The issue of variance components testing arises naturally when building mixed-effects models, to decide which effects should be modeled as fixed or random. While tests for fixed effects are available in R for models fitted with lme4, tools are missing when it comes to random effects. The varTestnlme package for R aims at filling this gap. It allows to test whether any subset of the variances and covariances corresponding to any subset of the random effects, are equal to zero using asymptotic property of the likelihood ratio test statistic. It also offers the possibility to test simultaneously for fixed effects and variance components. It can be used for linear, generalized linear or nonlinear mixed-effects models fitted via lme4, nlme or saemix. Theoretical properties of the used likelihood ratio test are recalled, numerical methods used to implement the test procedure are detailed and examples based on different real datasets using different mixed models are provided.
Meta-regression models are commonly used to synthesize and compare effect sizes. Unfortunately, traditional meta-regression methods are ill-equipped to handle the complex and often unknown correlations among non-independent effect sizes. Robust variance estimation (RVE) is a recently proposed meta-analytic method for dealing with dependent effect sizes. The robumeta package provides functions for performing robust variance meta-regression using both large and small sample RVE estimators under various weighting schemes. These methods are distribution free and provide valid point estimates, stan…
The R package "sensobol" provides several functions to conduct variance-based uncertainty and sensitivity analysis, from the estimation of sensitivity indices to the visual representation of the results. It implements several state-of-the-art first and total-order estimators and allows the computation of up to third-order effects, as well as of the approximation error, in a swift and user-friendly way. Its flexibility makes it also appropriate for models with either a scalar or a multivariate output. We illustrate its functionality by conducting a variance-based sensitivity analysis of three c…
The R package SamplingStrata was developed in 2011 as an instrument to optimize the design of stratified samples. The optimization is performed by considering the stratification variables available in the sampling frame, and the precision constraints on target estimates of the survey (Ballin & Barcaroli, 2014). The genetic algorithm at the basis of the optimization step explores the universe of the possible alternative stratifications determining for each of them the best allocation, that is the one of minumum total size that allows to satisfy the precision constraints: the final optimal solut…
Evolution & Ecology Research Centre, UNSW（新南威尔士大学进化与生态研究中心）；School of Mathematics and Statistics, UNSW（新南威尔士大学数学与统计学院）；Stats Central, Mark Wainwright Analytical Centre, UNSW（新南威尔士大学Mark Wainwright分析中心统计中心）；National Institute of Aquatic Resources, Danish Technical University（丹麦技术大学国家水产研究所）；Department of Mathematics & Statistics, McMaster University（麦克马斯特大学数学与统计系）；Department of Biology, McMaster University（麦克马斯特大学生物学系）；Department of Biological Sciences, Faculty of Science, The University of Alberta（阿尔伯塔大学理学院生物科学系）；Department of Biosystems Engineering, Zhejiang University（浙江大学农业生物系统工程系）；Department of Psychiatry and Neuropsychology, Maastricht University（马斯特里赫特大学精神病学与神经心理学系）
The rebmix package provides R functions for random univariate and multivariate finite mixture model generation, estimation, clustering and classification. The paper is focused on multivariate normal mixture models with unrestricted variance-covariance matrices. The objective is to show how to generate datasets for a known number of components, numbers of observations and component parameters, how to estimate the number of components, component weights and component parameters and how to predict cluster and class membership based upon a model trained by the REBMIX algorithm. The accompanying pl…
In multivariate nonparametric analysis, sparseness of the covariates also called curse of dimensionality, forces one to use large smoothing parameters. This leads to a biased smoother. Instead of focusing on optimally selecting the smoothing parameter, we fix it to some reasonably large value to ensure an over-smoothing of the data. The resulting base smoother has a small variance but a substantial bias. In this paper, we propose an R package named ibr to iteratively correct the initial bias of the (base) estimator by an estimate of the bias obtained by smoothing the residuals. After a brief d…
M-estimation, or estimating equation, methods are widely applicable for point estimation and asymptotic inference. In this paper, we present an R package that can find roots and compute the empirical sandwich variance estimator for any set of user-specified, unbiased estimating equations. Examples from the M-estimation primer by Stefanski and Boos (2002) demonstrate use of the software. The package also includes a framework for finite sample variance corrections and a website with an extensive collection of tutorials.
