# 3dMVM¶

## Welcome to 3dMVM¶

```
AFNI Group Analysis Program with Multi-Variate Modeling Approach
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Version 4.1.6, Nov 2, 2023
Author: Gang Chen (gangchen@mail.nih.gov)
Website - https://afni.nimh.nih.gov/MVM
SSCC/NIMH, National Institutes of Health, Bethesda MD 20892
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
```

## Usage:¶

```
3dMVM is a group-analysis program that performs traditional ANOVA- and ANCOVA-
style computations. In addition, it can run multivariate modeling in the sense
of multiple simultaneous response variables. For univariate analysis, no bound
is imposed on the numbers of explanatory variables, and these variables can be
either categorical (factor) or numerical/quantitative (covariate). F-statistics
for all main effects and interactions are automatically included in the output.
In addition, general linear tests (GLTs) can be requested via symbolic coding.
Input files for 3dMVM can be in AFNI, NIfTI, or surface (niml.dset) format.
Note that unequal number of subjects across groups are allowed, but scenarios
with missing data for a within-subject factor are better modeled with 3dLME or
3dLMEr. Cases with quantitative variables (covariates) that vary across the
levels of a within-subject variable are also better handled with 3dLME or 3dLMEr.
Computational cost with 3dMVM is higher relative to 3dttest++ or 3dANOVAx, but
it has the capability to correct for sphericity violations when within-subject
factors with more than two levels are involved.
```

## Please cite:¶

### If you want to cite the analysis approach for AN(C)OVA, use the following¶

```
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,
571-588. 10.1016/j.neuroimage.2014.06.027
https://afni.nimh.nih.gov/pub/dist/HBM2014/Chen_in_press.pdf
```

### For group analysis with effect estimates from multiple basis functions, cite:¶

```
Chen, G., Saad, Z.S., Adleman, N.E., Leibenluft, E., Cox, R.W. (2015).
Detecting the subtle shape differences in hemodynamic responses at the
group level. Front. Neurosci., 26 October 2015.
http://dx.doi.org/10.3389/fnins.2015.00375
```

## Installation requirements:¶

```
In addition to R installation, the following two R packages need to be acquired
in R first before running 3dMVM: "afex" and "phia". In addition, the "snow" package
is also needed if one wants to take advantage of parallel computing. To install
these packages, run the following command at the terminal:
rPkgsInstall -pkgs ALL
Alternatively, you may install them in R:
install.packages("afex")
install.packages("phia")
install.packages("snow")
More details about 3dMVM can be found at
https://afni.nimh.nih.gov/MVM
```

## Running:¶

```
Once the 3dMVM command script is constructed, it can be run by copying and
pasting to the terminal. Alternatively (and probably better) you save the
script as a text file, for example, called MVM.txt, and execute it with the
following (assuming on tcsh shell),
tcsh -x MVM.txt &
or,
tcsh -x MVM.txt > diary.txt &
tcsh -x MVM.txt |& tee diary.txt &
The advantage of the latter command is that the progression is saved into
the text file diary.txt and, if anything goes awry, can be examined later.
Thanks to the R community, Henrik Singmann, and Helios de Rosario for the
strong technical support.
```

