Linear Mixed-Effects Models using 'Eigen' and S4

Fit linear and generalized linear mixed-effects models. The models and their components are represented using S4 classes and methods. The core computational algorithms are implemented using the 'Eigen' C++ library for numerical linear algebra and 'RcppEigen' "glue".

Estimated Marginal Means, aka Least-Squares Means

Obtain estimated marginal means (EMMs) for many linear, generalized linear, and mixed models. Compute contrasts or linear functions of EMMs, trends, and comparisons of slopes. Plots and other displays. Least-squares means are discussed, and the term "estimated marginal means" is suggested, in Searle, Speed, and Milliken (1980) Population marginal means in the linear model: An alternative to least squares means, The American Statistician 34(4), 216-221 .

Analysis of Factorial Experiments

Convenience functions for analyzing factorial experiments using ANOVA or mixed models. aov_ez(), aov_car(), and aov_4() allow specification of between, within (i.e., repeated-measures), or mixed (i.e., split-plot) ANOVAs for data in long format (i.e., one observation per row), automatically aggregating multiple observations per individual and cell of the design. mixed() fits mixed models using lme4::lmer() and computes p-values for all fixed effects using either Kenward-Roger or Satterthwaite approximation for degrees of freedom (LMM only), parametric bootstrap (LMMs and GLMMs), or likelihood ratio tests (LMMs and GLMMs). afex_plot() provides a high-level interface for interaction or one-way plots using ggplot2, combining raw data and model estimates. afex uses type 3 sums of squares as default (imitating commercial statistical software).

Response Time Distributions

Provides response time distributions (density/PDF, distribution function/CDF, quantile function, and random generation): (a) Ratcliff diffusion model (Ratcliff & McKoon, 2008, ) based on C code by Andreas and Jochen Voss and (b) linear ballistic accumulator (LBA; Brown & Heathcote, 2008, ) with different distributions underlying the drift rate.

Various Plotting Functions

Lots of plots, various labeling, axis and color scaling functions. The author/maintainer died in September 2023.

Generalized Linear Models with Clustering

Binomial and Poisson regression for clustered data, fixed and random effects with bootstrapping.

Utilities from 'Seminar fuer Statistik' ETH Zurich

Useful utilities ['goodies'] from Seminar fuer Statistik ETH Zurich, some of which were ported from S-plus in the 1990s. For graphics, have pretty (Log-scale) axes eaxis(), an enhanced Tukey-Anscombe plot, combining histogram and boxplot, 2d-residual plots, a 'tachoPlot()', pretty arrows, etc. For robustness, have a robust F test and robust range(). For system support, notably on Linux, provides 'Sys.*()' functions with more access to system and CPU information. Finally, miscellaneous utilities such as simple efficient prime numbers, integer codes, Duplicated(), toLatex.numeric() and is.whole().

The R to MOSEK Optimization Interface

This is a meta-package designed to support the installation of Rmosek (>= 6.0) and bring the optimization facilities of MOSEK (>= 6.0) to the R-language. The interface supports large-scale optimization of many kinds: Mixed-integer and continuous linear, second-order cone, exponential cone and power cone optimization, as well as continuous semidefinite optimization. Rmosek and the R-language are open-source projects. MOSEK is a proprietary product, but unrestricted trial and academic licenses are available.

Data Only: Algorithmic Complexity of Short Strings (Computed via Coding Theorem Method)

Data only package providing the algorithmic complexity of short strings, computed using the coding theorem method. For a given set of symbols in a string, all possible or a large number of random samples of Turing machines (TM) with a given number of states (e.g., 5) and number of symbols corresponding to the number of symbols in the strings were simulated until they reached a halting state or failed to end. This package contains data on 4.5 million strings from length 1 to 12 simulated on TMs with 2, 4, 5, 6, and 9 symbols. The complexity of the string corresponds to the distribution of the halting states of the TMs.

Bridge Sampling for Marginal Likelihoods and Bayes Factors

Provides functions for estimating marginal likelihoods, Bayes factors, posterior model probabilities, and normalizing constants in general, via different versions of bridge sampling (Meng & Wong, 1996, < http://www3.stat.sinica.edu.tw/statistica/j6n4/j6n43/j6n43.htm>). Gronau, Singmann, & Wagenmakers (2020) .