siena08: Function to perform a meta analysis of a collection of Siena...
In RSiena: Siena - Simulation Investigation for Empirical Network Analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Estimates a meta analysis based on a collection of Siena fits.
Usage
1
Arguments
...
names of sienaFit objects, returned from
siena07.
They will be renamed if entered in format newname=oldname.
It is also allowed to give for ... a list of sienaFit
objects.
projname
Base name of report file if required
bound
Upper limit of standard error for inclusion in the meta analysis.
alpha
1 minus confidence level of confidence intervals.
maxit
Number of iterations of iterated least squares procedure.
Details
A meta analysis is performed as described
in the Siena manual, section "Meta-analysis of Siena results". This
consists of three parts: an iterated weighted least squares (IWLS)
modification of the method described in the reference below;
maximum likelihood estimates and confidence intervals based on
profile likelihoods under normality assumptions;
and Fisher combinations of left-sided and right-sided p-values.
These are produced for all effects separately.
Note that the corresponding effects must have the same effect name in each
model fit. This implies that at least covariates and behavior variables must
have the same name in each model fit.
Value
An object of class sienaMeta. There are print,
summary and plot methods for this class.
This object contains at least the following.
thetadf
Data frame containing the coefficients, standard errors
and score test results
projname
Root name for any output file to be produced by the print method
bound
Estimates with standard error above this value were
excluded from the calculations
scores
Object of class by indicating, for each effect in
the models, whether score test information was present.
requestedEffects
The requestedEffects component of the first
sienaFit object in ....
muhat
The vector of IWLS estimates.
se.muhat
The vector of standard errors of the IWLS estimates.
theta
The vector of ML estimates mu.ml (see below).
se
The vector of standard errors of the ML estimates mu.ml.se
(see below).
Then for each effect, there is a list with at least the following.
cor.est
Spearman rank correlation coefficient between estimates
and their standard errors.
cor.pval
p-value for above
regfit
Part of the result of the fit of iwlsm.
regsummary
The summary of the fit, which includes the
coefficient table.
Tsq
test statistic for effect zero in every model
pTsq
p-value for above
tratio
test statistics that mean effect is 0
ptratio
p-value for above
Qstat
Test statistic for variance of effects is zero
pttilde
p-value for above
cjplus
Test statistic for at least one theta strictly greater than 0
cjminus
Test statistic for at least one theta strictly less than 0
cjplusp
p-value for cjplus
cjminusp
p-value for cjminus
mu.ml
ML estimate of population mean
mu.ml.se
standard error of ML estimate of population mean
sigma.ml
ML estimate of population standard deviation
mu.confint
confidence interval for population mean
based on profile likelihood
sigma.confint
confidence interval for population standard deviation
based on profile likelihood
n1
Number of fits on which the meta analysis is based
cjplus
Test statistic for combination of right one-sided
Fisher combination tests
cjminus
Test statistic for combination of left one-sided
Fisher combination tests
cjplusp
p-value for cjplus
cjminusp
p-value for cjminus
scoreplus
Test statistic for combination of right one-sided
p-values from score tests
scoreminus
Test statistic for combination of left one-sided
p-values from score tests
scoreplusp
p-value for scoreplus
scoreminusp
p-value for scoreminus
ns
Number of fits on which the score test analysis is based
Author(s)
Ruth Ripley, Tom Snijders
References
T. A. B. Snijders and Chris Baerveldt (2003).
Multilevel network study of the effects
of delinquent behavior on friendship
evolution. Journal of Mathematical Sociology 27, 123–151.
See also the manual (Section 11.2)
and http://www.stats.ox.ac.uk/~snijders/siena/
See Also
print.sienaMeta, iwlsm, siena07
Examples
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## Not run:
# A meta-analysis for three groups does not make much sense
# for generalizing to a population of networks,
# but the Fisher combinations of p-values are meaningful.
# However, using three groups does show the idea.
Group1 <- sienaDependent(array(c(N3401, HN3401), dim=c(45, 45, 2)))
Group3 <- sienaDependent(array(c(N3403, HN3403), dim=c(37, 37, 2)))
Group4 <- sienaDependent(array(c(N3404, HN3404), dim=c(33, 33, 2)))
dataset.1 <- sienaDataCreate(Friends = Group1)
dataset.3 <- sienaDataCreate(Friends = Group3)
dataset.4 <- sienaDataCreate(Friends = Group4)
OneAlgorithm <- sienaAlgorithmCreate(projname = "SingleGroups", seed=128)
effects.1 <- getEffects(dataset.1)
effects.3 <- getEffects(dataset.3)
effects.4 <- getEffects(dataset.4)
effects.1 <- includeEffects(effects.1, transTrip)
effects.1 <- setEffect(effects.1, transRecTrip, fix=TRUE, test=TRUE)
effects.3 <- includeEffects(effects.3, transTrip)
effects.3 <- setEffect(effects.3, transRecTrip, fix=TRUE, test=TRUE)
effects.4 <- includeEffects(effects.4, transTrip)
effects.4 <- setEffect(effects.4, transRecTrip, fix=TRUE, test=TRUE)
ans.1 <- siena07(OneAlgorithm, data=dataset.1, effects=effects.1, batch=TRUE)
ans.3 <- siena07(OneAlgorithm, data=dataset.3, effects=effects.3, batch=TRUE)
ans.4 <- siena07(OneAlgorithm, data=dataset.4, effects=effects.4, batch=TRUE)
ans.1
ans.3
ans.4
(meta <- siena08(ans.1, ans.3, ans.4))
plot(meta, which=2:3, layout = c(2,1))
# For specifically presenting the Fisher combinations:
# First determine the components of meta with estimated effects:
which.est <- sapply(meta, function(x){ifelse(is.list(x),!is.null(x$cjplus),FALSE)})
Fishers <- t(sapply(1:sum(which.est),
function(i){c(meta[[i]]$cjplus, meta[[i]]$cjminus,
meta[[i]]$cjplusp, meta[[i]]$cjminusp, 2*meta[[i]]$n1 )}))
Fishers <- as.data.frame(Fishers, row.names=names(meta)[which.est])
names(Fishers) <- c('Fplus', 'Fminus', 'pplus', 'pminus', 'df')
Fishers
round(Fishers,4)
## End(Not run)
Example output
Warning message:
no DISPLAY variable so Tk is not available
siena07 will create an output file SingleGroups.txt .