Measurement error in a covariate or the outcome of regression models is common, but is often ignored, even though measurement error can lead to substantial bias in the estimated covariate-outcome association. While several texts on measurement error correction methods are available, these methods remain seldomly applied. To improve the use of measurement error correction methodology, we developed mecor, an R package that implements measurement error correction methods for regression models with continuous outcomes. Measurement error correction requires information about the measurement error m…
The sequential parameter optimization (SPOT) package for R is a toolbox for tuning and understanding simulation and optimization algorithms. Model-based investigations are common approaches in simulation and optimization. Sequential parameter optimization has been developed, because there is a strong need for sound statistical analysis of simulation and optimization algorithms. SPOT includes methods for tuning based on classical regression and analysis of variance techniques; tree-based models such as CART and random forest; Gaussian process models (Kriging), and combinations of different meta…
Compared to abundant classical statistics-based literature, to date, very little Bayesian literature exists on Procrustes shape analysis in Geometric Morphometrics, probably because of being a relatively new branch of statistical research and because of inherent computational difficulty associated with Bayesian analysis. Moreover, we may obtain a plethora of novel inferences from Bayesian Procrustes analysis of shape parameter distributions. In this paper, we propose to regard the posterior of Procrustes shape variance as morphological variability indicators. Here we propose novel Bayesian met…
The current statistical procedures implemented in statistical software packages for pooling of diagnostic test accuracy data include hSROC regression and the bivariate random-effects meta-analysis model (BRMA). However, these models do not report the overall mean but rather the mean for a central study with random-effect equal to zero and have difficulties estimating the correlation between sensitivity and specificity when the number of studies in the meta-analysis is small and/or when the between-study variance is relatively large. This tutorial on advanced statistical methods for meta-analys…
High-dimensional prediction considers data with more variables than samples. Generic research goals are to find the best predictor or to select variables. Results may be improved by exploiting prior information in the form of co-data, providing complementary data not on the samples, but on the variables. We consider adaptive ridge penalised generalised linear and Cox models, in which the variable specific ridge penalties are adapted to the co-data to give a priori more weight to more important variables. The R-package ecpc originally accommodated various and possibly multiple co-data sources, …
Robust variance estimation for multiple imputation using predictive mean matching or parametric imputation models
University of Washington（华盛顿大学）；University of Florida（佛罗里达大学）；Wake Forest University（维克森林大学）；Kaiser Permanente Washington Health Research Institute（凯撒永久华盛顿健康研究所）；Fred Hutchinson Cancer Center（弗雷德·哈钦森癌症中心）
kStatistics is a package in R that serves as a unified framework for estimating univariate and multivariate cumulants as well as products of univariate and multivariate cumulants of a random sample, using unbiased estimators with minimum variance. The main computational machinery of kStatistics is an algorithm for computing multi-index partitions. The same algorithm underlies the general-purpose multivariate Faà di Bruno's formula, which has been therefore included in the last release of the package. This formula gives the coefficients of formal power series compositions as well as the partial…
Model selection in mixed models based on the conditional distribution is appropriate for many practical applications and has been a focus of recent statistical research. In this paper we introduce the R-package cAIC4 that allows for the computation of the conditional Akaike Information Criterion (cAIC). Computation of the conditional AIC needs to take into account the uncertainty of the random effects variance and is therefore not straightforward. We introduce a fast and stable implementation for the calculation of the cAIC for linear mixed models estimated with lme4 and additive mixed models …
Deep autoencoders are often extended with a supervised or adversarial loss to learn latent representations with desirable properties, such as greater predictivity of labels and outcomes or fairness with respects to a sensitive variable. Despite the ubiquity of supervised and adversarial deep latent factor models, these methods should demonstrate improvement over simpler linear approaches to be preferred in practice. This necessitates a reproducible linear analog that still adheres to an augmenting supervised or adversarial objective. We address this methodological gap by presenting methods tha…
HLIBCov: Parallel Hierarchical Matrix Approximation of Large Covariance Matrices and Likelihoods with Applications in Parameter Identification
RWTH Aachen（亚琛工业大学）；Max-Planck-Institut für Mathematik in den Naturwissenschaften（马克斯·普朗克自然科学数学研究所）；King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
This paper describes an R package implementing large sample tests and confidence intervals (based on the central limit theorem) for various parameters. The one and two sample mean and variance contexts are considered. The statistics for all the tests are expressed in the same form, which facilitates their presentation. In the variance parameter cases, the asymptotic robustness of the classical tests depends on the departure of the data distribution from normality measured in terms of the kurtosis of the distribution.
