Classification and Regression Training

Misc functions for training and plotting classification and regression models.

Firth's Bias-Reduced Logistic Regression

Fit a logistic regression model using Firth's bias reduction method, equivalent to penalization of the log-likelihood by the Jeffreys prior. Confidence intervals for regression coefficients can be computed by penalized profile likelihood. Firth's method was proposed as ideal solution to the problem of separation in logistic regression, see Heinze and Schemper (2002) . If needed, the bias reduction can be turned off such that ordinary maximum likelihood logistic regression is obtained. Two new modifications of Firth's method, FLIC and FLAC, lead to unbiased predictions and are now available in the package as well, see Puhr et al (2017) .

An Introduction to Statistical Modeling of Extreme Values

Functions to support the computations carried out in `An Introduction to Statistical Modeling of Extreme Values' by Stuart Coles. The functions may be divided into the following groups; maxima/minima, order statistics, peaks over thresholds and point processes.

Core Functionality of the 'spatstat' Family

Functionality for data analysis and modelling of spatial data, mainly spatial point patterns, in the 'spatstat' family of packages. (Excludes analysis of spatial data on a linear network, which is covered by the separate package 'spatstat.linnet'.) Exploratory methods include quadrat counts, K-functions and their simulation envelopes, nearest neighbour distance and empty space statistics, Fry plots, pair correlation function, kernel smoothed intensity, relative risk estimation with cross-validated bandwidth selection, mark correlation functions, segregation indices, mark dependence diagnostics, and kernel estimates of covariate effects. Formal hypothesis tests of random pattern (chi-squared, Kolmogorov-Smirnov, Monte Carlo, Diggle-Cressie-Loosmore-Ford, Dao-Genton, two-stage Monte Carlo) and tests for covariate effects (Cox-Berman-Waller-Lawson, Kolmogorov-Smirnov, ANOVA) are also supported. Parametric models can be fitted to point pattern data using the functions ppm(), kppm(), slrm(), dppm() similar to glm(). Types of models include Poisson, Gibbs and Cox point processes, Neyman-Scott cluster processes, and determinantal point processes. Models may involve dependence on covariates, inter-point interaction, cluster formation and dependence on marks. Models are fitted by maximum likelihood, logistic regression, minimum contrast, and composite likelihood methods. A model can be fitted to a list of point patterns (replicated point pattern data) using the function mppm(). The model can include random effects and fixed effects depending on the experimental design, in addition to all the features listed above. Fitted point process models can be simulated, automatically. Formal hypothesis tests of a fitted model are supported (likelihood ratio test, analysis of deviance, Monte Carlo tests) along with basic tools for model selection (stepwise(), AIC()) and variable selection (sdr). Tools for validating the fitted model include simulation envelopes, residuals, residual plots and Q-Q plots, leverage and influence diagnostics, partial residuals, and added variable plots.

Multidimensional Item Response Theory

Analysis of discrete response data using unidimensional and multidimensional item analysis models under the Item Response Theory paradigm (Chalmers (2012) ). Exploratory and confirmatory item factor analysis models are estimated with quadrature (EM) or stochastic (MHRM) methods. Confirmatory bi-factor and two-tier models are available for modeling item testlets using dimension reduction EM algorithms, while multiple group analyses and mixed effects designs are included for detecting differential item, bundle, and test functioning, and for modeling item and person covariates. Finally, latent class models such as the DINA, DINO, multidimensional latent class, mixture IRT models, and zero-inflated response models are supported, as well as a wide family of probabilistic unfolding models.

Functional Data Analysis and Utilities for Statistical Computing

Routines for exploratory and descriptive analysis of functional data such as depth measurements, atypical curves detection, regression models, supervised classification, unsupervised classification and functional analysis of variance.

Weighting and Weighted Statistics

Provides a variety of functions for producing simple weighted statistics, such as weighted Pearson's correlations, partial correlations, Chi-Squared statistics, histograms, and t-tests as well as simple weighting graphics including weighted histograms, box plots, bar plots, and violin plots. Also includes software for quickly recoding survey data and plotting estimates from interaction terms in regressions (and multiply imputed regressions) both with and without weights and summarizing various types of regressions. Some portions of this package were assisted by AI-generated suggestions using OpenAI's GPT model, with human review and integration.

Causal Mediation Analysis

We implement parametric and non parametric mediation analysis. This package performs the methods and suggestions in Imai, Keele and Yamamoto (2010) , Imai, Keele and Tingley (2010) , Imai, Tingley and Yamamoto (2013) , and Imai and Yamamoto (2013) . In addition to the estimation of causal mediation effects, the software also allows researchers to conduct sensitivity analysis for certain parametric models.

Bayesian Applied Regression Modeling via Stan

Estimates previously compiled regression models using the 'rstan' package, which provides the R interface to the Stan C++ library for Bayesian estimation. Users specify models via the customary R syntax with a formula and data.frame plus some additional arguments for priors.

Bayesian Regression Models using 'Stan'

Fit Bayesian generalized (non-)linear multivariate multilevel models using 'Stan' for full Bayesian inference. A wide range of distributions and link functions are supported, allowing users to fit -- among others -- linear, robust linear, count data, survival, response times, ordinal, zero-inflated, hurdle, and even self-defined mixture models all in a multilevel context. Further modeling options include both theory-driven and data-driven non-linear terms, auto-correlation structures, censoring and truncation, meta-analytic standard errors, and quite a few more. In addition, all parameters of the response distribution can be predicted in order to perform distributional regression. Prior specifications are flexible and explicitly encourage users to apply prior distributions that actually reflect their prior knowledge. Models can easily be evaluated and compared using several methods assessing posterior or prior predictions. References: Bürkner (2017) ; Bürkner (2018) ; Bürkner (2021) ; Carpenter et al. (2017) .