effectName include fix test initialValue parm
1 transitive triplets TRUE FALSE FALSE 0 0
effectName include fix test initialValue parm
1 transitive recipr. triplets TRUE TRUE TRUE 0 0
effectName include fix test initialValue parm
1 transitive triplets TRUE FALSE FALSE 0 0
effectName include fix test initialValue parm
1 transitive recipr. triplets TRUE TRUE TRUE 0 0
effectName include fix test initialValue parm
1 transitive triplets TRUE FALSE FALSE 0 0
effectName include fix test initialValue parm
1 transitive recipr. triplets TRUE TRUE TRUE 0 0
Start phase 0
theta: -1.11 0.00 0.00 0.00
Start phase 1
Phase 1 Iteration 1 Progress: 0%
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Phase 1 Iteration 45 Progress: 2%
Phase 1 Iteration 50 Progress: 2%
theta: -1.4636 -0.0105 0.3180 0.0000
Start phase 2.1
Phase 2 Subphase 1 Iteration 1 Progress: 9%
Phase 2 Subphase 1 Iteration 2 Progress: 9%
theta -1.5689 0.0488 0.4136 0.0000
ac 0.668 1.290 1.331 1.121
Phase 2 Subphase 1 Iteration 3 Progress: 9%
Phase 2 Subphase 1 Iteration 4 Progress: 9%
theta -1.923 0.418 0.648 0.000
ac 0.531 1.144 0.479 0.510
Phase 2 Subphase 1 Iteration 5 Progress: 9%
Phase 2 Subphase 1 Iteration 6 Progress: 9%
theta -2.153 0.966 0.627 0.000
ac 0.560 0.988 0.315 0.360
Phase 2 Subphase 1 Iteration 7 Progress: 9%
Phase 2 Subphase 1 Iteration 8 Progress: 9%
theta -2.269 1.379 0.534 0.000
ac 0.555 0.953 0.262 0.286
Phase 2 Subphase 1 Iteration 9 Progress: 9%
Phase 2 Subphase 1 Iteration 10 Progress: 9%
theta -2.356 1.615 0.523 0.000
ac 0.3967 0.3922 -0.1190 -0.0929
theta -2.287 1.586 0.464 0.000
ac -0.0417 -0.0531 -0.3167 -0.2522
theta: -2.287 1.586 0.464 0.000
Start phase 2.2
Phase 2 Subphase 2 Iteration 1 Progress: 17%
Phase 2 Subphase 2 Iteration 2 Progress: 17%
Phase 2 Subphase 2 Iteration 3 Progress: 17%
Phase 2 Subphase 2 Iteration 4 Progress: 18%
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Phase 2 Subphase 2 Iteration 10 Progress: 18%
theta -2.256 1.560 0.467 0.000
ac -0.222 -0.315 -0.402 -0.232
theta: -2.256 1.560 0.467 0.000
Start phase 2.3
Phase 2 Subphase 3 Iteration 1 Progress: 27%
Phase 2 Subphase 3 Iteration 2 Progress: 27%
Phase 2 Subphase 3 Iteration 3 Progress: 27%
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theta -2.282 1.585 0.476 0.000
ac -0.316 -0.196 -0.374 -0.237
theta: -2.282 1.585 0.476 0.000
Start phase 2.4
Phase 2 Subphase 4 Iteration 1 Progress: 41%
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Phase 2 Subphase 4 Iteration 10 Progress: 41%
theta -2.264 1.540 0.472 0.000
ac -0.0615 -0.1049 -0.0778 0.0308
theta: -2.264 1.540 0.472 0.000
Start phase 3
Phase 3 Iteration 500 Progress 82%
Phase 3 Iteration 1000 Progress 100%
Start phase 0
theta: -1.24 0.00 0.00 0.00
Start phase 1
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theta: -1.525 0.500 0.564 0.000
Start phase 2.1
Phase 2 Subphase 1 Iteration 1 Progress: 9%
Phase 2 Subphase 1 Iteration 2 Progress: 9%
theta -1.676 0.803 1.003 0.000
ac 0.0395 1.1472 2.8981 1.6374
Phase 2 Subphase 1 Iteration 3 Progress: 9%
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theta -2.13 2.27 1.42 0.00
ac 0.183 1.172 0.523 0.650
Phase 2 Subphase 1 Iteration 5 Progress: 9%
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theta -2.212 3.265 0.551 0.000
ac 0.229 0.772 0.419 0.725
Phase 2 Subphase 1 Iteration 7 Progress: 9%
Phase 2 Subphase 1 Iteration 8 Progress: 9%
theta -2.40 2.85 1.03 0.00
ac 0.216 0.719 0.424 0.738
Phase 2 Subphase 1 Iteration 9 Progress: 9%
Phase 2 Subphase 1 Iteration 10 Progress: 9%
theta -2.52 3.12 1.31 0.00
ac 0.125 0.632 0.322 0.493
theta -2.37 2.62 1.17 0.00
ac -0.0226 -0.0353 -0.3378 -0.1079
theta: -2.37 2.62 1.17 0.00
Start phase 2.2
Phase 2 Subphase 2 Iteration 1 Progress: 17%
Phase 2 Subphase 2 Iteration 2 Progress: 17%
Phase 2 Subphase 2 Iteration 3 Progress: 17%
Phase 2 Subphase 2 Iteration 4 Progress: 18%
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Phase 2 Subphase 2 Iteration 10 Progress: 18%
theta -2.37 2.64 1.14 0.00
ac -0.00899 -0.04360 -0.30589 -0.09855
theta: -2.37 2.64 1.14 0.00
Start phase 2.3
Phase 2 Subphase 3 Iteration 1 Progress: 27%
Phase 2 Subphase 3 Iteration 2 Progress: 27%
Phase 2 Subphase 3 Iteration 3 Progress: 27%
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theta -2.34 2.60 1.13 0.00
ac -0.08458 -0.00363 -0.16300 0.11391
theta: -2.34 2.60 1.13 0.00
Start phase 2.4
Phase 2 Subphase 4 Iteration 1 Progress: 41%
Phase 2 Subphase 4 Iteration 2 Progress: 41%
Phase 2 Subphase 4 Iteration 3 Progress: 41%
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Phase 2 Subphase 4 Iteration 10 Progress: 41%
