Hi Laura
In the
wikihttps://surfer.nmr.mgh.harvard.edu/fswiki/LinearMixedEffectsModelswe
recommended to order the columns of the design matrix in thefollowing way:
Column 1: theintercept term (which is a column of ones)
Colum 2: the timecovariate if it varies across subjects (eg. time from baseline)
Column 3-q: anytime-varying covariates (eg. training: 0 before training, 1
aftertraining)
Column q+1-r: thegroup covariates of interest (eg. a binary variable
indicatingwhether or not the subject is a patient), for n groups you will
haven-1 binary covariates
Column r+1-s:interactions between group covariates with the
time-varyingcovariates (only the interesting interactions)
Column s+1-p: anyother nuisance time-invariant covariates (eg. age-at-baseline,
gender,etc...)
LME is a type oflinear regression model that integrates both a model for the
mean anda model for the covariance into a single statistical model. So ifyou
want to compare different models for the mean (with differentcovariates) then
you need to start with a “maximal model for themean” that includes all the
possible covariates of interest. Then you selectthe random effects for that
"maximal model" using the model selectionprocedure with lme_mass_LR. Random
effects can only be time-varyingcovariates (i.e a subset of the columns from 1
to q above, thosecomprise the Zcols parameter in lme_mass_fit_vw)
After you choosewhich time-varying covariates are going to be considered as
randomeffects then you can test if any single fixed effects covariate in your
designmatrix has a significant contribution to the model in the same wayyou
would for a traditional GLM. You will use F-tests for that.Covariates that do
not significantly contribute to the model can beruled out of the model and a
new model with less covariates but the same random effects can thenbe fitted.
Keep in mind thatfitting lme models is computationally expensive and the
computationoverhead quickly increases with the number of random effects and
fixedeffects in your model. Also considering one or two random effects
including the intercept term (or atmost three) is usually enough but this
really depends on the natureof the data.
Best-Jorge
De: Laura Rueda Delgado <laura.ruedadelg...@kuleuven.be>
Para: Freesurfer support list <freesurfer@nmr.mgh.harvard.edu>
Enviado: Lunes 11 de abril de 2016 13:05
Asunto: Re: [Freesurfer] LME for functional data, 3 factors
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div.yiv9346679664WordSection1 {}#yiv9346679664 Dear Martin, Thank you for
your quick response. My research question is focused on the group and day
effect, so I could simplify the model. From your response, I thought of
including in the design matrix the binary code for Condition 2, and for
Condition 3 in two columns, like you suggested; however, adding only the
interaction effect of group and day. This way, the model takes into account the
repeated measures of Condition while remaining relatively simple. Now, to
add more complexity and be more specific, I'm interested on neural correlates
of learning, which is (un)fortunately tangled with performance. Therefore, I
was thinking to add the learning gains (e.g. [performance_day_2 -
performance_day_1]/performance_day_1) as a fixed effect. Checking the example
datasets that come with the LME toolbox, I see that other measures (e.g. age,
gender) are repeated for all the measures at different days of the same
subject. And, when the age of participants at the first measurement is used as
a fixed effect, "baseline age", the value is repeated for the baseline day and
the other days. I was wondering if this could be applied for the Learning Gain
as well (which is a measure of change of performance over the training days). I
have my doubts because I would understand that this type of coding would
describe two mixed aspects: a “prediction” of Gain from the brain data at Day
1, along with the appropriate relationship of Gain with brain data at Day 2. I
would think that adding 0s for Day 1 in the variable Gain would be more
appropriate, and this way the fixed effect of Day would be coded in the
variable Gain. But of course, I recur to the experts to settle this issue.
Additionally, I see that I could compare two models with different number of
random effects with lme_mass_LR. However, I would like to compare models with
different covariates (other covariates of no interest, like gender and years of
education). Is this possible within this toolbox? Best regards, Laura
Rueda From: freesurfer-boun...@nmr.mgh.harvard.edu
[mailto:freesurfer-boun...@nmr.mgh.harvard.edu]On Behalf Of Martin Reuter
Sent: donderdag 7 april 2016 18:20
To: freesurfer@nmr.mgh.harvard.edu
Subject: Re: [Freesurfer] LME for functional data, 3 factors Hi Laura,
1)
you would need to model the 3 level variable differently, as 1,2,3 will be
understood as continuous and that is not what you want. Instead you have two
columns: one column for group 2, where all instances are binary (1 if group is
2, else 0), and one for group 3. Then the intercept and slope will be for group
1 and these columns contain the offsets for group 2 and 3 respectively.
