We introduce factor models designed to jointly analyze high-dimensional count data from multiple studies by extracting study-shared and specified factors. Our factor models account for heterogeneous noises and overdispersion among counts with augmented covariates. We propose an efficient and speedy variational estimation procedure for estimating model parameters, along with a novel criterion for selecting the optimal number of factors and the rank of regression coefficient matrix. More details can be referred to Liu et al. (2024) <doi:10.48550/arXiv.2402.15071>.

The detection of worrying approximate collinearity in a multiple linear regression model is a problem addressed in all existing statistical packages. However, we have detected deficits regarding to the incorrect treatment of qualitative independent variables and the role of the intercept of the model. The objective of this package is to correct these deficits. In this package will be available detection and treatment techniques traditionally used as the recently developed.

A set of tools to permute multisets without loops or hash tables and to generate integer partitions. The permutation functions are based on C code from Aaron Williams. Cool-lex order is similar to colexicographical order. The algorithm is described in Williams, A. Loopless Generation of Multiset Permutations by Prefix Shifts. SODA 2009, Symposium on Discrete Algorithms, New York, United States. The permutation code is distributed without restrictions. The code for stable and efficient computation of multinomial coefficients comes from Dave Barber. The code can be download from <http://tamivox.org/dave/multinomial/index.html> and is distributed without conditions. The package also generates the integer partitions of a positive, non-zero integer n. The C++ code for this is based on Python code from Jerome Kelleher which can be found here <https://jeromekelleher.net/category/combinatorics.html>. The C++ code and Python code are distributed without conditions.