## Examples:¶

### Example 1 — 3 between-subjects and 2 within-subject variables:¶

```
Three between-subjects (genotype, sex, and scanner) and two within-subject
(condition and emotion) variables.
3dMVM -prefix Example1 -jobs 4 \
-bsVars 'genotype*sex+scanner' \
-wsVars "condition*emotion" \
-mask myMask+tlrc \
-SS_type 2 \
-num_glt 14 \
-gltLabel 1 face_pos_vs_neg -gltCode 1 'condition : 1*face emotion : 1*pos -1*neg' \
-gltLabel 2 face_emot_vs_neu -gltCode 2 'condition : 1*face emotion : 1*pos +1*neg -2*neu' \
-gltLabel 3 sex_by_condition_interaction -gltCode 3 'sex : 1*male -1*female condition : 1*face -1*house' \
-gltLabel 4 3way_interaction -gltCode 4 'sex : 1*male -1*female condition : 1*face -1*house emotion : 1*pos -1*neg' \
-num_glf 3 \
-glfLabel 1 male_condXEmo -glfCode 1 'sex : 1*male condition : 1*face -1*house emotion : 1*pos -1*neg & 1*pos -1*neu' \
-glfLabel 2 face_sexXEmo -glfCode 2 'sex : 1*male -1*female condition : 1*face emotion : 1*pos -1*neg & 1*pos -1*neu' \
-glfLabel 3 face_sex2Emo -glfCode 3 'sex : 1*male & 1*female condition : 1*face emotion : 1*pos -1*neg & 1*pos -1*neu' \
-dataTable \
Subj genotype sex scanner condition emotion InputFile \
s1 TT male scan1 face pos s1+tlrc'[face_pos_beta]' \
s1 TT male scan1 face neg s1+tlrc'[face_neg_beta]' \
s1 TT male scan1 face neu s1+tlrc'[face_neu_beta]' \
s1 TT male scan1 house pos s1+tlrc'[house_pos_beta]' \
s68 TN female scan2 house pos s68+tlrc'[face_pos_beta]' \
s68 TN female scan2 house neg s68+tlrc'[face_neg_beta]' \
s68 TN female scan2 house neu s68+tlrc'[house_pos_beta]'
```

#### NOTE:¶

```
1) The 3rd GLT is for the 2-way 2 x 2 interaction between sex and condition, which
is essentially a t-test (or one degree of freedom for the numerator of F-statistic).
Multiple degrees of freedom for the numerator of F-statistic can be obtained through
option -glfCode (see GLFs #1, #2, and #3).
2) Similarly, the 4th GLT is a 3-way 2 x 2 x 2 interaction, which is a partial (not full)
interaction between the three factors because 'emotion' has three levels. The F-test for
the full 2 x 2 x 3 interaction is automatically spilled out by 3dMVM.
3) The three GLFs show the user how to specify sub-interactions.
4) Option '-SS_type 2' specifies the hierarchical type for the sums of squares in the
omnibus F-statistics in the output. See more details in the help.
```

### Example 2 — 2 between-subjects, 1 within-subject, 2 quantitative variables:¶

```
Two between-subjects (genotype and sex), one within-subject
(emotion) factor, plus two quantitative variables (age and IQ).
3dMVM -prefix Example2 -jobs 24 \
-mask myMask+tlrc \
-bsVars "genotype*sex+age+IQ" \
-wsVars emotion \
-qVars "age,IQ" \
-qVarCenters '25,105' \
-num_glt 10 \
-gltLabel 1 pos_F_vs_M -gltCode 1 'sex : 1*female -1*male emotion : 1*pos' \
-gltLabel 2 age_pos_vs_neg -gltCode 2 'emotion : 1*pos -1*neg age :' \
-gltLabel 3 age_pos_vs_neg -gltCode 3 'emotion : 1*pos -1*neg age : 5' \
-gltLabel 4 genotype_by_sex -gltCode 4 'genotype : 1*TT -1*NN sex : 1*male -1*female' \
-gltLabel 5 genotype_by_sex_emotion -gltCode 5 'genotype : 1*TT -1*NN sex : 1*male -1*female emotion : 1*pos -1*neg' \
-dataTable \
Subj genotype sex age IQ emotion InputFile \
s1 TT male 24 107 pos s1+tlrc'[pos_beta]' \
s1 TT male 24 107 neg s1+tlrc'[neg_beta]' \
s1 TT male 24 107 neu s1+tlrc'[neu_beta]' \
s63 NN female 29 110 pos s63+tlrc'[pos_beta]' \
s63 NN female 29 110 neg s63+tlrc'[neg_beta]' \
s63 NN female 29 110 neu s63+tlrc'[neu_beta]'
```

