This chapter reviews issues specific to the analysis of functional magnetic resonance imaging (fMRI) data. It extends the general linear model (GLM) introduced in Chapter 8 to convolution models, in which the blood oxygenation-level-dependent (BOLD) signal is modelled by neuronal causes that are expressed via a haemodynamic response function (HRF). We begin by considering linear convolution mod...

Inter-subject parcellation of functional Magnetic Resonance Imaging (fMRI) data based on a standard General Linear Model (GLM) and spectral clustering was recently proposed as a means to alleviate the issues associated with spatial normalization in fMRI. However, for all its appeal, a GLM-based parcellation approach introduces its own biases, in the form of a priori knowledge about the shape of...

Local canonical correlation analysis (CCA) is a multivariate method that has been proposed to more accurately determine activation patterns in fMRI data. In its conventional formulation, CCA has several drawbacks that limit its usefulness in fMRI. A major drawback is that, unlike the general linear model (GLM), a test of general linear contrasts of the temporal regressors has not been incorpora...

The objectives of this study are to: (1) examine the applicability of the double Poisson (DP) generalized linear model (GLM) for analyzing motor vehicle crash data characterized by over- and under-dispersion and (2) compare the performance of the DP GLM with the Conway-Maxwell-Poisson (COM-Poisson) GLM in terms of goodness-of-fit and theoretical soundness. The DP distribution has seldom been in...

Brundan and Kleshchev recently introduced a new family of presentations of the Yangian Y (gln) associated to the general linear Lie algebra gln, and thus provided a fresh approach to its study. In this article, we would like to show how some of their ideas can be fruitfully extended to consider the Yangian Y (glm|n) associated to the Lie superalgebra glm|n. In particular, we give a new proof of...

We consider the General Linear Model (GLM) which includes multivariate analysis of variance (MANOVA) and multiple linear regression as special cases. In practice, there are several widely used criteria for GLM: Wilks’ lambda, Bartlett–Nanda–Pillai test, Lawley–Hotelling Roy maximum root test. Limiting distributions first three mentioned tests known under different asymptotic settings. present p...

A new adaptive multiple-controller is proposed incorporating a neural network based Generalized Learning Model (GLM). The GLM assumes that the unknown complex plant is represented by an equivalent stochastic model consisting of a linear time-varying sub-model plus a Radial Basis Function (RBF) neural-network based learning sub-model . The proposed non-linear multiple-controller methodology prov...

Generalized linear models (GLMs) represent a class of fixed effects regression models for several types of dependent variables (i.e., continuous, dichotomous, counts). McCullagh and Nelder [32] describe these in great detail and indicate that the term ‘generalized linear model’ is due to Nelder and Wedderburn [35] who described how a collection of seemingly disparate statistical techniques coul...