Multivariate statistical analyses for neuroimaging data.

As the focus of neuroscience shifts from studying individual brain regions to entire networks of regions, methods for statistical inference have also become geared toward network analysis. The purpose of the present review is to survey the multivariate statistical techniques that have been used to study neural interactions. We have selected the most common techniques and developed a taxonomy that instructively reflects their assumptions and practical use. For each family of analyses, we describe their application and the types of experimental questions they can address, as well as how they relate to other analyses both conceptually and mathematically. We intend to show that despite their diversity, all of these techniques offer complementary information about the functional architecture of the brain.

[1]  Klaas E. Stephan,et al.  Dynamic causal modelling: A critical review of the biophysical and statistical foundations , 2011, NeuroImage.

[2]  Anthony Randal McIntosh,et al.  Partial Least Squares (PLS) methods for neuroimaging: A tutorial and review , 2011, NeuroImage.

[3]  Eugene S. Edgington,et al.  Randomization Tests , 2011, International Encyclopedia of Statistical Science.

[4]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[5]  Raymond J. Dolan,et al.  Computational and dynamic models in neuroimaging , 2010, NeuroImage.

[6]  Karl J. Friston,et al.  Dynamic causal modeling , 2010, Scholarpedia.

[7]  John A. E. Anderson,et al.  A multivariate analysis of age-related differences in default mode and task-positive networks across multiple cognitive domains. , 2010, Cerebral cortex.

[8]  Edward T. Bullmore,et al.  Whole-brain anatomical networks: Does the choice of nodes matter? , 2010, NeuroImage.

[9]  Karl J. Friston,et al.  Ten simple rules for dynamic causal modeling , 2010, NeuroImage.

[10]  Anthony R. McIntosh,et al.  Knowledge-Driven Contrast Gain Control is Characterized by Two Distinct Electrocortical Markers , 2009, Front. Hum. Neurosci..

[11]  Vasily A. Vakorin,et al.  Confounding effects of indirect connections on causality estimation , 2009, Journal of Neuroscience Methods.

[12]  Xiaoping Hu,et al.  Multivariate Granger causality analysis of fMRI data , 2009, Human brain mapping.

[13]  Karl J. Friston,et al.  Dynamic Causal Modeling of the Response to Frequency Deviants , 2009, Journal of neurophysiology.

[14]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[15]  Tom M. Mitchell,et al.  Machine learning classifiers and fMRI: A tutorial overview , 2009, NeuroImage.

[16]  Alan C. Evans,et al.  Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography. , 2009, Cerebral cortex.

[17]  Natasa Kovacevic,et al.  Modality-independent processes in cued motor preparation revealed by cortical potentials , 2008, NeuroImage.

[18]  V. Calhoun,et al.  Modulation of temporally coherent brain networks estimated using ICA at rest and during cognitive tasks , 2008, Human brain mapping.

[19]  O. Sporns,et al.  Mapping the Structural Core of Human Cerebral Cortex , 2008, PLoS biology.

[20]  Karl J. Friston,et al.  Dynamic causal modelling for fMRI: A two-state model , 2008, NeuroImage.

[21]  Karl J. Friston,et al.  Comparing hemodynamic models with DCM , 2007, NeuroImage.

[22]  Alice J. O'Toole,et al.  Theoretical, Statistical, and Practical Perspectives on Pattern-based Classification Approaches to the Analysis of Functional Neuroimaging Data , 2007, Journal of Cognitive Neuroscience.

[23]  Cornelis J Stam,et al.  Graph theoretical analysis of complex networks in the brain , 2007, Nonlinear biomedical physics.

[24]  Lester Melie-García,et al.  Characterizing brain anatomical connections using diffusion weighted MRI and graph theory , 2007, NeuroImage.

[25]  Jeremy B Caplan,et al.  Two distinct functional networks for successful resolution of proactive interference. , 2007, Cerebral cortex.

[26]  Karl J. Friston,et al.  Dynamic causal modelling of evoked potentials: A reproducibility study , 2007, NeuroImage.

[27]  Natasa Kovacevic,et al.  Groupwise independent component decomposition of EEG data and partial least square analysis , 2007, NeuroImage.

[28]  C. Stam,et al.  Small-world networks and functional connectivity in Alzheimer's disease. , 2006, Cerebral cortex.

[29]  Viktor K. Jirsa,et al.  Neuronal Dynamics and Brain Connectivity , 2007 .

[30]  Viktor K. Jirsa,et al.  Handbook of Brain Connectivity , 2007 .

[31]  Rolf Kötter,et al.  Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac Database , 2007, Neuroinformatics.

[32]  Steven L. Bressler,et al.  The Role of Neural Context in Large-Scale Neurocognitive Network Operations , 2007 .

[33]  S. Makeig,et al.  Imaging human EEG dynamics using independent component analysis , 2006, Neuroscience & Biobehavioral Reviews.