theta -2.35 2.61 1.15 0.00
ac -0.01063 -0.04381 -0.00104 0.18417
theta: -2.35 2.61 1.15 0.00
Start phase 3
Phase 3 Iteration 500 Progress 82%
Phase 3 Iteration 1000 Progress 100%
Start phase 0
theta: -1.62 0.00 0.00 0.00
Start phase 1
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theta: -1.851 0.130 0.273 0.000
Start phase 2.1
Phase 2 Subphase 1 Iteration 1 Progress: 9%
Phase 2 Subphase 1 Iteration 2 Progress: 9%
theta -2.230 0.546 0.792 0.000
ac 1.08 4.27 2.59 4.31
Phase 2 Subphase 1 Iteration 3 Progress: 9%
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theta -2.851 1.082 0.944 0.000
ac 1.343 0.879 4.101 4.682
Phase 2 Subphase 1 Iteration 5 Progress: 9%
Phase 2 Subphase 1 Iteration 6 Progress: 9%
theta -3.222 1.582 0.877 0.000
ac 0.882 0.164 0.402 1.064
Phase 2 Subphase 1 Iteration 7 Progress: 9%
Phase 2 Subphase 1 Iteration 8 Progress: 9%
theta -3.59 2.28 1.64 0.00
ac 0.574 -0.201 -0.302 -0.242
Phase 2 Subphase 1 Iteration 9 Progress: 9%
Phase 2 Subphase 1 Iteration 10 Progress: 9%
theta -3.615 2.614 0.925 0.000
ac 0.570 -0.230 -0.363 -0.428
theta -3.42 2.34 1.07 0.00
ac -0.1486 -0.2587 -0.3123 -0.0781
theta: -3.42 2.34 1.07 0.00
Start phase 2.2
Phase 2 Subphase 2 Iteration 1 Progress: 17%
Phase 2 Subphase 2 Iteration 2 Progress: 17%
Phase 2 Subphase 2 Iteration 3 Progress: 17%
Phase 2 Subphase 2 Iteration 4 Progress: 18%
Phase 2 Subphase 2 Iteration 5 Progress: 18%
Phase 2 Subphase 2 Iteration 6 Progress: 18%
Phase 2 Subphase 2 Iteration 7 Progress: 18%
Phase 2 Subphase 2 Iteration 8 Progress: 18%
Phase 2 Subphase 2 Iteration 9 Progress: 18%
Phase 2 Subphase 2 Iteration 10 Progress: 18%
theta -3.43 2.30 1.10 0.00
ac -0.2702 -0.1510 -0.5108 -0.0185
theta: -3.43 2.30 1.10 0.00
Start phase 2.3
Phase 2 Subphase 3 Iteration 1 Progress: 27%
Phase 2 Subphase 3 Iteration 2 Progress: 27%
Phase 2 Subphase 3 Iteration 3 Progress: 27%
Phase 2 Subphase 3 Iteration 4 Progress: 27%
Phase 2 Subphase 3 Iteration 5 Progress: 27%
Phase 2 Subphase 3 Iteration 6 Progress: 27%
Phase 2 Subphase 3 Iteration 7 Progress: 27%
Phase 2 Subphase 3 Iteration 8 Progress: 27%
Phase 2 Subphase 3 Iteration 9 Progress: 27%
Phase 2 Subphase 3 Iteration 10 Progress: 27%
theta -3.31 2.17 1.06 0.00
ac 0.0182 -0.1715 -0.1910 0.1650
theta: -3.31 2.17 1.06 0.00
Start phase 2.4
Phase 2 Subphase 4 Iteration 1 Progress: 41%
Phase 2 Subphase 4 Iteration 2 Progress: 41%
Phase 2 Subphase 4 Iteration 3 Progress: 41%
Phase 2 Subphase 4 Iteration 4 Progress: 41%
Phase 2 Subphase 4 Iteration 5 Progress: 41%
Phase 2 Subphase 4 Iteration 6 Progress: 41%
Phase 2 Subphase 4 Iteration 7 Progress: 41%
Phase 2 Subphase 4 Iteration 8 Progress: 41%
Phase 2 Subphase 4 Iteration 9 Progress: 41%
Phase 2 Subphase 4 Iteration 10 Progress: 41%
theta -3.37 2.29 1.06 0.00
ac -0.0406 -0.1446 -0.0444 0.2542
theta: -3.37 2.29 1.06 0.00
Start phase 3
Phase 3 Iteration 500 Progress 82%
Phase 3 Iteration 1000 Progress 100%
Estimates, standard errors and convergence t-ratios
Estimate Standard Convergence
Error t-ratio
Rate parameters:
0 Rate parameter 7.0715 ( 1.1900 )
Other parameters:
1. eval outdegree (density) -2.2642 ( 0.1283 ) 0.0486
2. eval reciprocity 1.5398 ( 0.2516 ) 0.0465
3. eval transitive triplets 0.4717 ( 0.0620 ) 0.1349
4. eval transitive recipr. triplets 0.0000 ( NA ) 0.5074
Overall maximum convergence ratio: 0.1774
Score test for 1 parameter:
chi-squared = 7.09, p = 0.0078.
Total of 1751 iteration steps.
Estimates, standard errors and convergence t-ratios
Estimate Standard Convergence
Error t-ratio
Rate parameters:
0 Rate parameter 3.6453 ( 0.6778 )
Other parameters:
1. eval outdegree (density) -2.3451 ( 0.1982 ) 0.0550
2. eval reciprocity 2.6109 ( 0.3967 ) 0.0029
3. eval transitive triplets 1.1499 ( 0.2944 ) 0.0451
4. eval transitive recipr. triplets 0.0000 ( NA ) 0.4707
Overall maximum convergence ratio: 0.0908
Score test for 1 parameter:
chi-squared = 2.55, p = 0.1102.
Total of 2062 iteration steps.
Estimates, standard errors and convergence t-ratios
Estimate Standard Convergence
Error t-ratio
Rate parameters:
0 Rate parameter 3.1010 ( 0.8098 )
Other parameters:
1. eval outdegree (density) -3.3692 ( 0.4412 ) -0.0315
2. eval reciprocity 2.2902 ( 0.7069 ) 0.0199
3. eval transitive triplets 1.0563 ( 0.3019 ) 0.0239
4. eval transitive recipr. triplets 0.0000 ( NA ) 0.5754
Overall maximum convergence ratio: 0.0996
Score test for 1 parameter:
chi-squared = 10.92, p = 0.0010.
Total of 1946 iteration steps.
Tests for mean parameters use a t-distribution with N-1 d.f.,
where N = number of included groups.
