# 3dLME¶

```
================== Welcome to 3dLME ==================
AFNI Group Analysis Program with Linear Mixed-Effects Modeling Approach
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Version 2.1.3, Jan 19, 2023
Author: Gang Chen (gangchen@mail.nih.gov)
Website - https://afni.nimh.nih.gov/sscc/gangc/lme.html
SSCC/NIMH, National Institutes of Health, Bethesda MD 20892
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Usage:
------
3dLME is a group-analysis program that performs linear mixed-effects (LME)
modeling analysis. One simple criterion to decide whether 3dLME is appropriate
is that each subject has to have two or more measurements at each spatial
location (except for a small portion of subjects with missing data). In other
words, at least one within-subject (or repeated-measures) factor serves as
explanatory variable. For complex random-effects structures, use 3dLMEr.
F-statistics for main effects and interactions are automatically included in
the output for all variables. In addition, Student t-tests for quantitative
variables are also in the output. In addition, general linear tests (GLTs) can
be requested via symbolic coding.
If you want to cite the analysis approach, use the following:
Chen, G., Saad, Z.S., Britton, J.C., Pine, D.S., Cox, R.W. (2013). Linear
Mixed-Effects Modeling Approach to FMRI Group Analysis. NeuroImage 73:176-190.
http://dx.doi.org/10.1016/j.neuroimage.2013.01.047
Input files for 3dLME can be in AFNI, NIfTI, or surface (niml.dset) format.
In addition to R installation, the following two R packages need to be acquired
in R first before running 3dLME: "nlme", "lme4" 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("nlme")
install.packages("lme4")
install.packages("phia")
install.packages("snow")
More details about 3dLME can be found at
https://afni.nimh.nih.gov/sscc/gangc/LME.html
Once the 3dLME 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 LME.txt, and execute it with the
following (assuming on tcsh shell),
tcsh -x LME.txt &
or,
tcsh -x LME.txt > diary.txt &
tcsh -x LME.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.
Example 1 --- one condition modeled with 8 basis functions (e.g., TENT or TENTzero)
for one group of 13 subjects. With the option -bounds, values beyond the range will
be treated as outliers and considered as missing. If you want to set a range, choose
the bounds that make sense with your input data.
--------------------------------
3dLME -prefix myOutput -jobs 4 \
-mask myMask+tlrc \
-model '0+Time' \
-bounds -2 2 \
-qVars order \
-qVarCenters 0 \
-ranEff '~1' \
-corStr 'order : AR1' \
-SS_type 3 \
-num_glf 1 \
-glfLabel 1 4TimePoints -glfCode 1 'Time : 1*Diff2 & 1*Diff3 & 1*Diff4 & 1*Diff5' \
-dataTable \
Subj Time order InputFile \
c101 Diff0 0 testData/c101time0+tlrc \
c101 Diff1 1 testData/c101time1+tlrc \
c101 Diff2 2 testData/c101time2+tlrc \
c101 Diff3 3 testData/c101time3+tlrc \
c101 Diff4 4 testData/c101time4+tlrc \
c101 Diff5 5 testData/c101time5+tlrc \
c101 Diff6 6 testData/c101time6+tlrc \
c101 Diff7 7 testData/c101time7+tlrc \
c103 Diff0 0 testData/c103time0+tlrc \
c103 Diff1 1 testData/c103time1+tlrc \
...
Example 2 --- one within-subject factor (conditions: House and Face), one
within-subject quantitative variable (reaction time, RT) and one between-
subjects covariate (age). RT values don't differ significantly between the
two conditions, and thus are centered via grand mean. Random effects are
intercept and RT effect whose correlation is estimated from the data. With
the option -bounds, values beyond [-2, 2] will be treated as outliers and
considered as missing.
-------------------------------------------------------------------------
3dLME -prefix Example2 -jobs 24 \
-model "cond*RT+age" \
-bounds -2 2 \
-qVars "RT,age" \
-qVarCenters "105.35,34.7" \
-ranEff '~1+RT' \
-SS_type 3 \
-num_glt 4 \
-gltLabel 1 'House' -gltCode 1 'cond : 1*House' \
-gltLabel 2 'Face-House' -gltCode 2 'cond : 1*Face -1*House' \
-gltLabel 3 'House-AgeEff' -gltCode 3 'cond : 1*House age :' \
-gltLabel 4 'House-Age2' -gltCode 4 'cond : 1*House age : 5.3' \
-num_glf 1 \
-glfLabel 1 'cond_age' -glfCode 1 'cond : 1*House & 1*Face age :' \
-dataTable \
Subj cond RT age InputFile \
s1 House 124 35 s1+tlrc'[House#0_Coef]' \
s2 House 97 51 s2+tlrc'[House#0_Coef]' \
s3 House 107 25 s3+tlrc'[House#0_Coef]' \
...
s1 Face 110 35 s1+tlrc'[Face#0_Coef]' \
s2 Face 95 51 s2+tlrc'[Face#0_Coef]' \
s3 Face 120 25 s3+tlrc'[Face#0_Coef]' \
...