[34]  E. Bullmore,et al.  Adaptive reconfiguration of fractal small-world human brain functional networks , 2006, Proceedings of the National Academy of Sciences.

[35]  Andrea B Protzner,et al.  Testing effective connectivity changes with structural equation modeling: What does a bad model tell us? , 2006, Human brain mapping.

[36]  S. Rombouts,et al.  Consistent resting-state networks across healthy subjects , 2006, Proceedings of the National Academy of Sciences.

[37]  Sean M. Polyn,et al.  Beyond mind-reading: multi-voxel pattern analysis of fMRI data , 2006, Trends in Cognitive Sciences.

[38]  Karl J. Friston,et al.  Dynamic causal modeling of evoked responses in EEG and MEG , 2006, NeuroImage.

[39]  Karl J. Friston,et al.  Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization , 2006, NeuroImage.

[40]  E. Bullmore,et al.  A Resilient, Low-Frequency, Small-World Human Brain Functional Network with Highly Connected Association Cortical Hubs , 2006, The Journal of Neuroscience.

[41]  Arnaud Delorme,et al.  Frontal midline EEG dynamics during working memory , 2005, NeuroImage.

[42]  G. Rees,et al.  Predicting the orientation of invisible stimuli from activity in human primary visual cortex , 2005, Nature Neuroscience.

[43]  C. F. Beckmann,et al.  Tensorial extensions of independent component analysis for multisubject FMRI analysis , 2005, NeuroImage.

[44]  Rainer Goebel,et al.  Mapping directed influence over the brain using Granger causality and fMRI , 2005, NeuroImage.

[45]  Anthony Randal McIntosh,et al.  Partial least squares analysis of neuroimaging data: applications and advances , 2004, NeuroImage.

[46]  A. R. McIntosh,et al.  Spatiotemporal analysis of event-related fMRI data using partial least squares , 2004, NeuroImage.

[47]  Vincent J Schmithorst,et al.  Comparison of three methods for generating group statistical inferences from independent component analysis of functional magnetic resonance imaging data , 2004, Journal of magnetic resonance imaging : JMRI.

[48]  Stephen M. Smith,et al.  Probabilistic independent component analysis for functional magnetic resonance imaging , 2004, IEEE Transactions on Medical Imaging.

[49]  C. J. Stam,et al.  Functional connectivity patterns of human magnetoencephalographic recordings: a ‘small-world’ network? , 2004, Neuroscience Letters.

[50]  Rainer Goebel,et al.  Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping. , 2003, Magnetic resonance imaging.

[51]  L. K. Hansen,et al.  Independent component analysis of functional MRI: what is signal and what is noise? , 2003, Current Opinion in Neurobiology.

[52]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[53]  Karl J. Friston,et al.  Lateralized Cognitive Processes and Lateralized Task Control in the Human Brain , 2003, Science.

[54]  T. Carlson,et al.  Patterns of Activity in the Categorical Representations of Objects , 2003, Journal of Cognitive Neuroscience.

[55]  Richard A. Harshman,et al.  Noise Reduction in BOLD-Based fMRI Using Component Analysis , 2002, NeuroImage.

[56]  T. Sejnowski,et al.  Dynamic Brain Sources of Visual Evoked Responses , 2002, Science.

[57]  Lars Kai Hansen,et al.  The Quantitative Evaluation of Functional Neuroimaging Experiments: The NPAIRS Data Analysis Framework , 2000, NeuroImage.

[58]  J. Pekar,et al.  fMRI Activation in a Visual-Perception Task: Network of Areas Detected Using the General Linear Model and Independent Components Analysis , 2001, NeuroImage.

[59]  J. Pekar,et al.  A method for making group inferences from functional MRI data using independent component analysis , 2001, Human brain mapping.

[60]  T. Sejnowski,et al.  Analysis and visualization of single‐trial event‐related potentials , 2001, Human brain mapping.

[61]  M. Young,et al.  Advanced database methodology for the Collation of Connectivity data on the Macaque brain (CoCoMac). , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[62]  Mingzhou Ding,et al.  Evaluating causal relations in neural systems: Granger causality, directed transfer function and statistical assessment of significance , 2001, Biological Cybernetics.

[63]  A. McIntosh,et al.  Spatiotemporal analysis of experimental differences in event-related potential data with partial least squares. , 2001, Psychophysiology.

[64]  Stephen C. Strother,et al.  Penalized Discriminant Analysis of [15O]-water PET Brain Images with Prediction Error Selection of Smoothness and Regularization , 2001, IEEE Trans. Medical Imaging.

[65]  V D Calhoun,et al.  Spatial and temporal independent component analysis of functional MRI data containing a pair of task‐related waveforms , 2001, Human brain mapping.

[66]  G L Shulman,et al.  INAUGURAL ARTICLE by a Recently Elected Academy Member:A default mode of brain function , 2001 .

[67]  Anthony Randal McIntosh,et al.  Towards a network theory of cognition , 2000, Neural Networks.

