Description
Modeling Moderated Networks.
Description
Methods for modeling moderator variables in cross-sectional, temporal, and multi-level networks. Includes model selection techniques and a variety of plotting functions. Implements the methods described by Swanson (2020) <https://www.proquest.com/openview/d151ab6b93ad47e3f0d5e59d7b6fd3d3>.
README.md
modnets
R package designed to afford exploratory and confirmatory estimation of 3 types of moderated networks:
- Cross-sectional moderated networks
- Involves nodewise estimation of a GGM with higher-order interactions
- Can accommodate any combination of continuous and binary variables.
- Nodewise regressions are fit using either OLS or logistic regression, depending on variable types.
- Idiographic (temporal) moderated networks
- Involves generalized least squares (GLS) estimation of multivariate time series model, as well as the inverse-covariance structure of the residuals.
- Currently only works for continuous variables, although exogenous moderators can be binary.
- Default estimation is seemingly unrelated regressions (SUR) via
systemfit, but OLS is also available (unconstrained SUR estimates are equivalent to OLS estimates).
- Multi-level moderated networks
- Uses one of two methods for estimation.
- One is a two-step multilevel model, where fixed/random effects are estimated separately from between-subject effects
- The other uses a formal multilevel moderated vector autoregressive model with
lmer - Only works for continuous variables, although exogenous moderators can be binary.
Additionally, model selection techniques based on penalized regression and iterative resampling are implemented alongside a variety of plotting and data-generating functions.
Installation
You can install the development version of modnets from GitHub with:
# install.packages('devtools')
devtools::install_github('tswanson222/modnets')
Usage
library(modnets)
data <- na.omit(psychTools::msq[, c('hostile', 'lonely', 'nervous', 'sleepy', 'depressed')])
fit <- fitNetwork(data, moderators = 'depressed')
plot(fit, threshold = TRUE)
Package Functions
Primary functions
- The primary function used for the first two types of models is:
fitNetwork. There are a variety of arguments and options that can be used for, e.g., penalized estimation, model specification, etc. - The primary functions used for the third model are:
mlGVARandlmerVAR, depending on which approach you wish to use.
Model selection
- For model selection, you can use
varSelectto employ either best-subset selection (vialeaps), the LASSO, ridge regression, or elastic net (viaglmnet), or the hierarchical LASSO (viaglinternet). These methods support various information criteria as well as cross-validation for model selection, and are embedded within thevarSelectfunction. - As a note, all of the model selection procedures in
varSelectoperate on a sequential, nodewise basis. - Additionally, you can use the
resamplefunction to use repeated subsampling or bootstrapping with thevarSelectalgorithm built in. - This latter method will take into account the actual model-fit values (such as those obtained in the GLS-driven SUR for temporal networks)
Stability & power analyses
- Currently, these methods are not supported in the multilevel setting.
- For bootstrapping/edge-weight accuracy analysis, you can use the
bootNetfunction. - For case-dropping stability analysis, you can use
bootNetwhile settingcaseDrop = TRUE. - For power analysis, you can use:
mnetPowerSimto simulate data based on expected network structure(s).
See the package description for an overview of these and other core functions.
library(modnets)
?modnets
Examples
Cross-sectional moderated network
library(modnets)
# Package is now loaded!
### ================================================ ###
### ======= SIMULATE MODERATED NETWORK DATA ======== ###
### ================================================ ###
# Can simulate data with no moderators, or with one exogenous moderator
set.seed(123)
x <- simNet(N = 500, p = 5, m = TRUE, m1 = .5, m2 = .2)
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#> Time difference of 21.95177 secs
str(x)
#> List of 6
#> $ data :'data.frame': 500 obs. of 6 variables:
#> ..$ V1: num [1:500] 0.25 -1.22 -0.396 -1.203 -0.383 ...
#> ..$ V2: num [1:500] 1.294 0.863 0.579 3.47 0.766 ...
#> ..$ V3: num [1:500] -0.355 0.12 0.102 -1.765 -0.218 ...
#> ..$ V4: num [1:500] -0.0265 1.3573 -1.543 -1.2674 0.5639 ...