Example 3 --- one within-subject factor (conditions: positive, negative,
and neutral), and one between-subjects factors (groups: control and patients).
Effect estimates for a few subjects are available for only one or two
conditions. These subjects with missing data would have to be abandoned in
the traditional ANOVA approach. All subjects can be included with 3dLME, and
a random intercept is considered.
-------------------------------------------------------------------------
3dLME -prefix Example3 -jobs 24 \
-mask myMask+tlrc \
-model "cond*group" \
-bounds -2 2 \
-ranEff '~1' \
-SS_type 3 \
-num_glt 6 \
-gltLabel 1 'pos-neu' -gltCode 1 'cond : 1*pos -1*neu' \
-gltLabel 2 'neg' -gltCode 2 'cond : 1*neg ' \
-gltLabel 3 'pos+nue-neg' -gltCode 3 'cond : 1*pos +1*neu -1*neg' \
-gltLabel 4 'pat_pos-neu' -gltCode 4 'cond : 1*pos -1*neu group : 1*pat' \
-gltLabel 5 'pat_neg-neu' -gltCode 5 'cond : 1*neg -1*neu group : 1*pat' \
-gltLabel 6 'pat_pos-neg' -gltCode 6 'cond : 1*pos -1*neg group : 1*pat' \
-num_glf 1 \
-glfLabel 1 'pos-neu' -glfCode 1 'Group : 1*ctr & 1*pat cond : 1*pos -1*neu & 1*pos -1*neg' \
-dataTable \
Subj cond group InputFile \
s1 pos ctr s1+tlrc'[pos#0_Coef]' \
s1 neg ctr s1+tlrc'[neg#0_Coef]' \
s1 neu ctr s1+tlrc'[neu#0_Coef]' \
...
s21 pos pat s21+tlrc'[pos#0_Coef]' \
s21 neg pat s21+tlrc'[neg#0_Coef]' \
s21 neu pat s21+tlrc'[neu#0_Coef]' \
...
Example 4 --- Computing ICC values for two within-subject factor (Cond:
positive, negative, and neutral; Scanner: one, and two) plus subjects (factor
Subj).
-------------------------------------------------------------------------
3dLME -prefix Example4 -jobs 12 \
-mask myMask+tlrc \
-model "1" \
-bounds -2 2 \
-ranEff 'Cond+Scanner+Subj' \
-ICCb \
-dataTable \
Subj Cond Scanner InputFile \
s1 pos one s1_1+tlrc'[pos#0_Coef]' \
s1 neg one s1_1+tlrc'[neg#0_Coef]' \
s1 neu one s1_1+tlrc'[neu#0_Coef]' \
s1 pos two s1_2+tlrc'[pos#0_Coef]' \
s1 neg two s1_2+tlrc'[neg#0_Coef]' \
s1 neu two s1_2+tlrc'[neu#0_Coef]' \
...
s21 pos two s21_2+tlrc'[pos#0_Coef]' \
s21 neg two s21_2+tlrc'[neg#0_Coef]' \
s21 neu two s21_2+tlrc'[neu#0_Coef]' \
...
Options in alphabetical order:
------------------------------
-bounds lb ub: This option is for outlier removal. Two numbers are expected from
the user: the lower bound (lb) and the upper bound (ub). The input data will
be confined within [lb, ub]: any values in the input data that are beyond
the bounds will be removed and treated as missing. Make sure the first number
less than the second. You do not have to use this option to censor your data!
-cio: Use AFNI's C io functions, which is default. Alternatively -Rio
can be used.
-corStr FORMULA: Specify the correlation structure of the residuals. For example,
when analyzing the effect estimates from multiple basis functions,
one may consider account for the temporal structure of residuals with
AR or ARMA.
-cutoff threshold: Specify the cutoff value to obtain voxel-wise accuracy
in logistic regression analysis. Default is 0 (no accuracy will
be estimated).
-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.
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. In the script specify the information with '-dataTable
@table.txt'. 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.
When the table is a stand-alone file, quotes should NOT be added around
the sub-brick selector -- square brackets [...]. Also, there is no need
to add a backslash at the end of each line.
