# Multivariate modeling approach for group analysis

## Introduction

Program 3dMVM in the AFNI suite is a program that runs FMRI group
analysis with a multivariate modeling approach that can handle situations with an ANOVA or ANCOVA-style structure. Input files for 3dMVM can be in AFNI, NIfTI, or
surface (niml.dset or 1D) format. If offers a comprehensive and valid approach and avoids the serious issues that have been plaguing some implementations in the field (e.g. GLM, flexible factorial design) for a long time.

## Why another group analysis program?

It seems that there are quite a few group analysis programs already in the AFNI suite: 3dttest++, 3dMEMA, 3dANOVAx, GroupAna, and 3dLME. Theoretically speaking, 3dLME could handle almost all of the complex situations of FMRI group analysis. However, there are a couple of thorny issues with the LME approach in practice even for some relatively simple analyses: flexible but difficult-to-standardize interface with the underlying R function, and controversial assignment of degrees of freedom to the testing statistics. For most experiments typically encountered in FMRI, it feels like taking a spear to kill a fly when using the LME method to handle the conventional AN(C)OVA-type data structure. This grey area between 3dLME and the other AFNI group analysis programs was the motivation for a new approach: multi-variate modeling.

Written in R, 3dMVM performs the typical ANOVA as well as ANCOVA. In other words, it can take both categorical and quantitative variables. More importantly, there is no bound on the number of explanatory variables that could be incorporated into the model. Similar to most group analysis programs (and unlike 3dMEMA), 3dMVM only takes the effect estimates (no *t*-statistics) as input. The approach would avoid some implementation problems involved in the general linear modeling method popularly adopted in other packages such as Flexible Factorial Design in SPM and FEAT in FSL. The technical details can be found in the following paper:

Chen, G., Adleman, N.E., Saad, Z.S., Leibenluft, E., Cox, R.W. (2014). Applications of Multivariate Modeling to Neuroimaging Group Analysis: A Comprehensive Alternative to Univariate General Linear Model. NeuroImage 99:571-88. (Download)

## How is 3dMVM compared to 3dANOVAx?

**Advantages of 3dANOVAx**:

1) Super fast!

2) You probably already know how to use it.

**Limitations of 3dANOVAx**:

1) Limited to only two explanatory variables.

2) Unequal number of subjects not allowed across groups in 3dANOVA2 and 3dANOVA3.

3) Quantitative variables (covariates) not allowed.

4) Sphericity assumption for F-statistic when a within-subject (repeated-measures) factor with more than two levels is involved.

**Advantages of 3dMVM**:

1) No limit on the number of explanatory variables.

2) Unequal number of subjects across groups is allowed

3) Quantitative variables (covariates) are allowed.

4) Correction for sphericity violation is possible.

**Limitations of 3dMVM**:

1) Super slow.

If you can analyze your data with 3dttest++, 3dMEMA, or 3dANOVAx, there is no point using 3dMVM unless you're concerned about sphericity violation whose correction usually decreases the original *t*-statistics.

## How is 3dMVM compared to GroupAna?

**Advantages of GroupAna**:

1) Maybe a little faster than 3dMVM?

**Limitations of GroupAna**:

1) Have to purchase commercial software Matlab and an expensive toolbox Statistics.

2) Limited to four explanatory variables.

3) Quantitative variables (covariates) not allowed.

4) Only pairwise comparisons are available

5) Sphericity assumption for *F*-statistic when a within-subject (repeated-measures) factor with more than two levels is involved.

**Advantages of 3dMVM**:

1) No limit on the number of explanatory variables.

2) Quantitative variables (covariates) are allowed.

3) Correction for sphericity violation is possible.

4) General linear tests are available: weights don't have to add up to 0!

**Limitations of 3dMVM**:

1) Probably a little slower than GroupAna.

I guess GroupAna can pretty much retire now into history? Unless you're too fond of it...

## How is 3dMVM compared to 3dLME?

3dMVM was written to relieve some of the burden from 3dLME so that the latter would be only used for some really sophisticated scenarios (not exhaustive here):

1) Group analysis when the BOLD response is modeled with multiple basis functions AND when there is one group of subjects under one condition.

2) A within-subject quantitative variable is involved (e.g., separate reaction time for each level of condition (positive, neutral, and negative)).

3) Missing data of a within-subject factor.

4) Subjects are family numbers or twins.

## 3dMVM usage

3dMVM has the standard AFNI-style interface, and most of the usage information can be found at the terminal:

3dMVM -help | less

Three examples are also provided in the help. Input files can be in AFNI, NIfTI, or surface (.niml.dset) format.

Last modified 2014-09-17 17:04