As gene expression measurement technology is shifting from microarrays to sequencing, the statistical tools available for their analysis must be adapted since RNA-seq data are measured as counts. Recently, it has been proposed to tackle the count nature of these data by modeling log-count reads per million as continuous variables, using nonparametric regression to account for their inherent heteroscedasticity. Adopting such a framework, we propose tcgsaseq, a principled, model-free and efficient top-down method for detecting longitudinal changes in RNA-seq gene sets. Considering gene sets defi…
Eli Lilly and Company（礼来公司）；Cleveland Clinic Lerner Research Institute（克利夫兰诊所勒纳研究所）；Amazon.com, Inc.（亚马逊公司）；Case Western Reserve University（凯斯西储大学）
Large sequences of images (or movies) can now be obtained on an unprecedented scale, which poses fundamental challenges to the existing image analysis techniques. The challenges include heterogeneity, (automatic) alignment, multiple comparisons, potential artifacts, and hidden noises. This paper introduces our MATLAB package, Longitudinal Image Sequence Analysis (LISA), as a one-stop ensemble of image processing and analysis tool for comparing a general class of images from either different times, sessions, or subjects. Given two contrasting sequences of images, the image processing in LISA st…
Percentiles and more generally, quantiles are commonly used in various contexts to summarize data. For most distributions, there is exactly one quantile that is unbiased. For distributions like the Gaussian that have the same mean and median, that becomes the medians. There are different ways to estimate quantiles from finite samples described in the literature and implemented in statistics packages. It is possible to leverage the memory-less property of the exponential distribution and design high quality estimators that are unbiased and have low variance and mean squared errors. Naturally, t…
The increasing availability of individual-level data has led to numerous applications of individualized (or personalized) treatment rules (ITRs). Policy makers often wish to empirically evaluate ITRs and compare their relative performance before implementing them in a target population. We propose a new evaluation metric, the population average prescriptive effect (PAPE). The PAPE compares the performance of ITR with that of non-individualized treatment rule, which randomly treats the same proportion of units. Averaging the PAPE over a range of budget constraints yields our second evaluation m…
Hedges' d, an existing unbiased effect size of the difference between means, assumes the variance equality. However, the assumption of the variance equality is fragile, and is often violated in practical applications. Here, we define e, a new effect size of the difference between means, which does not assume the variance equality. In addition, another novel statistic c is defined as an effect size of the difference between a mean and a known constant. Hedges' g, our c, and e correspond to Student's unpaired two-sample t test, Student's one-sample t test, and Welch's t test, respectively. An R …
Solutions of the bivariate, linear errors-in-variables estimation problem with unspecified errors are expected to be invariant under interchange and scaling of the coordinates. The appealing model of normally distributed true values and errors is unidentified without additional information. I propose a prior density that incorporates the fact that the slope and variance parameters together determine the covariance matrix of the unobserved true values but is otherwise diffuse. The marginal posterior density of the slope is invariant to interchange and scaling of the coordinates and depends on t…
Generalized linear mixed models (GLMMs) are used to model responses from exponential families with a combination of fixed and random effects. For variance components in GLMMs, we propose an approximate restricted likelihood ratio test that conducts testing on the working responses used in penalized quasi-likelihood estimation. This presents the hypothesis test in terms of normalized responses, allowing for application of existing testing methods for linear mixed models. Our test is flexible, computationally efficient, and outperforms several competitors. We illustrate the utility of the propos…
