# 1dSEM¶

```
Usage: 1dSEM [options] -theta 1dfile -C 1dfile -psi 1dfile -DF nn.n
Computes path coefficients for connection matrix in Structural Equation
Modeling (SEM)
The program takes as input :
1. A 1D file with an initial representation of the connection matrix
with a 1 for each interaction component to be modeled and a 0 if
if it is not to be modeled. This matrix should be PxP rows and column
2. A 1D file of the C, correlation matrix, also with dimensions PxP
3. A 1D file of the residual variance vector, psi
4. The degrees of freedom, DF
Output is printed to the terminal and may be redirected to a 1D file
The path coefficient matrix is printed for each matrix computed
Options:
-theta file.1D = connection matrix 1D file with initial representation
-C file.1D = correlation matrix 1D file
-psi file.1D = residual variance vector 1D file
-DF nn.n = degrees of freedom
-max_iter n = maximum number of iterations for convergence (Default=10000).
Values can range from 1 to any positive integer less than 10000.
-nrand n = number of random trials before optimization (Default = 100)
-limits m.mmm n.nnn = lower and upper limits for connection coefficients
(Default = -1.0 to 1.0)
-calccost = no modeling at all, just calculate the cost function for the
coefficients as given in the theta file. This may be useful for verifying
published results
-verbose nnnnn = print info every nnnnn steps
Model search options:
Look for best model. The initial connection matrix file must follow these
specifications. Each entry must be 0 for entries excluded from the model,
1 for each required entry in the minimum model, 2 for each possible path
to try.
-tree_growth or
-model_search = search for best model by growing a model for one additional
coefficient from the previous model for n-1 coefficients. If the initial
theta matrix has no required coefficients, the initial model will grow from
the best model for a single coefficient
-max_paths n = maximum number of paths to include (Default = 1000)
-stop_cost n.nnn = stop searching for paths when cost function is below
this value (Default = 0.1)
-forest_growth or
-grow_all = search over all possible models by comparing models at
incrementally increasing number of path coefficients. This
algorithm searches all possible combinations; for the number of coeffs
this method can be exceptionally slow, especially as the number of
coefficients gets larger, for example at n>=9.
-leafpicker = relevant only for forest growth searches. Expands the search
optimization to look at multiple paths to avoid local minimum. This method
is the default technique for tree growth and standard coefficient searches
This program uses a Powell optimization algorithm to find the connection
coefficients for any particular model.
References:
Powell, MJD, "The NEWUOA software for unconstrained optimization without
derivatives", Technical report DAMTP 2004/NA08, Cambridge University
Numerical Analysis Group:
See: http://www.ii.uib.no/~lennart/drgrad/Powell2004.pdf
Bullmore, ET, Horwitz, B, Honey, GD, Brammer, MJ, Williams, SCR, Sharma, T,
How Good is Good Enough in Path Analysis of fMRI Data?
NeuroImage 11, 289-301 (2000)
Stein, JL, et al., A validated network of effective amygdala connectivity,
NeuroImage (2007), doi:10.1016/j.neuroimage.2007.03.022
The initial representation in the theta file is non-zero for each element
to be modeled. The 1D file can have leading columns for labels that will
be used in the output. Label rows must be commented with the # symbol
If using any of the model search options, the theta file should have a '1' for
each required coefficient, '0' for each excluded coefficient, '2' for an
optional coefficient. Excluded coefficients are not modeled. Required
coefficients are included in every computed model.
N.B. - Connection directionality in the path connection matrices is from
column to row of the output connection coefficient matrices.
Be very careful when interpreting those path coefficients.
First of all, they are not correlation coefficients. Suppose we have a
network with a path connecting from region A to region B. The meaning
of the coefficient theta (e.g., 0.81) is this: if region A increases by
one standard deviation from its mean, region B would be expected to increase
by 0.81 its own standard deviations from its own mean while holding all other
relevant regional connections constant. With a path coefficient of -0.16,
when region A increases by one standard deviation from its mean, region B
would be expected to decrease by 0.16 its own standard deviations from its
own mean while holding all other relevant regional connections constant.
So theoretically speaking the range of the path coefficients can be anything,
but most of the time they range from -1 to 1. To save running time, the
default values for -limits are set with -1 and 1, but if the result hits
the boundary, increase them and re-run the analysis.
Examples:
To confirm a specific model:
1dSEM -theta inittheta.1D -C SEMCorr.1D -psi SEMvar.1D -DF 30
To search models by growing from the best single coefficient model
up to 12 coefficients
1dSEM -theta testthetas_ms.1D -C testcorr.1D -psi testpsi.1D \
-limits -2 2 -nrand 100 -DF 30 -model_search -max_paths 12
To search all possible models up to 8 coefficients:
1dSEM -theta testthetas_ms.1D -C testcorr.1D -psi testpsi.1D \
-nrand 10 -DF 30 -stop_cost 0.1 -grow_all -max_paths 8 | & tee testgrow.txt
For more information, see https://afni.nimh.nih.gov/sscc/gangc/PathAna.html
and our HBM 2007 poster at
https://sscc.nimh.nih.gov/sscc/posters/file.2007-06-07.0771819246
If you find this program useful, please cite:
G Chen, DR Glen, JL Stein, AS Meyer-Lindenberg, ZS Saad, RW Cox,
Model Validation and Automated Search in FMRI Path Analysis:
A Fast Open-Source Tool for Structural Equation Modeling,
Human Brain Mapping Conference, 2007
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