Upper bound used for standard error is 5.00.
--------------------------------------------------------------------------------
Parameter 1: eval : outdegree (density)
--------------------------------------------------------------------------------
3 datasets used.
Test that estimates and standard errors are uncorrelated:
Spearman's rank correlation rho = -1, two-sided p = 0.333
Estimates and test based on IWLS modification of Snijders & Baerveldt (2003)
----------------------------------------------------------------------------
Test that all parameters are 0 :
chi-squared = 509.5535, d.f. = 3, p < 0.001
Estimated mean parameter -2.5566 (s.e. 0.3255), two-sided p = 0.016
Estimated standard deviation 0.5637
Test that variance of parameter is 0 :
Chi-squared = 5.7833 (d.f. = 2), p = 0.055
Estimates and confidence intervals under normality assumptions
------------------------------------------------------- -------
Estimated mean parameter -2.3489 (s.e. 0.1047), two-sided p = 0.002
0.95 level confidence interval [ -3.0634 , -2.09 ]
Estimated standard deviation < 0.0001
0.95 level confidence interval [ 0 , 0.9427 ]
Fisher's combination of one-sided tests
----------------------------------------
Combination of right one-sided p-values:
Chi-squared = 0 (d.f. = 6), p = 1.000
Combination of left one-sided p-values:
Chi-squared = 529.8684 (d.f. = 6), p < 0.001
--------------------------------------------------------------------------------
Parameter 2: eval : reciprocity
--------------------------------------------------------------------------------
3 datasets used.
Test that estimates and standard errors are uncorrelated:
Spearman's rank correlation rho = 0.5, two-sided p = 1.000
Estimates and test based on IWLS modification of Snijders & Baerveldt (2003)
----------------------------------------------------------------------------
Test that all parameters are 0 :
chi-squared = 91.2626, d.f. = 3, p < 0.001
Estimated mean parameter 2.0505 (s.e. 0.3596), two-sided p = 0.029
Estimated standard deviation 0.6229
Test that variance of parameter is 0 :
Chi-squared = 5.5594 (d.f. = 2), p = 0.062
Estimates and confidence intervals under normality assumptions
------------------------------------------------------- -------
Estimated mean parameter 2.0237 (s.e. 0.3173), two-sided p = 0.024
0.95 level confidence interval [ 1.2349 , 2.9875 ]
Estimated standard deviation 0.371
0.95 level confidence interval [ 0 , 1.5081 ]
Fisher's combination of one-sided tests
----------------------------------------
Combination of right one-sided p-values:
Chi-squared = 106.7713 (d.f. = 6), p < 0.001
Combination of left one-sided p-values:
Chi-squared = 0.0012 (d.f. = 6), p = 1.000
--------------------------------------------------------------------------------
Parameter 3: eval : transitive triplets
--------------------------------------------------------------------------------
3 datasets used.
Test that estimates and standard errors are uncorrelated:
Spearman's rank correlation rho = 0.5, two-sided p = 1.000
Estimates and test based on IWLS modification of Snijders & Baerveldt (2003)
----------------------------------------------------------------------------
Test that all parameters are 0 :
chi-squared = 85.2941, d.f. = 3, p < 0.001
Estimated mean parameter 0.8079 (s.e. 0.229), two-sided p = 0.072
Estimated standard deviation 0.3966
Test that variance of parameter is 0 :
Chi-squared = 8.3368 (d.f. = 2), p = 0.015
Estimates and confidence intervals under normality assumptions
------------------------------------------------------- -------
Estimated mean parameter 0.7742 (s.e. 0.194), two-sided p = 0.057
0.95 level confidence interval [ 0.317 , 1.4045 ]
Estimated standard deviation 0.2614
0.95 level confidence interval [ 0 , 0.9531 ]
Fisher's combination of one-sided tests
----------------------------------------
Combination of right one-sided p-values:
Chi-squared = 100.3808 (d.f. = 6), p < 0.001
Combination of left one-sided p-values:
Chi-squared = 6e-04 (d.f. = 6), p = 1.000
--------------------------------------------------------------------------------
Parameter 4: eval : transitive recipr. triplets
--------------------------------------------------------------------------------
0 datasets used.
There were no data sets satisfying the bounds for this parameter.
No combined output is given.
-----------------------------------------------------------------
Score tests:
Fisher combination
-----------------------------------------------------------------
(4) eval : transitive recipr. triplets
Data set 1, SingleGroups(ans.1) : z = -2.6624
Data set 2, SingleGroups(ans.3) : z = -1.5974
Data set 3, SingleGroups(ans.4) : z = -3.3044
Combination of right one-sided p-values:
Chi-squared = 0.122 (d.f. = 6), p = 1.000
Combination of left one-sided p-values:
Chi-squared = 32.2028 (d.f. = 6), p < 0.001
Fplus Fminus pplus pminus df
eval : outdegree (density) 2.244881e-14 5.298684e+02 1 0 6
eval : reciprocity 1.067713e+02 1.196272e-03 0 1 6
eval : transitive triplets 1.003808e+02 5.619543e-04 0 1 6
Fplus Fminus pplus pminus df
eval : outdegree (density) 0.0000 529.8684 1 0 6
eval : reciprocity 106.7713 0.0012 0 1 6
eval : transitive triplets 100.3808 0.0006 0 1 6
RSiena documentation built on Sept. 24, 2020, 3 p.m.
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Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Estimates a meta analysis based on a collection of Siena fits.
Usage
1 |
Arguments
... |
names of |
projname |
Base name of report file if required |
bound |
Upper limit of standard error for inclusion in the meta analysis. |
alpha |
1 minus confidence level of confidence intervals. |
maxit |
Number of iterations of iterated least squares procedure. |
Details
A meta analysis is performed as described in the Siena manual, section "Meta-analysis of Siena results". This consists of three parts: an iterated weighted least squares (IWLS) modification of the method described in the reference below; maximum likelihood estimates and confidence intervals based on profile likelihoods under normality assumptions; and Fisher combinations of left-sided and right-sided p-values. These are produced for all effects separately.
Note that the corresponding effects must have the same effect name in each model fit. This implies that at least covariates and behavior variables must have the same name in each model fit.
Value
An object of class sienaMeta. There are print,
summary and plot methods for this class.
