ﻻ يوجد ملخص باللغة العربية
The R package RegressionFactory provides expander functions for constructing the high-dimensional gradient vector and Hessian matrix of the log-likelihood function for generalized linear models (GLMs), from the lower-dimensional base-distribution derivatives. The software follows a modular implementation using the chain rule of derivatives. Such modularity offers a clear separation of case-specific components (base distribution functional form and link functions) from common steps (e.g., matrix algebra operations needed for expansion) in calculating log-likelihood derivatives. In doing so, RegressionFactory offers several advantages: 1) It provides a fast and convenient method for constructing log-likelihood and its derivatives by requiring only the low-dimensional, base-distribution derivatives, 2) The accompanying definiteness-invariance theorem allows researchers to reason about the negative-definiteness of the log-likelihood Hessian in the much lower-dimensional space of the base distributions, 3) The factorized, abstract view of regression suggests opportunities to generate novel regression models, and 4) Computational techniques for performance optimization can be developed generically in the abstract framework and be readily applicable across all the specific regression instances. We expect RegressionFactory to facilitate research and development on optimization and sampling techniques for GLM log-likelihoods as well as construction of composite models from GLM lego blocks, such as Hierarchical Bayesian models.
Due to the ease of modern data collection, applied statisticians often have access to a large set of covariates that they wish to relate to some observed outcome. Generalized linear models (GLMs) offer a particularly interpretable framework for such
We introduce and illustrate through numerical examples the R package texttt{SIHR} which handles the statistical inference for (1) linear and quadratic functionals in the high-dimensional linear regression and (2) linear functional in the high-dimensi
This paper introduces the R package sgmcmc; which can be used for Bayesian inference on problems with large datasets using stochastic gradient Markov chain Monte Carlo (SGMCMC). Traditional Markov chain Monte Carlo (MCMC) methods, such as Metropolis-
The R package MfUSampler provides Monte Carlo Markov Chain machinery for generating samples from multivariate probability distributions using univariate sampling algorithms such as Slice Sampler and Adaptive Rejection Sampler. The sampler function pe
Process data refer to data recorded in the log files of computer-based items. These data, represented as timestamped action sequences, keep track of respondents response processes of solving the items. Process data analysis aims at enhancing educatio