-dbgArgs: This option will enable R to save the parameters in a
file called .3dLME.dbg.AFNI.args in the current directory
so that debugging can be performed.
-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 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 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 effect for a quantitative variable can be specified with,
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 categorial variable has to be followed
by the linear combination of its levels. Only a quantitative
is allowed to have a dangling coding as seen in 'Age :'
-gltLabel k label: Specify the label for the k-th general linear test
(GLT). A symbolic coding for the GLT is assumed to follow with
each -gltLabel.
-help: this help message
-ICC: This option allows 3dLME to compute voxel-wise intra-class correlation
for the variables specified through option -ranEff. See Example 4 in
in the help. Consider using a more flexible program 3dICC. If trial-
level data are available, a more accurate approach is to use the
program TRR at the region level or use the program 3dLMEr at the
level. Refer to the following paper for more detail:
Chen, G., Pine, D.S., Brotman, M.A., Smith, A.R., Cox, R.W., Haller,
S.P., 2021. Trial and error: A hierarchical modeling approach to
test-retest reliability. NeuroImage 245, 118647.
-ICCb: This option allows 3dLME to compute voxel-wise intra-class correlation
through a Bayesian approach with Gamma priors for the variables
specified through option -ranEff. The computation will take much
longer due the sophistication involved. However, the Bayesian method is
preferred to the old approach with -ICC for the typical FMRI data. R
package 'blme' is required for this option. Consider using a more
flexible program 3dICC
-jobs NJOBS: On a multi-processor machine, parallel computing will speed
up the program significantly.
Choose 1 for a single-processor computer.
-LOGIT: This option allows 3dLME to perform voxel-wise logistic modeling.
Currently no random effects are allowed ('-ranEff NA'), but this
limitation can be removed later if demand occurs. The InputFile
column is expected to list subjects' responses in 0s and 1s. In
addition, one voxel-wise covariate is currently allowed. Each
regression coefficient (including the intercept) and its z-statistic
are saved in the output.
-logLik: Add this option if the voxel-wise log likelihood is wanted in the output.
This option currently cannot be combined with -ICC, -ICCb, -LOGIT.
-mask MASK: Process voxels inside this mask only.
Default is no masking.
-ML: Add this option if Maximum Likelihood is wanted instead of the default
method, Restricted Maximum Likelihood (REML).
-model FORMULA: Specify the terms of fixed effects for all explanatory,
including quantitative, variables. 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. Subject should not occur in the model
specification here.
-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 effect with each factor
at the reference level (alphabetically the lowest level) for each
factor and with each quantitative covariate at the center value.
-qVarCenters VALUES: Specify centering values for quantitative variables
identified under -qVars. Multiple centers are separated by
commas (,) without any other characters such as spaces and should
be surrounded within (single or double) quotes. The order of the
values should match that of the quantitative variables in -qVars.
Default (absence of option -qVarsCenters) 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 -qVarsCenters 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 are better modeled with 3dLME.
-ranEff FORMULA: Specify the random effects. The simplest and most common
one is random intercept, "~1", meaning that each subject deviates some
amount (called random effect) from the group average. "~RT" or "~1+RT"
means that each subject has a unique intercept as well as a slope,
and the correlation between the two random effects are estimated, not
assumed, from the data. "~0+RT" indicates that only a random effect
of slope is desired. Compound symmetry for a variance-covariance metric
across the levels of factor A can be specified through pdCompSymm(~0+A)
The list of random terms should be separated by space within (single or
double) quotes.
Notice: In the case of computing ICC values, list all the factors with
which the ICC is to be obtained. For example, with two factors "Scanner"
and "Subj", set it as -ranEff "Scanner+Subj". See Example 4 in the
the help.
-RE: Specify the list of variables whose random effects are saved in the output.
For example, "RE "Intercept"" requests for saving the random
intercept for all subjects while "RE "Intercept,time"" asks for
saving both the random intercept and random slope of time for all subjects
The output filename is specified through -REprefix. All random effects are
stored in the same file with each sub-brick named by the variable name plus
the subject label.
-REprefix: Specify the output filename for random effects. All random effects are
stored in the same file with each sub-brick named by the variable name plus
the subject label.
-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. The sub-brick labeled with the '(Intercept)',
if present, should be interpreted as the effect with each factor
at the reference level (alphabetically the lowest level) for each
factor and with each quantitative covariate at the center value.
-Rio: Use R's io functions. The alternative is -cio.
-show_allowed_options: list of allowed options
-SS_type NUMBER: Specify the type for sums of squares in the F-statistics.
Two options are currently supported: sequential (1) and marginal (3).
-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 -vVarsCenters) 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.
```