This object contains at least the following.
thetadf |
Data frame containing the coefficients, standard errors and score test results |
projname |
Root name for any output file to be produced by the print method |
bound |
Estimates with standard error above this value were excluded from the calculations |
scores |
Object of class |
requestedEffects |
The |
muhat |
The vector of IWLS estimates. |
se.muhat |
The vector of standard errors of the IWLS estimates. |
theta |
The vector of ML estimates |
se |
The vector of standard errors of the ML estimates |
Then for each effect, there is a list with at least the following.
cor.est |
Spearman rank correlation coefficient between estimates and their standard errors. |
cor.pval |
p-value for above |
regfit |
Part of the result of the fit of |
regsummary |
The summary of the fit, which includes the coefficient table. |
Tsq |
test statistic for effect zero in every model |
pTsq |
p-value for above |
tratio |
test statistics that mean effect is 0 |
ptratio |
p-value for above |
Qstat |
Test statistic for variance of effects is zero |
pttilde |
p-value for above |
cjplus |
Test statistic for at least one theta strictly greater than 0 |
cjminus |
Test statistic for at least one theta strictly less than 0 |
cjplusp |
p-value for |
cjminusp |
p-value for |
mu.ml |
ML estimate of population mean |
mu.ml.se |
standard error of ML estimate of population mean |
sigma.ml |
ML estimate of population standard deviation |
mu.confint |
confidence interval for population mean based on profile likelihood |
sigma.confint |
confidence interval for population standard deviation based on profile likelihood |
n1 |
Number of fits on which the meta analysis is based |
cjplus |
Test statistic for combination of right one-sided Fisher combination tests |
cjminus |
Test statistic for combination of left one-sided Fisher combination tests |
cjplusp |
p-value for |
cjminusp |
p-value for |
scoreplus |
Test statistic for combination of right one-sided p-values from score tests |
scoreminus |
Test statistic for combination of left one-sided p-values from score tests |
scoreplusp |
p-value for |
scoreminusp |
p-value for |
ns |
Number of fits on which the score test analysis is based |
Author(s)
Ruth Ripley, Tom Snijders
References
T. A. B. Snijders and Chris Baerveldt (2003). Multilevel network study of the effects of delinquent behavior on friendship evolution. Journal of Mathematical Sociology 27, 123–151.
See also the manual (Section 11.2) and http://www.stats.ox.ac.uk/~snijders/siena/
See Also
print.sienaMeta, iwlsm, siena07
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | ## Not run:
# A meta-analysis for three groups does not make much sense
# for generalizing to a population of networks,
# but the Fisher combinations of p-values are meaningful.
# However, using three groups does show the idea.
Group1 <- sienaDependent(array(c(N3401, HN3401), dim=c(45, 45, 2)))
Group3 <- sienaDependent(array(c(N3403, HN3403), dim=c(37, 37, 2)))
Group4 <- sienaDependent(array(c(N3404, HN3404), dim=c(33, 33, 2)))
dataset.1 <- sienaDataCreate(Friends = Group1)
dataset.3 <- sienaDataCreate(Friends = Group3)
dataset.4 <- sienaDataCreate(Friends = Group4)
OneAlgorithm <- sienaAlgorithmCreate(projname = "SingleGroups", seed=128)
effects.1 <- getEffects(dataset.1)
effects.3 <- getEffects(dataset.3)
effects.4 <- getEffects(dataset.4)
effects.1 <- includeEffects(effects.1, transTrip)
effects.1 <- setEffect(effects.1, transRecTrip, fix=TRUE, test=TRUE)
effects.3 <- includeEffects(effects.3, transTrip)
effects.3 <- setEffect(effects.3, transRecTrip, fix=TRUE, test=TRUE)
effects.4 <- includeEffects(effects.4, transTrip)
effects.4 <- setEffect(effects.4, transRecTrip, fix=TRUE, test=TRUE)
ans.1 <- siena07(OneAlgorithm, data=dataset.1, effects=effects.1, batch=TRUE)
ans.3 <- siena07(OneAlgorithm, data=dataset.3, effects=effects.3, batch=TRUE)
ans.4 <- siena07(OneAlgorithm, data=dataset.4, effects=effects.4, batch=TRUE)
ans.1
ans.3
ans.4
(meta <- siena08(ans.1, ans.3, ans.4))
plot(meta, which=2:3, layout = c(2,1))
# For specifically presenting the Fisher combinations:
# First determine the components of meta with estimated effects:
which.est <- sapply(meta, function(x){ifelse(is.list(x),!is.null(x$cjplus),FALSE)})
Fishers <- t(sapply(1:sum(which.est),
function(i){c(meta[[i]]$cjplus, meta[[i]]$cjminus,
meta[[i]]$cjplusp, meta[[i]]$cjminusp, 2*meta[[i]]$n1 )}))
Fishers <- as.data.frame(Fishers, row.names=names(meta)[which.est])
names(Fishers) <- c('Fplus', 'Fminus', 'pplus', 'pminus', 'df')
Fishers
round(Fishers,4)
## End(Not run)
|
Example output
Warning message:
no DISPLAY variable so Tk is not available
siena07 will create an output file SingleGroups.txt .
