Direct MLE for Multivariate Normal Mixture Distributions

Multivariate Normal (i.e. Gaussian) Mixture Models (S3) Classes. Fitting models to data using 'MLE' (maximum likelihood estimation) for multivariate normal mixtures via smart parametrization using the 'LDL' (Cholesky) decomposition, see McLachlan and Peel (2000, ISBN:9780471006268), Celeux and Govaert (1995) .

Biodemography Functions

The Biodem package provides a number of functions for Biodemographic analysis.

Data Sets for Copula Modeling

Data sets used for copula modeling in addition to those in the R package 'copula'. These include a random subsample from the US National Education Longitudinal Study (NELS) of 1988 and nursing home data from Wisconsin.

The Ranking Project: Visualizations for Comparing Populations

Functions to generate plots and tables for comparing independently- sampled populations. Companion package to "A Primer on Visualizations for Comparing Populations, Including the Issue of Overlapping Confidence Intervals" by Wright, Klein, and Wieczorek (2019) and "A Joint Confidence Region for an Overall Ranking of Populations" by Klein, Wright, and Wieczorek (2020) .

Fast Library for Number Theory

An R interface to 'FLINT' < https://flintlib.org/>, a C library for number theory. 'FLINT' extends GNU 'MPFR' < https://www.mpfr.org/> and GNU 'MP' < https://gmplib.org/> with support for operations on standard rings (the integers, the integers modulo n, finite fields, the rational, p-adic, real, and complex numbers) as well as matrices and polynomials over rings. 'FLINT' implements midpoint-radius interval arithmetic, also known as ball arithmetic, in the real and complex numbers, enabling computation in arbitrary precision with rigorous propagation of rounding and other errors; see Johansson (2017) . Finally, 'FLINT' provides ball arithmetic implementations of many special mathematical functions, with high coverage of reference works such as the NIST Digital Library of Mathematical Functions < https://dlmf.nist.gov/>. The R interface defines S4 classes, generic functions, and methods for representation and basic operations as well as plain R functions mirroring and vectorizing entry points in the C library.

Estimation in Optimal Adaptive Two-Stage Designs

Methods to evaluate the performance characteristics of various point and interval estimators for optimal adaptive two-stage designs as described in Meis et al. (2024) . Specifically, this package is written to work with trial designs created by the 'adoptr' package (Kunzmann et al. (2021) ; Pilz et al. (2021) )). Apart from the a priori evaluation of performance characteristics, this package also allows for the evaluation of the implemented estimators on real datasets, and it implements methods to calculate p-values.

Big Data Statistical Analysis for High-Dimensional Models

Big data statistical analysis for high-dimensional models is made possible by modifying lasso.proj() in 'hdi' package by replacing its nodewise-regression with sparse precision matrix computation using 'BigQUIC'.

A Toolbox for Writing Pretty Papers and Reports

A toolbox for writing 'knitr', 'Sweave' or other 'LaTeX'- or 'markdown'-based reports and to prettify the output of various estimated models.

Estimation of Order of Mixture Distributions

Methods for estimating the order of a mixture model. The approaches considered are based on the following papers (extensive list of references is available in the vignette): 1. Dacunha-Castelle, Didier, and Elisabeth Gassiat. The estimation of the order of a mixture model. Bernoulli 3, no. 3 (1997): 279-299. < https://projecteuclid.org/download/pdf_1/euclid.bj/1177334456>. 2. Woo, Mi-Ja, and T. N. Sriram. Robust estimation of mixture complexity. Journal of the American Statistical Association 101, no. 476 (2006): 1475-1486. . 3. Woo, Mi-Ja, and T. N. Sriram. Robust estimation of mixture complexity for count data. Computational statistics & data analysis 51, no. 9 (2007): 4379-4392. . 4. Umashanger, T., and T. N. Sriram. L2E estimation of mixture complexity for count data. Computational statistics & data analysis 53, no. 12 (2009): 4243-4254. . 5. Karlis, Dimitris, and Evdokia Xekalaki. On testing for the number of components in a mixed Poisson model. Annals of the Institute of Statistical Mathematics 51, no. 1 (1999): 149-162. . 6. Cutler, Adele, and Olga I. Cordero-Brana. Minimum Hellinger Distance Estimation for Finite Mixture Models. Journal of the American Statistical Association 91, no. 436 (1996): 1716-1723. . A number of datasets are included. 1. accidents, from Karlis, Dimitris, and Evdokia Xekalaki. On testing for the number of components in a mixed Poisson model. Annals of the Institute of Statistical Mathematics 51, no. 1 (1999): 149-162. . 2. acidity, from Sybil L. Crawford, Morris H. DeGroot, Joseph B. Kadane & Mitchell J. Small (1992) Modeling Lake-Chemistry Distributions: Approximate Bayesian Methods for Estimating a Finite-Mixture Model, Technometrics, 34:4, 441-453. . 3. children, from Thisted, R. A. (1988). Elements of statistical computing: Numerical computation (Vol. 1). CRC Press. 4. faithful, from R package "datasets"; Azzalini, A. and Bowman, A. W. (1990). A look at some data on the Old Faithful geyser. Applied Statistics, 39, 357--365. < https://www.jstor.org/stable/2347385>. 5. shakespeare, from Efron, Bradley, and Ronald Thisted. "Estimating the number of unseen species: How many words did Shakespeare know?." Biometrika 63.3 (1976): 435-447. .

Generalized Additive Latent and Mixed Models

Estimates generalized additive latent and mixed models using maximum marginal likelihood, as defined in Sorensen et al. (2023) , which is an extension of Rabe-Hesketh and Skrondal (2004)'s unifying framework for multilevel latent variable modeling . Efficient computation is done using sparse matrix methods, Laplace approximation, and automatic differentiation. The framework includes generalized multilevel models with heteroscedastic residuals, mixed response types, factor loadings, smoothing splines, crossed random effects, and combinations thereof. Syntax for model formulation is close to 'lme4' (Bates et al. (2015) ) and 'PLmixed' (Rockwood and Jeon (2019) ).