Testing the (in)equality of variances is an important problem in many statistical applications. We develop default Bayes factor tests to assess the (in)equality of two or more population variances, as well as a test for whether the population variances equal a specific value. The resulting test can be used to check assumptions for commonly used procedures such as the $t$-test or ANOVA, or test substantive hypotheses concerning variances directly. We show that our Bayes factor fulfills a number of desiderata. Researchers may have directed hypotheses such as $σ_{1}^{2} > σ_{2}^{2}$, they may wan…
Efficient frequentist fractional polynomials for skewed dose-response and survival data: a variance-reducing alternative to OLS-FP
Cherkasy State Business College（切尔卡瑟国立商业学院）；State Scientific Research Institute of Armament and Military Equipment Testing and Certification（国家武器和军事装备测试与认证科学研究院）；Uzhhorod National University（乌日霍罗德国立大学）
This paper introduces the \proglang{R} package \pkg{meta4diag} for implementing Bayesian bivariate meta-analyses of diagnostic test studies. Our package \pkg{meta4diag} is a purpose-built front end of the \proglang{R} package \pkg{INLA}. While \pkg{INLA} offers full Bayesian inference for the large set of latent Gaussian models using integrated nested Laplace approximations, \pkg{meta4diag} extracts the features needed for bivariate meta-analysis and presents them in an intuitive way. It allows the user a straightforward model-specification and offers user-specific prior distributions. Further…
We propose a two-stage estimation method of variance components in time series models known as FDSLRMs, whose observations can be described by a linear mixed model (LMM). We based estimating variances, fundamental quantities in a time series forecasting approach called kriging, on the empirical (plug-in) best linear unbiased predictions of unobservable random components in FDSLRM. The method, providing invariant non-negative quadratic estimators, can be used for any absolutely continuous probability distribution of time series data. As a result of applying the convex optimization and the LMM m…
Investigating the problem of setting control limits in the case of parameter uncertainty is more accessible when monitoring the variance because only one parameter has to be estimated. Simply ignoring the induced uncertainty frequently leads to control charts with poor false alarm performances. Adjusting the unconditional in-control (IC) average run length (ARL) makes the situation even worse. Guaranteeing a minimum conditional IC ARL with some given probability is another very popular approach to solving these difficulties. However, it is very conservative as well as more complex and more dif…
Peptide microarrays have emerged as a powerful technology in immunoproteomics as they provide a tool to measure the abundance of different antibodies in patient serum samples. The high dimensionality and small sample size of many experiments challenge conventional statistical approaches, including those aiming to control the false discovery rate (FDR). Motivated by limitations in reproducibility and power of current methods, we advance an empirical Bayesian tool that computes local false discovery rate statistics and local false sign rate statistics when provided with data on estimated effects…
Frequentist prediction intervals for random-effects meta-analysis via confidence-distribution propagation
The Institute of Statistical Mathematics（日本统计科学研究所）；The Graduate University for Advanced Studies（高级研究院）；Institute of Medical Biometry and Statistics, Medical Faculty and Medical Center – University of Freiburg（弗赖堡大学医学院医学中心医学生物统计学与统计研究所）
In medical device comparison studies, equivalency test is commonly used to demonstrate two measurement methods agree up to a pre-specified performance goal based on the paired repeated measures. Such equivalency test often involves controlling the absolute differences that depend on both the mean and variance parameters, and poses some challenges for statistical analysis. For example, for the oximetry comparison study that motivates our research, FDA has clear guidelines approving an investigational pulse oximeter in comparison to a standard oximeter via testing the root mean squares (RMS), a …
Fitting Generalized Linear Mixed-Effects Models using lme4
McMaster University（麦克马斯特大学）；Copenhagen Research Centre for Biological and Precision Psychiatry（哥本哈根生物与精准精神病学研究中心）；University of Wisconsin - Madison（威斯康星大学麦迪逊分校）；ETH Zurich（苏黎世联邦理工学院）