effectName include fix test initialValue parm
1 transitive triplets TRUE FALSE FALSE 0 0
effectName include fix test initialValue parm
1 transitive recipr. triplets TRUE TRUE TRUE 0 0
effectName include fix test initialValue parm
1 transitive triplets TRUE FALSE FALSE 0 0
effectName include fix test initialValue parm
1 transitive recipr. triplets TRUE TRUE TRUE 0 0
effectName include fix test initialValue parm
1 transitive triplets TRUE FALSE FALSE 0 0
effectName include fix test initialValue parm
1 transitive recipr. triplets TRUE TRUE TRUE 0 0
Start phase 0
theta: -1.11 0.00 0.00 0.00
Start phase 1
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Phase 1 Iteration 35 Progress: 1%
Phase 1 Iteration 40 Progress: 1%
Phase 1 Iteration 45 Progress: 2%
Phase 1 Iteration 50 Progress: 2%
theta: -1.4636 -0.0105 0.3180 0.0000
Start phase 2.1
Phase 2 Subphase 1 Iteration 1 Progress: 9%
Phase 2 Subphase 1 Iteration 2 Progress: 9%
theta -1.5689 0.0488 0.4136 0.0000
ac 0.668 1.290 1.331 1.121
Phase 2 Subphase 1 Iteration 3 Progress: 9%
Phase 2 Subphase 1 Iteration 4 Progress: 9%
theta -1.923 0.418 0.648 0.000
ac 0.531 1.144 0.479 0.510
Phase 2 Subphase 1 Iteration 5 Progress: 9%
Phase 2 Subphase 1 Iteration 6 Progress: 9%
theta -2.153 0.966 0.627 0.000
ac 0.560 0.988 0.315 0.360
Phase 2 Subphase 1 Iteration 7 Progress: 9%
Phase 2 Subphase 1 Iteration 8 Progress: 9%
theta -2.269 1.379 0.534 0.000
ac 0.555 0.953 0.262 0.286
Phase 2 Subphase 1 Iteration 9 Progress: 9%
Phase 2 Subphase 1 Iteration 10 Progress: 9%
theta -2.356 1.615 0.523 0.000
ac 0.3967 0.3922 -0.1190 -0.0929
theta -2.287 1.586 0.464 0.000
ac -0.0417 -0.0531 -0.3167 -0.2522
theta: -2.287 1.586 0.464 0.000
Start phase 2.2
Phase 2 Subphase 2 Iteration 1 Progress: 17%
Phase 2 Subphase 2 Iteration 2 Progress: 17%
Phase 2 Subphase 2 Iteration 3 Progress: 17%
Phase 2 Subphase 2 Iteration 4 Progress: 18%
Phase 2 Subphase 2 Iteration 5 Progress: 18%
Phase 2 Subphase 2 Iteration 6 Progress: 18%
Phase 2 Subphase 2 Iteration 7 Progress: 18%
Phase 2 Subphase 2 Iteration 8 Progress: 18%
Phase 2 Subphase 2 Iteration 9 Progress: 18%
Phase 2 Subphase 2 Iteration 10 Progress: 18%
theta -2.256 1.560 0.467 0.000
ac -0.222 -0.315 -0.402 -0.232
theta: -2.256 1.560 0.467 0.000
Start phase 2.3
Phase 2 Subphase 3 Iteration 1 Progress: 27%
Phase 2 Subphase 3 Iteration 2 Progress: 27%
Phase 2 Subphase 3 Iteration 3 Progress: 27%
Phase 2 Subphase 3 Iteration 4 Progress: 27%
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Phase 2 Subphase 3 Iteration 10 Progress: 27%
theta -2.282 1.585 0.476 0.000
ac -0.316 -0.196 -0.374 -0.237
theta: -2.282 1.585 0.476 0.000
Start phase 2.4
Phase 2 Subphase 4 Iteration 1 Progress: 41%
Phase 2 Subphase 4 Iteration 2 Progress: 41%
Phase 2 Subphase 4 Iteration 3 Progress: 41%
Phase 2 Subphase 4 Iteration 4 Progress: 41%
Phase 2 Subphase 4 Iteration 5 Progress: 41%
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Phase 2 Subphase 4 Iteration 9 Progress: 41%
Phase 2 Subphase 4 Iteration 10 Progress: 41%
theta -2.264 1.540 0.472 0.000
ac -0.0615 -0.1049 -0.0778 0.0308
theta: -2.264 1.540 0.472 0.000
Start phase 3
Phase 3 Iteration 500 Progress 82%
Phase 3 Iteration 1000 Progress 100%
Start phase 0
theta: -1.24 0.00 0.00 0.00
Start phase 1
Phase 1 Iteration 1 Progress: 0%
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Phase 1 Iteration 50 Progress: 2%
theta: -1.525 0.500 0.564 0.000
Start phase 2.1
Phase 2 Subphase 1 Iteration 1 Progress: 9%
Phase 2 Subphase 1 Iteration 2 Progress: 9%
theta -1.676 0.803 1.003 0.000
ac 0.0395 1.1472 2.8981 1.6374
Phase 2 Subphase 1 Iteration 3 Progress: 9%
Phase 2 Subphase 1 Iteration 4 Progress: 9%
theta -2.13 2.27 1.42 0.00
ac 0.183 1.172 0.523 0.650
Phase 2 Subphase 1 Iteration 5 Progress: 9%
Phase 2 Subphase 1 Iteration 6 Progress: 9%
theta -2.212 3.265 0.551 0.000
ac 0.229 0.772 0.419 0.725
Phase 2 Subphase 1 Iteration 7 Progress: 9%
Phase 2 Subphase 1 Iteration 8 Progress: 9%
theta -2.40 2.85 1.03 0.00
ac 0.216 0.719 0.424 0.738
Phase 2 Subphase 1 Iteration 9 Progress: 9%
Phase 2 Subphase 1 Iteration 10 Progress: 9%
theta -2.52 3.12 1.31 0.00
ac 0.125 0.632 0.322 0.493
theta -2.37 2.62 1.17 0.00
ac -0.0226 -0.0353 -0.3378 -0.1079
theta: -2.37 2.62 1.17 0.00
Start phase 2.2
Phase 2 Subphase 2 Iteration 1 Progress: 17%
Phase 2 Subphase 2 Iteration 2 Progress: 17%
Phase 2 Subphase 2 Iteration 3 Progress: 17%
Phase 2 Subphase 2 Iteration 4 Progress: 18%
Phase 2 Subphase 2 Iteration 5 Progress: 18%
Phase 2 Subphase 2 Iteration 6 Progress: 18%
Phase 2 Subphase 2 Iteration 7 Progress: 18%
Phase 2 Subphase 2 Iteration 8 Progress: 18%
Phase 2 Subphase 2 Iteration 9 Progress: 18%
Phase 2 Subphase 2 Iteration 10 Progress: 18%
theta -2.37 2.64 1.14 0.00
ac -0.00899 -0.04360 -0.30589 -0.09855
theta: -2.37 2.64 1.14 0.00
Start phase 2.3
Phase 2 Subphase 3 Iteration 1 Progress: 27%