#### NOTE:¶

```
1) The 2nd GLT shows the age effect (slope) while the 3rd GLT reveals the contrast
between the emotions at the age of 30 (5 above the center). On the other hand,
all the other GLTs (1st, 4th, and 5th) should be interpreted at the center Age
value, 25 years old.
2) The 4th GLT is for the 2-way 2 x 2 interaction between genotype and sex, which
is essentially a t-test (or one degree of freedom for the numerator of F-statistic).
Multiple degrees of freedom for the numerator of F-statistic is currently unavailable.
3) Similarly, the 5th GLT is a 3-way 2 x 2 x 2 interaction, which is a partial (not full)
interaction between the three factors because 'emotion' has three levels. The F-test for
the full 2 x 2 x 3 interaction is automatically spilled out by 3dMVM.
```

### Example 3 — Getting more complicated:¶

```
BOLD response was modeled with multiple basis functions at individual
subject level. In addition, there are one between-subjects (Group) and one within-
subject (Condition) variable. Furthermore, the variable corresponding to the number
of basis functions, Time, is also a within-subject variable. In the end, the F-
statistics for the interactions of Group:Condition:Time, Group:Time, and
Condition:Time are of specific interest. And these interactions can be further
explored with GLTs in 3dMVM.
3dMVM -prefix Example3 -jobs 12 \
-mask myMask+tlrc \
-bsVars Group \
-wsVars 'Condition*Time' \
-num_glt 32 \
-gltLabel 1 old_t0 -gltCode 1 'Group : 1*old Time : 1*t0' \
-gltLabel 2 old_t1 -gltCode 2 'Group : 1*old Time : 1*t1' \
-gltLabel 3 old_t2 -gltCode 3 'Group : 1*old Time : 1*t2' \
-gltLabel 4 old_t3 -gltCode 4 'Group : 1*old Time : 1*t3' \
-gltLabel 5 yng_t0 -gltCode 5 'Group : 1*yng Time : 1*t0' \
-gltLabel 6 yng_t1 -gltCode 6 'Group : 1*yng Time : 1*t1' \
-gltLabel 7 yng_t2 -gltCode 7 'Group : 1*yng Time : 1*t2' \
-gltLabel 8 yng_t3 -gltCode 8 'Group : 1*yng Time : 1*t3' \
-gltLabel 17 old_face_t0 -gltCode 17 'Group : 1*old Condition : 1*face Time : 1*t0' \
-gltLabel 18 old_face_t1 -gltCode 18 'Group : 1*old Condition : 1*face Time : 1*t1' \
-gltLabel 19 old_face_t2 -gltCode 19 'Group : 1*old Condition : 1*face Time : 1*t2' \
-gltLabel 20 old_face_t3 -gltCode 20 'Group : 1*old Condition : 1*face Time : 1*t3' \
-dataTable \
Subj Group Condition Time InputFile \
s1 old face t0 s1+tlrc'[face#0_beta]' \
s1 old face t1 s1+tlrc'[face#1_beta]' \
s1 old face t2 s1+tlrc'[face#2_beta]' \
s1 old face t3 s1+tlrc'[face#3_beta]' \
s40 yng house t0 s40+tlrc'[house#0_beta]' \
s40 yng house t1 s40+tlrc'[house#1_beta]' \
s40 yng house t2 s40+tlrc'[house#2_beta]' \
s40 yng house t3 s40+tlrc'[house#3_beta]'
```