[68]  E. Bullmore,et al.  How Good Is Good Enough in Path Analysis of fMRI Data? , 2000, NeuroImage.

[69]  T. Sejnowski,et al.  Removing electroencephalographic artifacts by blind source separation. , 2000, Psychophysiology.

[70]  G Tononi,et al.  Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. , 2000, Cerebral cortex.

[71]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[72]  Thomas E. Nichols,et al.  Statistical limitations in functional neuroimaging. I. Non-inferential methods and statistical models. , 1999, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[73]  L. K. Hansen,et al.  Generalizable Patterns in Neuroimaging: How Many Principal Components? , 1999, NeuroImage.

[74]  T. Sejnowski,et al.  Functionally Independent Components of the Late Positive Event-Related Potential during Visual Spatial Attention , 1999, The Journal of Neuroscience.

[75]  A. McIntosh,et al.  Understanding Neural Interactions in Learning and Memory Using Functional Neuroimaging , 1998, Annals of the New York Academy of Sciences.

[76]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.

[77]  S Makeig,et al.  Spatially independent activity patterns in functional MRI data during the stroop color-naming task. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[78]  S Makeig,et al.  Analysis of fMRI data by blind separation into independent spatial components , 1998, Human brain mapping.

[79]  Karl J. Friston,et al.  Characterizing the Response of PET and fMRI Data Using Multivariate Linear Models , 1997, NeuroImage.

[80]  Karl J. Friston,et al.  Psychophysiological and Modulatory Interactions in Neuroimaging , 1997, NeuroImage.

[81]  S Makeig,et al.  Blind separation of auditory event-related brain responses into independent components. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[82]  E. Tulving,et al.  Network Analysis of Positron Emission Tomography Regional Cerebral Blood Flow Data: Ensemble Inhibition during Episodic Memory Retrieval , 1996, The Journal of Neuroscience.

[83]  J. V. Haxby,et al.  Spatial Pattern Analysis of Functional Brain Images Using Partial Least Squares , 1996, NeuroImage.

[84]  Karl J. Friston,et al.  A multivariate analysis of PET activation studies , 1996, Human brain mapping.

[85]  R. Woods,et al.  Principal Component Analysis and the Scaled Subprofile Model Compared to Intersubject Averaging and Statistical Parametric Mapping: I. “Functional Connectivity” of the Human Motor System Studied with [15O]Water PET , 1995, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[86]  R. Turner,et al.  Characterizing Dynamic Brain Responses with fMRI: A Multivariate Approach , 1995, NeuroImage.

[87]  Leslie G. Ungerleider,et al.  Network analysis of cortical visual pathways mapped with PET , 1994, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[88]  G. Alexander,et al.  Application of the scaled subprofile model to functional imaging in neuropsychiatric disorders: A principal component approach to modeling brain function in disease , 1994 .

[89]  F. Gonzalez-Lima,et al.  Structural equation modeling and its application to network analysis in functional brain imaging , 1994 .

[90]  Karl J. Friston,et al.  Functional Connectivity: The Principal-Component Analysis of Large (PET) Data Sets , 1993, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[91]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[92]  Karl J. Friston,et al.  Comparing Functional (PET) Images: The Assessment of Significant Change , 1991, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[93]  A. McIntosh,et al.  Structural modeling of functional neural pathways mapped with 2-deoxyglucose: effects of acoustic startle habituation on the auditory system , 1991, Brain Research.

[94]  J R Moeller,et al.  A Regional Covariance Approach to the Analysis of Functional Patterns in Positron Emission Tomographic Data , 1991, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[95]  M K Habib,et al.  Dynamics of neuronal firing correlation: modulation of "effective connectivity". , 1989, Journal of neurophysiology.

[96]  S. Strother,et al.  Scaled Subprofile Model: A Statistical Approach to the Analysis of Functional Patterns in Positron Emission Tomographic Data , 1987, Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism.

[97]  K. Bollen Sample size and bentler and Bonett's nonnormed fit index , 1986 .

[98]  C Loehlin John,et al.  Latent variable models: an introduction to factor, path, and structural analysis , 1986 .

[99]  Robert Tibshirani,et al.  Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy , 1986 .

[100]  R. P. McDonald,et al.  Some algebraic properties of the Reticular Action Model for moment structures. , 1984, The British journal of mathematical and statistical psychology.

[101]  Herman Wold,et al.  Soft modelling: The Basic Design and Some Extensions , 1982 .

[102]  W. Atchley,et al.  THE GEOMETRY OF CANONICAL VARIATE ANALYSIS , 1981 .

[103]  Jay Magidson,et al.  Advances in factor analysis and structural equation models , 1980 .

[104]  C. Granger Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[105]  H. Hotelling Relations Between Two Sets of Variates , 1936 .

[106]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[107]  Karl Pearson F.R.S. LIII. On lines and planes of closest fit to systems of points in space , 1901 .