Applications of multivariate modeling to neuroimaging group analysis: A comprehensive alternative to univariate general linear model

• Published in: NeuroImage (Orlando, Fla.) Vol. 99; pp. 571 - 588
• Main Authors: Chen, Gang, Adleman, Nancy E., Saad, Ziad S., Leibenluft, Ellen, Cox, Robert W.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-10-2014; Elsevier; Elsevier Limited
• Subjects: Adolescent; Biological and medical sciences; Child; Estimates; False Positive Reactions; Female; Fundamental and applied biological sciences. Psychology; Humans; Hypotheses; Image Processing, Computer-Assisted; Linear Models; Magnetic Resonance Imaging; Male; Medical imaging; Models, Neurological; Multivariate Analysis; Neuroimaging - methods; Reaction Time - physiology; Reading; Reproducibility of Results; Sample Size; Statistics; Symmetry; Variables; Vertebrates: nervous system and sense organs; Models
• ISSN: 1053-8119; 1095-9572
• DOI: 10.1016/j.neuroimage.2014.06.027

All neuroimaging packages can handle group analysis with t-tests or general linear modeling (GLM). However, they are quite hamstrung when there are multiple within-subject factors or when quantitative covariates are involved in the presence of a within-subject factor. In addition, sphericity is typically assumed for the variance–covariance structure when there are more than two levels in a within-subject factor. To overcome such limitations in the traditional AN(C)OVA and GLM, we adopt a multivariate modeling (MVM) approach to analyzing neuroimaging data at the group level with the following advantages: a) there is no limit on the number of factors as long as sample sizes are deemed appropriate; b) quantitative covariates can be analyzed together with within-subject factors; c) when a within-subject factor is involved, three testing methodologies are provided: traditional univariate testing (UVT) with sphericity assumption (UVT-UC) and with correction when the assumption is violated (UVT-SC), and within-subject multivariate testing (MVT-WS); d) to correct for sphericity violation at the voxel level, we propose a hybrid testing (HT) approach that achieves equal or higher power via combining traditional sphericity correction methods (Greenhouse–Geisser and Huynh–Feldt) with MVT-WS.
To validate the MVM methodology, we performed simulations to assess the controllability for false positives and power achievement. A real FMRI dataset was analyzed to demonstrate the capability of the MVM approach. The methodology has been implemented into an open source program 3dMVM in AFNI, and all the statistical tests can be performed through symbolic coding with variable names instead of the tedious process of dummy coding. Our data indicates that the severity of sphericity violation varies substantially across brain regions. The differences among various modeling methodologies were addressed through direct comparisons between the MVM approach and some of the GLM implementations in the field, and the following two issues were raised: a) the improper formulation of test statistics in some univariate GLM implementations when a within-subject factor is involved in a data structure with two or more factors, and b) the unjustified presumption of uniform sphericity violation and the practice of estimating the variance–covariance structure through pooling across brain regions.
•AN(C)OVA can be analyzed via multivariate modeling.•There is no limit on the number of explanatory variables.•Quantitative covariates can be modeled in the presence of a within subject factor.•Sphericity violation can be corrected at the voxel level.•Model and all tests can be specified via symbolic labels.