#### NOTE:¶

```
The model for the analysis can also be set up as and is equivalent to
'Group*Condition*Time'.
```

## Options:¶

```
Options in alphabetical order:
-bsVars FORMULA: Specify the fixed effects for between-subjects factors
and quantitative variables. When no between-subject factors
are present, simply put 1 for FORMULA. The expression FORMULA
with more than one variable has to be surrounded within (single or
double) quotes. No spaces are allowed in the FORMULA expression.
Variable names in the formula should be consistent with the ones
used in the header underneath -dataTable. A+B represents the
additive effects of A and B, A:B is the interaction between A
and B, and A*B = A+B+A:B. The effects of within-subject
factors, if present under -wsVars are automatically assumed
to interact with the ones specified here. Subject as a variable
should not occur in the model specification here.
-cio: Use AFNI's C io functions, which is default. Alternatively -Rio
can be used.
-dataTable TABLE: List the data structure with a header as the first line.
NOTE:
1) This option has to occur last; that is, no other options are
allowed thereafter. Each line should end with a backslash except for
the last line.
2) The first column is fixed and reserved with label 'Subj', and the
last is reserved for 'InputFile'. Each row should contain only one
effect estimate in the table of long format (cf. wide format) as
defined in R. The level labels of a factor should contain at least
one character. Input files can be in AFNI, NIfTI or surface format.
AFNI files can be specified with sub-brick selector (square brackets
[] within quotes) specified with a number or label. Unequal number of
subjects across groups are allowed, but situations with missing data
for a within-subject factor are better handled with 3dLME or 3dLMEr.
3) It is fine to have variables (or columns) in the table that are
not modeled in the analysis.
4) The context of the table can be saved as a separate file, e.g.,
called table.txt. Do not forget to include a backslash at the end of
each row. In the script specify the data with '-dataTable @table.txt'.
Do NOT put any quotes around the square brackets for each sub-brick!
Otherwise, the program cannot properly read the files for some reason.
This option is useful: (a) when there are many input files so that
the program complains with an 'Arg list too long' error; (b) when
you want to try different models with the same dataset (see 3) above).
-dbgArgs: This option will enable R to save the parameters in a
file called .3dMVM.dbg.AFNI.args in the current directory
so that debugging can be performed.
-GES: As an analog of the determination coefficient R^2 in multiple
regression, generalized eta-squared (GES) provides a measure
of effect size for each F-stat in ANOVA or general GLM, and
renders a similar interpretation: proportion of variance in
the response variable by the explanatory variable on hand.
It ranges within [0, 1]. Notice that this option is only
available with R version 3.2 and afex version 0.14 or later.
-glfCode k CODING: Specify the k-th general linear F-test (GLF) through a
weighted combination among factor levels. The symbolic coding has
to be within (single or double) quotes. For example, the coding
'Condition : 1*A -1*B & 1*A -1*C Emotion : 1*pos' tests the main
effect of Condition at the positive Emotion. Similarly, the coding
'Condition : 1*A -1*B & 1*A -1*C Emotion : 1*pos -1*neg' shows
the interaction between the three levels of Condition and the two
levels of Emotion.
NOTE:
1) The weights for a variable do not have to add up to 0.
2) When a quantitative variable is present, other effects are
tested at the center value of the covariate unless the covariate
value is specified as, for example, 'Group : 1*Old Age : 2', where
the Old Group is tested at the Age of 2 above the center.
3) The absence of a categorical variable in a coding means the
levels of that factor are averaged (or collapsed) for the GLF.
4) The appearance of a categorical variable has to be followed
by the linear combination of its levels.
-glfLabel k label: Specify the label for the k-th general linear F-test
(GLF). A symbolic coding for the GLF is assumed to follow with
each -glfLabel.
-gltCode k CODING: Specify the k-th general linear t-test (GLT) through a
weighted combination among factor levels. The symbolic coding has
to be within (single or double) quotes. For example, the following
'Condition : 2*House -3*Face Emotion : 1*positive '
requests for a test of comparing 2 times House condition
with 3 times Face condition while Emotion is held at positive
valence.
NOTE:
1) The weights for a variable do not have to add up to 0.
2) When a quantitative covariate is involved in the model, the
absence of the covariate in the GLT coding means that the test
will be performed at the center value of the covariate. However,
if the covariate value is specified with a value after the colon,
for example, 'Group : 1*Old Age : 2', the effect of the Old Group
would be tested at the value of 2 above the center. On the other
