Derivatives of the First-Passage Time Density and Cumulative Distribution Function, and Random Sampling from the (Truncated) First-Passage Time Distribution

First, we provide functions to calculate the partial derivative of the first-passage time diffusion probability density function (PDF) and cumulative distribution function (CDF) with respect to the first-passage time t (only for PDF), the upper barrier a, the drift rate v, the relative starting point w, the non-decision time t0, the inter-trial variability of the drift rate sv, the inter-trial variability of the rel. starting point sw, and the inter-trial variability of the non-decision time st0. In addition the PDF and CDF themselves are also provided. Most calculations are done on the logarithmic scale to make it more stable. Since the PDF, CDF, and their derivatives are represented as infinite series, we give the user the option to control the approximation errors with the argument 'precision'. For the numerical integration we used the C library cubature by Johnson, S. G. (2005-2013) < https://github.com/stevengj/cubature>. Numerical integration is required whenever sv, sw, and/or st0 is not zero. Note that numerical integration reduces speed of the computation and the precision cannot be guaranteed anymore. Therefore, whenever numerical integration is used an estimate of the approximation error is provided in the output list. Note: The large number of contributors (ctb) is due to copying a lot of C/C++ code chunks from the GNU Scientific Library (GSL). Second, we provide methods to sample from the first-passage time distribution with or without user-defined truncation from above. The first method is a new adaptive rejection sampler building on the works of Gilks and Wild (1992; ) and Hartmann and Klauer (in press). The second method is a rejection sampler provided by Drugowitsch (2016; ). The third method is an inverse transformation sampler. The fourth method is a "pseudo" adaptive rejection sampler that builds on the first method. For more details see the corresponding help files.

Efficient Serialization of R Objects

Streamlines and accelerates the process of saving and loading R objects, improving speed and compression compared to other methods. The package provides two compression formats: the 'qs2' format, which uses R serialization via the C API while optimizing compression and disk I/O, and the 'qdata' format, featuring custom serialization for slightly faster performance and better compression. Additionally, the 'qs2' format can be directly converted to the standard 'RDS' format, ensuring long-term compatibility with future versions of R.

Simulation and Resampling Methods for Epistemic Fuzzy Data

Random simulations of fuzzy numbers are still a challenging problem. The aim of this package is to provide the respective procedures to simulate fuzzy random variables, especially in the case of the piecewise linear fuzzy numbers (PLFNs, see Coroianua et al. (2013) for the further details). Additionally, the special resampling algorithms known as the epistemic bootstrap are provided (see Grzegorzewski and Romaniuk (2022) , Grzegorzewski and Romaniuk (2022) ) together with the functions to apply statistical tests and estimate various characteristics based on the epistemic bootstrap. The package also includes a real-life data set of epistemic fuzzy triangular numbers. The fuzzy numbers used in this package are consistent with the 'FuzzyNumbers' package.

PLINK 2 Binary (.pgen) Reader

A thin wrapper over PLINK 2's core libraries which provides an R interface for reading .pgen files. A minimal .pvar loader is also included. Chang et al. (2015) \doi{10.1186/s13742-015-0047-8}.

Bayesian Hierarchical Analysis of Cognitive Models of Choice

Fit Bayesian (hierarchical) cognitive models using a linear modeling language interface using particle Metropolis Markov chain Monte Carlo sampling with Gibbs steps. The diffusion decision model (DDM), linear ballistic accumulator model (LBA), racing diffusion model (RDM), and the lognormal race model (LNR) are supported. Additionally, users can specify their own likelihood function and/or choose for non-hierarchical estimation, as well as for a diagonal, blocked or full multivariate normal group-level distribution to test individual differences. Prior specification is facilitated through methods that visualize the (implied) prior. A wide range of plotting functions assist in assessing model convergence and posterior inference. Models can be easily evaluated using functions that plot posterior predictions or using relative model comparison metrics such as information criteria or Bayes factors. References: Stevenson et al. (2024) .

Shed Light on Black Box Machine Learning Models

Shed light on black box machine learning models by the help of model performance, variable importance, global surrogate models, ICE profiles, partial dependence (Friedman J. H. (2001) ), accumulated local effects (Apley D. W. (2016) ), further effects plots, interaction strength, and variable contribution breakdown (Gosiewska and Biecek (2019) ). All tools are implemented to work with case weights and allow for stratified analysis. Furthermore, multiple flashlights can be combined and analyzed together.

Datasets to Help Teach Statistics

In the spirit of Anscombe's quartet, this package includes datasets that demonstrate the importance of visualizing your data, the importance of not relying on statistical summary measures alone, and why additional assumptions about the data generating mechanism are needed when estimating causal effects. The package includes "Anscombe's Quartet" (Anscombe 1973) , D'Agostino McGowan & Barrett (2023) "Causal Quartet" , "Datasaurus Dozen" (Matejka & Fitzmaurice 2017), "Interaction Triptych" (Rohrer & Arslan 2021) , "Rashomon Quartet" (Biecek et al. 2023) , and Gelman "Variation and Heterogeneity Causal Quartets" (Gelman et al. 2023) .