409.03292>.

This package provides methods for the interpolation of large spatial datasets. This package uses a basis function approach that provides a surface fitting method that can approximate standard spatial data models. Using a large number of basis functions allows for estimates that can come close to interpolating the observations (a spatial model with a small nugget variance.) Moreover, the covariance model for this method can approximate the Matern covariance family but also allows for a multi-resolution model and supports efficient computation of the profile likelihood for estimating covariance parameters. This is accomplished through compactly supported basis functions and a Markov random field model for the basis coefficients. These features lead to sparse matrices for the computations and this package makes of the R spam package for sparse linear algebra. An extension of this version over previous ones ( < 5.4 ) is the support for different geometries besides a rectangular domain. The Markov random field approach combined with a basis function representation makes the implementation of different geometries simple where only a few specific R functions need to be added with most of the computation and evaluation done by generic routines that have been tuned to be efficient. One benefit of this package's model/approach is the facility to do unconditional and conditional simulation of the field for large numbers of arbitrary points. There is also the flexibility for estimating non-stationary covariances and also the case when the observations are a linear combination (e.g. an integral) of the spatial process. Included are generic methods for prediction, standard errors for prediction, plotting of the estimated surface and conditional and unconditional simulation. See the LatticeKrigRPackage GitHub repository for a vignette of this package. Development of this package was supported in part by the National Science Foundation Grant 1417857 and the National Center for Atmospheric Research.

Illustrates the concepts developed in Sarkar and Rashid (2019, ISSN:0025-5742) <http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwiH4deL3q3xAhWX73MBHR_wDaYQFnoECAUQAw&url=https%3A%2F%2Fwww.indianmathsociety.org.in%2Fmathstudent-part-2-2019.pdf&usg=AOvVaw3SY--3T6UAWUnH5-Nj6bSc>. This package helps a user guess four things (mean, MD, scaled MSD, and RMSD) before they get the SD. 1) The package displays the Empirical Cumulative Distribution Function (ECDF) of the given data. The user must choose the value of the mean by equating the areas of two colored (blue and green) regions. The package gives feedback to improve the choice until it is correct. Alternatively, the reader may continue with a different guess for the center (not necessarily the mean). 2) The user chooses the values of the Mean Deviation (MD) based on the ECDF of the deviations by equating the areas of two newly colored (blue and green) regions, with feedback from the package until the user guesses correctly. 3) The user chooses the Scaled Mean Squared Deviation (MSD) based on the ECDF of the scaled square deviations by equating the areas of two newly colored (blue and green) regions, with feedback from the package until the user guesses correctly. 4) The user chooses the Root Mean Squared Deviation (RMSD) by ensuring that its intersection with the ECDF of the deviations is at the same height as the intersection between the scaled MSD and the ECDF of the scaled squared deviations. Additionally, the intersection of two blue lines (the green dot) should fall on the vertical line at the maximum deviation. 5) Finally, if the mean is chosen correctly, only then the user can view the population SD (the same as the RMSD) and the sample SD (sqrt(n/(n-1))*RMSD) by clicking the respective buttons. If the mean is chosen incorrectly, the user is asked to correct it.

The aim of the R package treebalance is to provide functions for the computation of a large variety of (im)balance indices for rooted trees. The package accompanies the book Tree balance indices: a comprehensive survey by M. Fischer, L. Herbst, S. Kersting, L. Kuehn and K. Wicke (2023) <ISBN: 978-3-031-39799-8>, <doi:10.1007/978-3-031-39800-1>, which gives a precise definition for the terms balance index and imbalance index (Chapter 4) and provides an overview of the terminology in this manual (Chapter 2). For further information on (im)balance indices, see also Fischer et al. (2021) <https://treebalance.wordpress.com>. Considering both established and new (im)balance indices, treebalance provides (among others) functions for calculating the following 18 established indices and index families: the average leaf depth, the B1 and B2 index, the Colijn-Plazzotta rank, the normal, corrected, quadratic and equal weights Colless index, the family of Colless-like indices, the family of I-based indices, the Rogers J index, the Furnas rank, the rooted quartet index, the s-shape statistic, the Sackin index, the symmetry nodes index, the total cophenetic index and the variance of leaf depths. Additionally, we include 9 tree shape statistics that satisfy the definition of an (im)balance index but have not been thoroughly analyzed in terms of tree balance in the literature yet. These are: the total internal path length, the total path length, the average vertex depth, the maximum width, the modified maximum difference in widths, the maximum depth, the maximum width over maximum depth, the stairs1 and the stairs2 index. As input, most functions of treebalance require a rooted (phylogenetic) tree in phylo format (as introduced in ape 1.9 in November 2006). phylo is used to store (phylogenetic) trees with no vertices of out-degree one. For further information on the format we kindly refer the reader to E. Paradis (2012) <http://ape-package.ird.fr/misc/FormatTreeR_24Oct2012.pdf>.