Phase 2 Subphase 3 Iteration 2 Progress: 27%
Phase 2 Subphase 3 Iteration 3 Progress: 27%
Phase 2 Subphase 3 Iteration 4 Progress: 27%
Phase 2 Subphase 3 Iteration 5 Progress: 27%
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Phase 2 Subphase 3 Iteration 10 Progress: 27%
theta -2.34 2.60 1.13 0.00
ac -0.08458 -0.00363 -0.16300 0.11391
theta: -2.34 2.60 1.13 0.00
Start phase 2.4
Phase 2 Subphase 4 Iteration 1 Progress: 41%
Phase 2 Subphase 4 Iteration 2 Progress: 41%
Phase 2 Subphase 4 Iteration 3 Progress: 41%
Phase 2 Subphase 4 Iteration 4 Progress: 41%
Phase 2 Subphase 4 Iteration 5 Progress: 41%
Phase 2 Subphase 4 Iteration 6 Progress: 41%
Phase 2 Subphase 4 Iteration 7 Progress: 41%
Phase 2 Subphase 4 Iteration 8 Progress: 41%
Phase 2 Subphase 4 Iteration 9 Progress: 41%
Phase 2 Subphase 4 Iteration 10 Progress: 41%
theta -2.35 2.61 1.15 0.00
ac -0.01063 -0.04381 -0.00104 0.18417
theta: -2.35 2.61 1.15 0.00
Start phase 3
Phase 3 Iteration 500 Progress 82%
Phase 3 Iteration 1000 Progress 100%
Start phase 0
theta: -1.62 0.00 0.00 0.00
Start phase 1
Phase 1 Iteration 1 Progress: 0%
Phase 1 Iteration 2 Progress: 0%
Phase 1 Iteration 3 Progress: 0%
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Phase 1 Iteration 45 Progress: 2%
Phase 1 Iteration 50 Progress: 2%
theta: -1.851 0.130 0.273 0.000
Start phase 2.1
Phase 2 Subphase 1 Iteration 1 Progress: 9%
Phase 2 Subphase 1 Iteration 2 Progress: 9%
theta -2.230 0.546 0.792 0.000
ac 1.08 4.27 2.59 4.31
Phase 2 Subphase 1 Iteration 3 Progress: 9%
Phase 2 Subphase 1 Iteration 4 Progress: 9%
theta -2.851 1.082 0.944 0.000
ac 1.343 0.879 4.101 4.682
Phase 2 Subphase 1 Iteration 5 Progress: 9%
Phase 2 Subphase 1 Iteration 6 Progress: 9%
theta -3.222 1.582 0.877 0.000
ac 0.882 0.164 0.402 1.064
Phase 2 Subphase 1 Iteration 7 Progress: 9%
Phase 2 Subphase 1 Iteration 8 Progress: 9%
theta -3.59 2.28 1.64 0.00
ac 0.574 -0.201 -0.302 -0.242
Phase 2 Subphase 1 Iteration 9 Progress: 9%
Phase 2 Subphase 1 Iteration 10 Progress: 9%
theta -3.615 2.614 0.925 0.000
ac 0.570 -0.230 -0.363 -0.428
theta -3.42 2.34 1.07 0.00
ac -0.1486 -0.2587 -0.3123 -0.0781
theta: -3.42 2.34 1.07 0.00
Start phase 2.2
Phase 2 Subphase 2 Iteration 1 Progress: 17%
Phase 2 Subphase 2 Iteration 2 Progress: 17%
Phase 2 Subphase 2 Iteration 3 Progress: 17%
Phase 2 Subphase 2 Iteration 4 Progress: 18%
Phase 2 Subphase 2 Iteration 5 Progress: 18%
Phase 2 Subphase 2 Iteration 6 Progress: 18%
Phase 2 Subphase 2 Iteration 7 Progress: 18%
Phase 2 Subphase 2 Iteration 8 Progress: 18%
Phase 2 Subphase 2 Iteration 9 Progress: 18%
Phase 2 Subphase 2 Iteration 10 Progress: 18%
theta -3.43 2.30 1.10 0.00
ac -0.2702 -0.1510 -0.5108 -0.0185
theta: -3.43 2.30 1.10 0.00
Start phase 2.3
Phase 2 Subphase 3 Iteration 1 Progress: 27%
Phase 2 Subphase 3 Iteration 2 Progress: 27%
Phase 2 Subphase 3 Iteration 3 Progress: 27%
Phase 2 Subphase 3 Iteration 4 Progress: 27%
Phase 2 Subphase 3 Iteration 5 Progress: 27%
Phase 2 Subphase 3 Iteration 6 Progress: 27%
Phase 2 Subphase 3 Iteration 7 Progress: 27%
Phase 2 Subphase 3 Iteration 8 Progress: 27%
Phase 2 Subphase 3 Iteration 9 Progress: 27%
Phase 2 Subphase 3 Iteration 10 Progress: 27%
theta -3.31 2.17 1.06 0.00
ac 0.0182 -0.1715 -0.1910 0.1650
theta: -3.31 2.17 1.06 0.00
Start phase 2.4
Phase 2 Subphase 4 Iteration 1 Progress: 41%
Phase 2 Subphase 4 Iteration 2 Progress: 41%
Phase 2 Subphase 4 Iteration 3 Progress: 41%
Phase 2 Subphase 4 Iteration 4 Progress: 41%
Phase 2 Subphase 4 Iteration 5 Progress: 41%
Phase 2 Subphase 4 Iteration 6 Progress: 41%
Phase 2 Subphase 4 Iteration 7 Progress: 41%
Phase 2 Subphase 4 Iteration 8 Progress: 41%
Phase 2 Subphase 4 Iteration 9 Progress: 41%
Phase 2 Subphase 4 Iteration 10 Progress: 41%
theta -3.37 2.29 1.06 0.00
ac -0.0406 -0.1446 -0.0444 0.2542
theta: -3.37 2.29 1.06 0.00
Start phase 3
Phase 3 Iteration 500 Progress 82%
Phase 3 Iteration 1000 Progress 100%
Estimates, standard errors and convergence t-ratios
Estimate Standard Convergence
Error t-ratio
Rate parameters:
0 Rate parameter 7.0715 ( 1.1900 )
Other parameters:
1. eval outdegree (density) -2.2642 ( 0.1283 ) 0.0486
2. eval reciprocity 1.5398 ( 0.2516 ) 0.0465
3. eval transitive triplets 0.4717 ( 0.0620 ) 0.1349
4. eval transitive recipr. triplets 0.0000 ( NA ) 0.5074
Overall maximum convergence ratio: 0.1774
Score test for 1 parameter:
chi-squared = 7.09, p = 0.0078.
Total of 1751 iteration steps.
Estimates, standard errors and convergence t-ratios
Estimate Standard Convergence
Error t-ratio
Rate parameters:
0 Rate parameter 3.6453 ( 0.6778 )
Other parameters:
1. eval outdegree (density) -2.3451 ( 0.1982 ) 0.0550
2. eval reciprocity 2.6109 ( 0.3967 ) 0.0029
3. eval transitive triplets 1.1499 ( 0.2944 ) 0.0451
4. eval transitive recipr. triplets 0.0000 ( NA ) 0.4707
Overall maximum convergence ratio: 0.0908
Score test for 1 parameter:
chi-squared = 2.55, p = 0.1102.
