k-FWER control without multiplicity correction, with application to detection of genetic determinants of multiple sclerosis in Italian twins

We show a novel approach for k-FWER control which does not involve any correction, but only testing the hypotheses along a (possibly datadriven) order until a suitable number of p-values are found above the uncorrected α level. p-values can arise from any linear model in a parametric or non parametric setting. The approach is not only very simple and computationally light, but also the data-driven order enhances power when the sample size is small (and also when k and/or m is large). We illustrate the method on an original study about gene discovery in multiple sclerosis, in which were involved a small number of couples of twins, discordant by disease

Exact Multivariate Permutation Tests for Fixed Effects in Mixed-Models

A test for the fixed effect in mixed-models is proposed. It is based on permutation strategy and is exact. The testing approach presented is very general and the class of model covered is very broad. Multivariate responses with different type of variables (e.g. continuous, categorical and ranks) are usually tested with separated models and the overall test are usually reached trough Bonferroni-like combinations, i.e. without taking in account the joint distribution of the tests statistics. On the contrary in this approach the joint distribution is immediately obtained and the dependence among tests is taken in account in the overall test

Procrustes analysis for high-dimensional data

The Procrustes-based perturbation model \citep{Goodall} allows to minimize the Frobenius distance between matrices by similarity transformation. However, it suffers from non-identifiability, critical interpretation of the transformed matrices, and non-applicability in high-dimensional data. We provide an extension of the perturbation model focused on the high-dimensional data framework, called the ProMises (Procrustes von Mises-Fisher) model. The ill-posed and interpretability problems are solved by imposing a proper prior distribution for the orthogonal matrix parameter, i.e., the von Mises-Fisher distribution, which is a conjugate prior, resulting in a fast estimation process. Furthermore, we present the Efficient ProMises model for the high-dimensional framework, useful in neuroimaging, where the problem has much more than three dimensions. We found a great improvement in functional Magnetic Resonance Imaging connectivity analysis since the ProMises model permits to incorporate topological brain information in the alignment's estimation process.Comment: 20 pages, 7 figure

A Maximum Entropy Procedure to Solve Likelihood Equations

In this article, we provide initial findings regarding the problem of solving likelihood equations by means of a maximum entropy (ME) approach. Unlike standard procedures that require equating the score function of the maximum likelihood problem at zero, we propose an alternative strategy where the score is instead used as an external informative constraint to the maximization of the convex Shannon\u2019s entropy function. The problem involves the reparameterization of the score parameters as expected values of discrete probability distributions where probabilities need to be estimated. This leads to a simpler situation where parameters are searched in smaller (hyper) simplex space. We assessed our proposal by means of empirical case studies and a simulation study, the latter involving the most critical case of logistic regression under data separation. The results suggested that the maximum entropy reformulation of the score problem solves the likelihood equation problem. Similarly, when maximum likelihood estimation is difficult, as is the case of logistic regression under separation, the maximum entropy proposal achieved results (numerically) comparable to those obtained by the Firth\u2019s bias-corrected approach. Overall, these first findings reveal that a maximum entropy solution can be considered as an alternative technique to solve the likelihood equation

TextWiller: Collection of functions for text mining, specially devoted to the Italian language

TextWilleris the development version of a R package that collects some text mining utilities intended for the Italian language. It’s available at https://github.com/livioivil/TextWiller. The aim of TextWiller is to help to deal with the pre-processing of a corpus and it also provides some functions about word classification and polarity

Enhanced hyperalignment via spatial prior information

Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group-level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high-dimensional space and thereby improving inter-subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole-brain analysis. To resolve these issues, we propose the ProMises (Procrustes von Mises-Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises-Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high-dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole-brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter-subject classification in terms of between-subject accuracy and interpretability compared to standard hyperalignment algorithms.Comment: 28 pages, 9 figure

Enhanced hyperalignment via spatial prior information

Functional alignment between subjects is an important assumption of functional magnetic resonance imaging (fMRI) group-level analysis. However, it is often violated in practice, even after alignment to a standard anatomical template. Hyperalignment, based on sequential Procrustes orthogonal transformations, has been proposed as a method of aligning shared functional information into a common high-dimensional space and thereby improving inter-subject analysis. Though successful, current hyperalignment algorithms have a number of shortcomings, including difficulties interpreting the transformations, a lack of uniqueness of the procedure, and difficulties performing whole-brain analysis. To resolve these issues, we propose the ProMises (Procrustes von Mises–Fisher) model. We reformulate functional alignment as a statistical model and impose a prior distribution on the orthogonal parameters (the von Mises–Fisher distribution). This allows for the embedding of anatomical information into the estimation procedure by penalizing the contribution of spatially distant voxels when creating the shared functional high-dimensional space. Importantly, the transformations, aligned images, and related results are all unique. In addition, the proposed method allows for efficient whole-brain functional alignment. In simulations and application to data from four fMRI studies we find that ProMises improves inter-subject classification in terms of between-subject accuracy and interpretability compared to standard hyperalignment algorithms

Robust testing in generalized linear models by sign-flipping score contributions

Generalized linear models are often misspecified due to overdispersion, heteroscedasticity and ignored nuisance variables. Existing quasi-likelihood methods for testing in misspecified models often do not provide satisfactory type-I error rate control. We provide a novel semi-parametric test, based on sign-flipping individual score contributions. The tested parameter is allowed to be multi-dimensional and even high-dimensional. Our test is often robust against the mentioned forms of misspecification and provides better type-I error control than its competitors. When nuisance parameters are estimated, our basic test becomes conservative. We show how to take nuisance estimation into account to obtain an asymptotically exact test. Our proposed test is asymptotically equivalent to its parametric counterpart.Comment: To appear in Journal of the Royal Statistical Society: Series B (Methodology). Early view version (2020