About interactions, make sure you really want to model all interactions. Some
may be not very meaningful and keeping the model simple is usually a good idea.
But if you want them all, add them all.
2) Zcols: Vector with the indices of the colums of X that will be considered
as random effects. Usually the intercept is a random effect and maybe other
variables (e.g. the time, if you want to allow slopes to be different across
subjects). For just the intercept column use [ 1]
ni should be correct
3) yes, but with the design above, since you model a global intercept and then
the offset of each group (or whatever that three condition variable is) you
need to make sure you interpret things correctly. E.g. a 1 in such a column for
group 2 or three indicates that there is a difference from the first group.
This is not the group 2 effect.
4) Sorry, I don't know. Maybe someone else has a suggest.
Since you have all interactions, you should be able to specify contrast
according to your test in this model and don't need to create a new one. Your
setup is a little complicated, so it would be wise to involve a local
statistician to make sure you are interpreting things correctly.
Best, Martin
On 04/07/2016 10:57 AM, Laura Rueda Delgado wrote:
Dear FreeSurfers and LME experts, I've just started using the LME toolbox by
Bernal-Rusiel et al (2012, 2013) in Matlab, apart from FreeSurfer. My
experimental design includes one between-subjects factor (group with two
levels, 24 vs 22 subjects), and two within-subjects (WS) factors (day with two
levels, and condition with three levels). As far as I understand, the LME
toolbox can be used for longitudinal data and for investigating modulations of
neural activity with behavioral measures. However, it's been difficult for me
to set up both the design matrix and the input of the LME functions given three
fixed factors in my design (I haven't included behavior yet). So I have a few
questions that I hope you can help me answer. I follow these steps: 1)
Following the wiki, I've created a pre-design matrix, M, with: First column:
Day factor coded as 0 (first day) and 7 (7 days later, as during acquisition).
Second column: Group factor binary coded. Third column: Condition factor coded
with dummy variables 1 to 3 (three conditions in total). I don’t know if this
is correct; I have failed to find in the mailing list any reference to an
additional repeated measure besides time in LME models. From here, I've created
the design matrix X adding a column of 1's for the intercept, adding the pre
design matrix M, and adding columns for every possible interaction by
multiplying element-wise the columns of M (including two-way and three-way
interactions). 2) I then use lme_mass_fit_vw, but I have doubts about some
inputs Zcols: column 1 in X ni: created a vector with 6 for all subjects (in
total there are 6 repeated measures, 2 of day and 3 of condition) I kept the
others as default. 3) lme_mass_F for statistics of fixed effects. I check
main effects and interactions with contrasts based on the design matrix X:
placing a 1 in the column position corresponding to each effect of interest.
4) lme_mass_FDR2 for correcting the F stats for multiple comparisons. I would
like to compare the results using AlphaSim's Monte-Carlo simulations, however
I'm not sure what image to use to estimate the smoothness. Would you have a
suggestion? Could you please let me know if this procedure is sound? Also, if
I’m interested in specific comparisons or post-hoc tests, e.g. Group 1$Day
1$Condition 3 vs. Group 1$Day 2$Condition 3, would I need a separate model for
that? And lastly, for the analysis including the behavioral measures, should I
just include them as a forth column in the pre-design matrix M and add the
relevant effects in X? I hope I haven’t overwhelmed you with so many
questions. I would greatly appreciate any suggestion you can provide. Best
regards, Laura Rueda
_______________________________________________ Freesurfer mailing list
Freesurfer@nmr.mgh.harvard.edu
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-- Martin Reuter, PhD Assistant Professor of Radiology, Harvard Medical
School Assistant Professor of Neurology, Harvard Medical School A.A.Martinos
Center for Biomedical Imaging Massachusetts General Hospital Research
Affiliate, CSAIL, MIT Phone: +1-617-724-5652 Web : http://reuter.mit.edu
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