An eikosogram (ancient Greek for probability picture) divides the unit square into rectangular regions whose areas, sides, and widths, represent various probabilities associated with the values of one or more categorical variates. Rectangle areas are joint probabilities, widths are always marginal (though possibly joint margins, i.e. marginal joint distributions of two or more variates), and heights of rectangles are always conditional probabilities. Eikosograms embed the rules of probability and are useful for introducing elementary probability theory, including axioms, marginal, conditional, and joint probabilities, and their relationships (including Bayes theorem as a completely trivial consequence). They are markedly superior to Venn diagrams for this purpose, especially in distinguishing probabilistic independence, mutually exclusive events, coincident events, and associations. They also are useful for identifying and understanding conditional independence structure. As data analysis tools, eikosograms display categorical data in a manner similar to Mosaic plots, especially when only two variates are involved (the only case in which they are essentially identical, though eikosograms purposely disallow spacing between rectangles). Unlike Mosaic plots, eikosograms do not alternate axes as each new categorical variate (beyond two) is introduced. Instead, only one categorical variate, designated the "response", presents on the vertical axis and all others, designated the "conditioning" variates, appear on the horizontal. In this way, conditional probability appears only as height and marginal probabilities as widths. The eikosogram is therefore much better suited to a response model analysis (e.g. logistic model) than is a Mosaic plot. Mosaic plots are better suited to log-linear style modelling as in discrete multivariate analysis. Of course, eikosograms are also suited to discrete multivariate analysis with each variate in turn appearing as the response. This makes it better suited than Mosaic plots to discrete graphical models based on conditional independence graphs (i.e. "Bayesian Networks" or "BayesNets"). The eikosogram and its superiority to Venn diagrams in teaching probability is described in W.H. Cherry and R.W. Oldford (2003) <https://math.uwaterloo.ca/~rwoldfor/papers/eikosograms/paper.pdf>, its value in exploring conditional independence structure and relation to graphical and log-linear models is described in R.W. Oldford (2003) <https://math.uwaterloo.ca/~rwoldfor/papers/eikosograms/independence/paper.pdf>, and a number of problems, puzzles, and paradoxes that are easily explained with eikosograms are given in R.W. Oldford (2003) <https://math.uwaterloo.ca/~rwoldfor/papers/eikosograms/examples/paper.pdf>.

The following several classes of frailty models using a penalized likelihood estimation on the hazard function but also a parametric estimation can be fit using this R package: 1) A shared frailty model (with gamma or log-normal frailty distribution) and Cox proportional hazard model. Clustered and recurrent survival times can be studied. 2) Additive frailty models for proportional hazard models with two correlated random effects (intercept random effect with random slope). 3) Nested frailty models for hierarchically clustered data (with 2 levels of clustering) by including two iid gamma random effects. 4) Joint frailty models in the context of the joint modelling for recurrent events with terminal event for clustered data or not. A joint frailty model for two semi-competing risks and clustered data is also proposed. 5) Joint general frailty models in the context of the joint modelling for recurrent events with terminal event data with two independent frailty terms. 6) Joint Nested frailty models in the context of the joint modelling for recurrent events with terminal event, for hierarchically clustered data (with two levels of clustering) by including two iid gamma random effects. 7) Multivariate joint frailty models for two types of recurrent events and a terminal event. 8) Joint models for longitudinal data and a terminal event. 9) Trivariate joint models for longitudinal data, recurrent events and a terminal event. 10) Joint frailty models for the validation of surrogate endpoints in multiple randomized clinical trials with failure-time and/or longitudinal endpoints with the possibility to use a mediation analysis model. 11) Conditional and Marginal two-part joint models for longitudinal semicontinuous data and a terminal event. 12) Joint frailty-copula models for the validation of surrogate endpoints in multiple randomized clinical trials with failure-time endpoints. 13) Generalized shared and joint frailty models for recurrent and terminal events. Proportional hazards (PH), additive hazard (AH), proportional odds (PO) and probit models are available in a fully parametric framework. For PH and AH models, it is possible to consider type-varying coefficients and flexible semiparametric hazard function. Prediction values are available (for a terminal event or for a new recurrent event). Left-truncated (not for Joint model), right-censored data, interval-censored data (only for Cox proportional hazard and shared frailty model) and strata are allowed. In each model, the random effects have the gamma or normal distribution. Now, you can also consider time-varying covariates effects in Cox, shared and joint frailty models (1-5). The package includes concordance measures for Cox proportional hazards models and for shared frailty models. 14) Competing Joint Frailty Model: A single type of recurrent event and two terminal events. 15) functions to compute power and sample size for four Gamma-frailty-based designs: Shared Frailty Models, Nested Frailty Models, Joint Frailty Models, and General Joint Frailty Models. Each design includes two primary functions: a power function, which computes power given a specified sample size; and a sample size function, which computes the required sample size to achieve a specified power. Moreover, the package can be used with its shiny application, in a local mode or by following the link below.