Total of 2062 iteration steps.
Estimates, standard errors and convergence t-ratios
Estimate Standard Convergence
Error t-ratio
Rate parameters:
0 Rate parameter 3.1010 ( 0.8098 )
Other parameters:
1. eval outdegree (density) -3.3692 ( 0.4412 ) -0.0315
2. eval reciprocity 2.2902 ( 0.7069 ) 0.0199
3. eval transitive triplets 1.0563 ( 0.3019 ) 0.0239
4. eval transitive recipr. triplets 0.0000 ( NA ) 0.5754
Overall maximum convergence ratio: 0.0996
Score test for 1 parameter:
chi-squared = 10.92, p = 0.0010.
Total of 1946 iteration steps.
Tests for mean parameters use a t-distribution with N-1 d.f.,
where N = number of included groups.
Upper bound used for standard error is 5.00.
--------------------------------------------------------------------------------
Parameter 1: eval : outdegree (density)
--------------------------------------------------------------------------------
3 datasets used.
Test that estimates and standard errors are uncorrelated:
Spearman's rank correlation rho = -1, two-sided p = 0.333
Estimates and test based on IWLS modification of Snijders & Baerveldt (2003)
----------------------------------------------------------------------------
Test that all parameters are 0 :
chi-squared = 509.5535, d.f. = 3, p < 0.001
Estimated mean parameter -2.5566 (s.e. 0.3255), two-sided p = 0.016
Estimated standard deviation 0.5637
Test that variance of parameter is 0 :
Chi-squared = 5.7833 (d.f. = 2), p = 0.055
Estimates and confidence intervals under normality assumptions
------------------------------------------------------- -------
Estimated mean parameter -2.3489 (s.e. 0.1047), two-sided p = 0.002
0.95 level confidence interval [ -3.0634 , -2.09 ]
Estimated standard deviation < 0.0001
0.95 level confidence interval [ 0 , 0.9427 ]
Fisher's combination of one-sided tests
----------------------------------------
Combination of right one-sided p-values:
Chi-squared = 0 (d.f. = 6), p = 1.000
Combination of left one-sided p-values:
Chi-squared = 529.8684 (d.f. = 6), p < 0.001
--------------------------------------------------------------------------------
Parameter 2: eval : reciprocity
--------------------------------------------------------------------------------
3 datasets used.
Test that estimates and standard errors are uncorrelated:
Spearman's rank correlation rho = 0.5, two-sided p = 1.000
Estimates and test based on IWLS modification of Snijders & Baerveldt (2003)
----------------------------------------------------------------------------
Test that all parameters are 0 :
chi-squared = 91.2626, d.f. = 3, p < 0.001
Estimated mean parameter 2.0505 (s.e. 0.3596), two-sided p = 0.029
Estimated standard deviation 0.6229
Test that variance of parameter is 0 :
Chi-squared = 5.5594 (d.f. = 2), p = 0.062
Estimates and confidence intervals under normality assumptions
------------------------------------------------------- -------
Estimated mean parameter 2.0237 (s.e. 0.3173), two-sided p = 0.024
0.95 level confidence interval [ 1.2349 , 2.9875 ]
Estimated standard deviation 0.371
0.95 level confidence interval [ 0 , 1.5081 ]
Fisher's combination of one-sided tests
----------------------------------------
Combination of right one-sided p-values:
Chi-squared = 106.7713 (d.f. = 6), p < 0.001
Combination of left one-sided p-values:
Chi-squared = 0.0012 (d.f. = 6), p = 1.000
--------------------------------------------------------------------------------
Parameter 3: eval : transitive triplets
--------------------------------------------------------------------------------
3 datasets used.
Test that estimates and standard errors are uncorrelated:
Spearman's rank correlation rho = 0.5, two-sided p = 1.000
Estimates and test based on IWLS modification of Snijders & Baerveldt (2003)
----------------------------------------------------------------------------
Test that all parameters are 0 :
chi-squared = 85.2941, d.f. = 3, p < 0.001
Estimated mean parameter 0.8079 (s.e. 0.229), two-sided p = 0.072
Estimated standard deviation 0.3966
Test that variance of parameter is 0 :
Chi-squared = 8.3368 (d.f. = 2), p = 0.015
Estimates and confidence intervals under normality assumptions
------------------------------------------------------- -------
Estimated mean parameter 0.7742 (s.e. 0.194), two-sided p = 0.057
0.95 level confidence interval [ 0.317 , 1.4045 ]
Estimated standard deviation 0.2614
0.95 level confidence interval [ 0 , 0.9531 ]
Fisher's combination of one-sided tests
----------------------------------------
Combination of right one-sided p-values:
Chi-squared = 100.3808 (d.f. = 6), p < 0.001
Combination of left one-sided p-values:
Chi-squared = 6e-04 (d.f. = 6), p = 1.000
--------------------------------------------------------------------------------
Parameter 4: eval : transitive recipr. triplets
--------------------------------------------------------------------------------
0 datasets used.
There were no data sets satisfying the bounds for this parameter.
No combined output is given.
-----------------------------------------------------------------
Score tests:
Fisher combination
-----------------------------------------------------------------
(4) eval : transitive recipr. triplets
Data set 1, SingleGroups(ans.1) : z = -2.6624
Data set 2, SingleGroups(ans.3) : z = -1.5974
Data set 3, SingleGroups(ans.4) : z = -3.3044
Combination of right one-sided p-values:
Chi-squared = 0.122 (d.f. = 6), p = 1.000
Combination of left one-sided p-values:
Chi-squared = 32.2028 (d.f. = 6), p < 0.001
Fplus Fminus pplus pminus df
eval : outdegree (density) 2.244881e-14 5.298684e+02 1 0 6
eval : reciprocity 1.067713e+02 1.196272e-03 0 1 6
eval : transitive triplets 1.003808e+02 5.619543e-04 0 1 6
Fplus Fminus pplus pminus df
eval : outdegree (density) 0.0000 529.8684 1 0 6
eval : reciprocity 106.7713 0.0012 0 1 6
eval : transitive triplets 100.3808 0.0006 0 1 6
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