This package provides sampling and density functions for matrix variate normal, t, and inverted t distributions; ML estimation for matrix variate normal and t distributions using the EM algorithm, including some restrictions on the parameters; and classification by linear and quadratic discriminant analysis for matrix variate normal and t distributions described in Thompson et al. (2019) <doi:10.1080/10618600.2019.1696208>. Performs clustering with matrix variate normal and t mixture models.

Kernel-based methods are powerful methods for integrating heterogeneous types of data. mixKernel aims at providing methods to combine kernel for unsupervised exploratory analysis. Different solutions are provided to compute a meta-kernel, in a consensus way or in a way that best preserves the original topology of the data. mixKernel also integrates kernel PCA to visualize similarities between samples in a non linear space and from the multiple source point of view <doi:10.1093/bioinformatics/btx682>. A method to select (as well as funtions to display) important variables is also provided <doi:10.1093/nargab/lqac014>.

Various functions are provided to estimate parametric mixture models (with Gaussian, t, Laplace, log-concave distributions, etc.) and non-parametric mixture models. The package performs hypothesis tests and addresses label switching issues in mixture models. The package also allows for parameter estimation in mixture of regressions, proportion-varying mixture of regressions, and robust mixture of regressions.

Mixedpower uses pilotdata and a linear mixed model fitted with lme4 to simulate new data sets. Power is computed separate for every effect in the model output as the relation of significant simulations to all simulations. More conservative simulations as a protection against a bias in the pilotdata are available as well as methods for plotting the results.

In longitudinal studies, the same subjects are measured repeatedly over time, leading to correlations among the repeated measurements. Properly accounting for the intra-cluster correlations in the presence of data heterogeneity and long tailed distributions of the disease phenotype is challenging, especially in the context of high dimensional regressions. In this package, we developed a Bayesian quantile mixed effects model with spike- and -slab priors to dissect important gene - environment interactions under longitudinal genomics studies. An efficient Gibbs sampler has been developed to facilitate fast computation. The Markov chain Monte Carlo algorithms of the proposed and alternative methods are efficiently implemented in C++'. The development of this software package and the associated statistical methods have been partially supported by an Innovative Research Award from Johnson Cancer Research Center, Kansas State University.

The estimation of the parameters in mixed Poisson models.

Developed to deal with multi-locus genotype data, this package is especially designed for those panel which include different type of markers. Basic genetic parameters like allele frequency, genotype frequency, heterozygosity and Hardy-Weinberg test of mixed genetic data can be obtained. In addition, a new test for mutual independence which is compatible for mixed genetic data is developed in this package.

This package provides supplemental functions for the mixRasch package (Willse, 2014), <https://cran.r-project.org/package=mixRasch/mixRasch.pdf> including a plotting function to compare item parameters for multiple class models and a function that provides average theta values for each class in a mixture model.

This package provides functions for testing randomness for a univariate time series with arbitrary distribution (discrete, continuous, mixture of both types) and for testing independence between random variables with arbitrary distributions. The test statistics are based on the multilinear empirical copula and multipliers are used to compute P-values. The test of independence between random variables appeared in Genest, Nešlehová, Rémillard & Murphy (2019) and the test of randomness appeared in Nasri (2022).

This package provides a function to perform bias diagnostics on linear mixed models fitted with lmer() from the lme4 package. Implements permutation tests for assessing the bias of fixed effects, as described in Karl and Zimmerman (2021) <doi:10.1016/j.jspi.2020.06.004>. Karl and Zimmerman (2020) <doi:10.17632/tmynggddfm.1> provide R code for implementing the test using mvglmmRank output. Development of this package was assisted by GPT o1-preview for code structure and documentation.

Fits mixed Poisson regression models (Poisson-Inverse Gaussian or Negative-Binomial) on data sets with response variables being count data. The models can have varying precision parameter, where a linear regression structure (through a link function) is assumed to hold on the precision parameter. The Expectation-Maximization algorithm for both these models (Poisson Inverse Gaussian and Negative Binomial) is an important contribution of this package. Another important feature of this package is the set of functions to perform global and local influence analysis. See Barreto-Souza and Simas (2016) <doi:10.1007/s11222-015-9601-6> for further details.

Implementations of various robust and flexible model-based clustering methods for data sets with missing values at random. Two main models are: Multivariate Contaminated Normal Mixture (MCNM, Tong and Tortora, 2022, <doi:10.1007/s11634-021-00476-1>) and Multivariate Generalized Hyperbolic Mixture (MGHM, Wei et al., 2019, <doi:10.1016/j.csda.2018.08.016>). Mixtures via some special or limiting cases of the multivariate generalized hyperbolic distribution are also included: Normal-Inverse Gaussian, Symmetric Normal-Inverse Gaussian, Skew-Cauchy, Cauchy, Skew-t, Student's t, Normal, Symmetric Generalized Hyperbolic, Hyperbolic Univariate Marginals, Hyperbolic, and Symmetric Hyperbolic.

Response Surface Designs (RSDs) involving factors not all at same levels are called Mixed Level RSDs (or Asymmetric RSDs). In many practical situations, RSDs with asymmetric levels will be more suitable as it explores more regions in the design space. (J.S. Mehta and M.N. Das (1968) <doi:10.2307/1267046>. "Asymmetric rotatable designs and orthogonal transformations").This package contains function named ATORDs_I() for generating asymmetric third order rotatable designs (ATORDs) based on third order designs given by Das and Narasimham (1962). Function ATORDs_II() generates asymmetric third order rotatable designs developed using t-design of unequal set sizes, which are smaller in size as compared to design generated by function ATORDs_I(). In general, third order rotatable designs can be classified into two classes viz., designs that are suitable for sequential experimentation and designs for non-sequential experimentation. The sequential experimentation approach involves conducting the trials step by step whereas, in the non-sequential experimentation approach, the entire runs are executed in one go (M. N. Das and V. Narasimham (1962) <doi:10.1214/AOMS/1177704374>. "Construction of Rotatable Designs through Balanced Incomplete Block Designs"). ATORDs_I() and ATORDs_II() functions generate non-sequential asymmetric third order designs. Function named SeqTORD() generates symmetric sequential third order design in blocks and also gives G-efficiency of the given design. Function named Asymseq() generates asymmetric sequential third order designs in blocks (M. Hemavathi, Eldho Varghese, Shashi Shekhar and Seema Jaggi (2020) <doi:10.1080/02664763.2020.1864817>. "Sequential asymmetric third order rotatable designs (SATORDs)"). In response surface design, situations may arise in which some of the factors are qualitative in nature (Jyoti Divecha and Bharat Tarapara (2017) <doi:10.1080/08982112.2016.1217338>. "Small, balanced, efficient, optimal, and near rotatable response surface designs for factorial experiments asymmetrical in some quantitative, qualitative factors"). The Function named QualRSD() generates second order design with qualitative factors along with their D-efficiency and G-efficiency. The function named RotatabilityQ() calculates a measure of rotatability (measure Q, 0 <= Q <= 1) given by Draper and Pukelshiem(1990) for given a design based on a second order model, (Norman R. Draper and Friedrich Pukelsheim(1990) <doi:10.1080/00401706.1990.10484635>. "Another look at rotatability").