hand, 'Group : 1*Old' tests for the effect of the Old Group at the
center age.
3) The effect for a quantitative variable (or slope) can be specified
by omitting the value after the colon. For example,
'Group : 1*Old Age : ', or 'Group : 1*Old - 1*Young Age : '.
4) The absence of a categorical variable in a coding means the
levels of that factor are averaged (or collapsed) for the GLT.
5) The appearance of a categorical variable has to be followed
by the linear combination of its levels. Only a quantitative variable
is allowed to have a dangling coding as seen in 'Age :'.
6) Some special interaction effects can be tested under -gltCode
when the numerical DF is 1. For example, 'Group : 1*Old -1*Young
Condition : 1*House -1*Face Emotion : 1*positive'. Even though
this is typically an F-test that can be coded under -glfCode, it
can be tested under -gltCode as well. An extra bonus is that the
t-test shows the directionality while F-test does not.
-gltLabel k label: Specify the label for the k-th general linear t-test
(GLT). A symbolic coding for the GLT is assumed to follow with
each -gltLabel.
-help: this help message
-jobs NJOBS: On a multi-processor machine, parallel computing will speed
up the program significantly.
Choose 1 for a single-processor computer.
-mask MASK: Process voxels inside this mask only.
Default is no masking.
-model FORMULA: This option will phase out at some point. So use -bsVars
instead. Specify the fixed effects for between-subjects factors
and quantitative variables. When no between-subject factors
are present, simply put 1 for FORMULA. The expression FORMULA
with more than one variable has to be surrounded within (single or double)
quotes. Variable names in the formula should be consistent with
the ones used in the header of -dataTable. A+B represents the
additive effects of A and B, A:B is the interaction between A
and B, and A*B = A+B+A:B. The effects of within-subject
factors, if present under -wsVars, are automatically assumed
to interact with the ones specified here. Subject as a variable
should not occur in the model specification here.
-mVar variable: With this option, the levels of the within-subject factor
will be treated as simultaneous variables in a multivariate model.
For example, when the hemodynamic response time course is modeled
through multiple basis functions such as TENT, TENTzero, CSPLIN,
CSPLINzero, SPMG2/3, etc., the effect estimates at the multiple
time points can be treated as simultaneous response variables in
a multivariate model. Only one within-subject variable is allowed
currently under -mVar. In addition, in the presence of -mVar, no
other within-subject factors should be included. If modeling
extra within-subject factors with -mVar is desirable, consider
flattening such factors; that is, perform multiple analyses
at each level or their contrasts of the factor. The output
for multivariate testing are labeled with -MV0- in the sub-brick
names.
-num_glf NUMBER: Specify the number of general linear F-tests (GLFs). A glf
involves the union of two or more simple tests. See details in
-glfCode.
-num_glt NUMBER: Specify the number of general linear t-tests (GLTs). A glt
is a linear combination of a factor levels. See details in
-gltCode.
-prefix PREFIX: Output file name. For AFNI format, provide prefix only,
with no view+suffix needed. Filename for NIfTI format should have
.nii attached, while file name for surface data is expected
to end with .niml.dset. The sub-brick labeled with the '(Intercept)',
if present, should be interpreted as the overall average
across factor levels at the center value of each covariate.
-qVarCenters VALUES: Specify centering values for quantitative variables
identified under -qVars. Multiple centers are separated by
commas (,) within (single or double) quotes. The order of the
values should match that of the quantitative variables in -qVars.
Default (absence of option -qVarCetners) means centering on the
average of the variable across ALL subjects regardless their
grouping. If within-group centering is desirable, center the
variable YOURSELF first before the values are fed into -dataTable.
-qVars variable_list: Identify quantitative variables (or covariates) with
this option. The list with more than one variable has to be
separated with comma (,) without any other characters such as
spaces, and should be surrounded within (single or double) quotes.
For example, -qVars "Age,IQ"
WARNINGS:
1) Centering a quantitative variable through -qVarCenters is
very critical when other fixed effects are of interest.
2) Between-subjects covariates are generally acceptable.
However EXTREME caution should be taken when the groups
differ significantly in the average value of the covariate.
3) Within-subject covariates vary across the levels of a
within-subject factor, and can be analyzed with 3dLME or 3dLMEr,
but not 3dMVM.
-resid PREFIX: Output file name for the residuals. For AFNI format, provide
prefix only without view+suffix. Filename for NIfTI format should