#> ..$ V5: num [1:500] 0.742 -1.374 1.199 2.171 0.538 ...
#> ..$ M : num [1:500] -0.0154 -2.0282 -0.3164 -1.5306 -1.8338 ...
#> $ b1 : num [1:5, 1:5] 0 0 -0.445 0 0 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : NULL
#> $ b2 : num [1:5, 1:5] 0 0 0 0 0.193 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : NULL
#> .. ..$ : NULL
#> $ intercepts: num [1:5] 0 0 0 0 0
#> $ m : num -0.56
#> $ m1 : num [1:5] 0.233 -0.34 -0.137 0 -0.162
#> - attr(*, "m2")= num 2
#> - attr(*, "modType")= chr "none"
#> - attr(*, "class")= chr [1:2] "list" "ggmSim"
#> - attr(*, "time")= 'difftime' num 21.9515688419342
#> ..- attr(*, "units")= chr "secs"
### Contents:
# x$data -------- 500x6 dataset, where 'M' is the moderator
# x$b1 ---------- true regression coefficients, where columns --> rows
# x$b2 ---------- true interaction coefficients, where (M * columns) --> rows
# x$intercepts -- true intercepts; defaults to 0
# x$m ----------- true mean of 'M'
# x$m1 ---------- coefficents for main effects of M on outcomes; default to 0
head(x$data)
#> V1 V2 V3 V4 V5 M
#> 1 0.2503133 1.2941247 -0.3551904 -0.0265180 0.7419560 -0.01537839
#> 2 -1.2199405 0.8633412 0.1199374 1.3572920 -1.3739953 -2.02821907
#> 3 -0.3964995 0.5792081 0.1020903 -1.5429760 1.1990735 -0.31635159
#> 4 -1.2029323 3.4699356 -1.7648713 -1.2674076 2.1714251 -1.53060311
#> 5 -0.3833459 0.7655554 -0.2175814 0.5639044 0.5379368 -1.83380340
#> 6 -1.8996645 1.4409709 -0.1385961 -0.0816034 2.0968175 -0.19894797
print(x$b1)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.000000 0.0000000 -0.4449240 0.0000000 0.0000000
#> [2,] 0.000000 0.0000000 0.2829328 0.0000000 0.3307213
#> [3,] -0.444924 0.2829328 0.0000000 0.2991120 0.0000000
#> [4,] 0.000000 0.0000000 0.2991120 0.0000000 -0.3089766
#> [5,] 0.000000 0.3307213 0.0000000 -0.3089766 0.0000000
print(x$b2)
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.0000000 0 0.0000000 0 0.1931925
#> [2,] 0.0000000 0 0.0000000 0 0.0000000
#> [3,] 0.0000000 0 0.0000000 0 0.2715655
#> [4,] 0.0000000 0 0.0000000 0 0.0000000
#> [5,] 0.1931925 0 0.2715655 0 0.0000000
print(x$intercepts)
#> [1] 0 0 0 0 0
print(x$m)
#> [1] -0.5604756
print(x$m1)
#> [1] 0.2326600 -0.3396775 -0.1365698 0.0000000 -0.1619594
dat0 <- x$data[, -6]
dat1 <- x$data
# First, lets save an object that excludes the moderator (dat0)
# and save a second with the moderator (dat1)
### ================================================ ###
### =============== FITTING MODELS ================= ###
### ================================================ ###
# First, lets fit an unmoderated network, leaving out 'M' entirely
fit0 <- fitNetwork(data = dat0)
# Next, lets fit a model that only includes 'M' as a covariate
fit1 <- fitNetwork(data = dat1, covariates = 6)
# Now, lets fit the saturated model where 'M' moderates all edges in the network
fit2 <- fitNetwork(data = dat1, moderators = 6)
### ================= PLOTTING ===================== ###
plot(fit0)
plot(fit1)
plot(fit2)
# We can plot each of these models to see the resultant undirected network
plot(fit0, threshold = .05)
plot(fit1, threshold = .05)
plot(fit2, threshold = .05)