have .nii attached, while file name for surface data is expected
to end with .niml.dset.
-Rio: Use R's io functions. The alternative is -cio.
-robust: Robust regression is performed so that outliers can be
reasonably handled through MM-estimation. Currently it
only works without involving any within-subject factors.
That is, anything that can be done with 3dttest++ could
be analyzed through robust regression here (except for
one-sample case which can be added later on if requested).
Pairwise comparisons can be performed by providing
contrast from each subject as input). Post hoc F-tests
through option -glfCode are currently not available with
robust regression. This option requires that the user
install R package robustbase.
-SC: If a within-subject factor with more than *two* levels is
involved in the model, 3dMVM automatically provides the
F-statistics for main and interaction effects with
sphericity assumption. If the assumption is violated,
the F-statistics could be inflated to some extent. This option,
will enable 3dMVM to additionally output the F-statistics of
sphericity correction for main and interaction effects, which
are labeled with -SC- in the sub-brick names.
NOTE: this option should be used only when at least one
within-subject factor has more than TWO levels.
-show_allowed_options: list of allowed options
-SS_type 2/3: Specify the type for the sums of squares for the omnibus
F-statistics. Type 2 is hierarchical or partially sequential
while type 3 is marginal. Type 2 is more powerful if all the
relevant higher-order interactions do not exist. The default
is 3. The controversy surrounding the different types can be
found at https://sscc.nimh.nih.gov/sscc/gangc/SS.html
-verb VERB: Specify verbosity level.
-vVarCenters VALUES: Specify centering values for voxel-wise covariates
identified under -vVars. Multiple centers are separated by
commas (,) within (single or double) quotes. The order of the
values should match that of the quantitative variables in -qVars.
Default (absence of option -vVarsCetners) means centering on the
average of the variable across ALL subjects regardless their
grouping. If within-group centering is desirable, center the
variable YOURSELF first before the files are fed into -dataTable.
-vVars variable_list: Identify voxel-wise covariates with this option.
Currently one voxel-wise covariate is allowed only, but this
may change if demand occurs...
By default, mean centering is performed voxel-wise across all
subjects. Alternatively centering can be specified through a
global value under -vVarsCenters. If the voxel-wise covariates
have already been centered, set the centers at 0 with -vVarsCenters.
-wsE2: If at least one within-subject factor is involved in the model, any
omnibus F-test associated with a within-subject factor is assessed
with both univariate and within-subject multivariate tests. Use
the option only if at least one within-subject factor has more
than two levels. By default, 3dMVM provides an F-stat through the
univariate testing (UVT) method for each effect that involves a
within-subject factor. With option -wsE2 UVT is combined with the
within-subject multivariate approach, and the merged result remains
the same as UVT most of the time (or in most brain regions), but
occasionally it may be more powerful.
-wsMVT: By default, 3dMVM provides an F-stat through univariate testing (UVT)
for each effect that involves a within-subject factor. If at least
one within-subject factor is involved in the model, option -wsMVT
provides within-subject multivariate testing for any effect
associated with a within-subject variable. The testing strategy is
different from the conventional univariate GLM, see more details in
Chen et al. (2014), Applications of Multivariate Modeling to
Neuroimaging Group Analysis: A Comprehensive Alternative to
Univariate General Linear Model. NeuroImage 99, 571-588. If
all the within-subject factors have two levels, the multivariate
testing would render the same results as the univariate version.
So, use the option only if at least one within-subject factor has
more than two levels. The F-statistics from the multivariate
testing are labeled with -wsMVT- in the sub-brick names. Note that
the conventional univariate F-statistics are automatically included
in the beginning of the output regardless the presence of this option.
-wsVars FORMULA: Within-subject factors, if present, have to be listed
here, otherwise the program will choke. If no within-subject
exists, don't include this option in the script. Coding for
additive effects and interactions is the same as in -bsVars. The
FORMULA with more than one variable has to be surrounded
within (single or double) quotes. Note that the within-subject
variables are assumed to interact with those between-subjects
variables specified under -bsVars. The hemodynamic response
time courses are better modeled as simultaneous outcomes through
option -mVar, and not as the levels of a within-subject factor.
The variables under -wsVars and -mVar are exclusive from each
other.
```