# Plot only significant edges (p < threshold) of the network.
plot(fit0, threshold = TRUE, predict = TRUE)
plot(fit1, threshold = TRUE, predict = 'R2')
plot(fit2, threshold = TRUE, predict = 'adjR2')
# Using 'threshold = TRUE' is the same as 'threshold = .05'
# 'predict = TRUE' plots R2 values for each regression
# This can also be specified as a string, as shown
plot(fit2, threshold = TRUE, predict = fit0)
# This can also be used to visually compare networks
# Here, the light blue ring around each node shows
# the R2 for 'fit0', while the slightly darker piece
# shows the increase in R2 that we see with 'fit2'
predictNet(fit2)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 0.279 0.265 1.022 1.011
#> 2 V2 0.314 0.301 1.071 1.035
#> 3 V3 0.428 0.418 1.059 1.029
#> 4 V4 0.278 0.265 0.955 0.977
#> 5 V5 0.295 0.282 1.103 1.050
predictNet(fit2, fit0)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 0.074 0.066 -0.092 -0.044
#> 2 V2 0.080 0.073 -0.112 -0.053
#> 3 V3 0.043 0.038 -0.069 -0.033
#> 4 V4 0.010 0.003 -0.003 -0.002
#> 5 V5 0.045 0.039 -0.059 -0.028
# We can extract these values using this function
# And can take the differences by supplying two networks
# Values for the second model are subtracted from those for the first
plot(fit2, mnet = TRUE)
plot(fit2, threshold = TRUE, mnet = TRUE)
# 'mnet = TRUE' plots the exogenous moderator
### ============= VARIABLE SELECTION =============== ###
# These methods demonstrate the two-stage process for variable selection
# In the first stage, we use the data to select the active set of predictors
# In the second stage, we use those predictors to re-fit the models using OLS
### UNMODERATED NETWORKS
vars0 <- varSelect(data = dat0, criterion = 'BIC', method = 'glmnet')
#> =================================================================================================================================
vfit0 <- fitNetwork(data = dat0, type = vars0)
vfit1 <- fitNetwork(data = dat0, type = 'varSelect', criterion = 'BIC')
predictNet(vfit0, vfit1)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 0 0 0 0
#> 2 V2 0 0 0 0
#> 3 V3 0 0 0 0
#> 4 V4 0 0 0 0
#> 5 V5 0 0 0 0
# In the first method, we use glmnet to perform variable selection for
# each of the nodewise models. Then, we can subsequently include this in the
# 'fitNetwork' function. In the second approach, we can simply include everything
# in one command. We see that these produce the exact same models
vfit2 <- fitNetwork(data = dat0, type = 'varSelect', criterion = 'BIC', method = 'subset')
# We can also use best-subsets selection instead of the LASSO
predictNet(vfit2, vfit1)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 -0.001 0.001 -0.001 0.000
#> 2 V2 -0.001 0.001 -0.002 -0.001
#> 3 V3 0.000 0.000 0.000 0.000
#> 4 V4 0.000 0.000 0.000 0.000
#> 5 V5 -0.017 -0.013 0.020 0.009
# In this case, we see that best-subsets produced lower R2 for three nodes
vfit3 <- fitNetwork(data = dat0, type = 'varSelect', criterion = 'CV', seed = 1)
vfit3.1 <- fitNetwork(data = dat0, type = 'varSelect', criterion = 'CV', seed = 1)
vfit3.2 <- fitNetwork(data = dat0, type = 'varSelect', criterion = 'CV', seed = 99)
# We can also use cross-validation with glmnet (but not best-subsets)
predictNet(vfit3, vfit3.1)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 0 0 0 0
#> 2 V2 0 0 0 0
#> 3 V3 0 0 0 0
#> 4 V4 0 0 0 0
#> 5 V5 0 0 0 0
predictNet(vfit3, vfit3.2)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 0 0 0 0
#> 2 V2 0 0 0 0
#> 3 V3 0 0 0 0
#> 4 V4 0 0 0 0
#> 5 V5 0 0 0 0
# We see that setting a seed leads to reproducible results
### MODERATED NETWORKS
vars1 <- varSelect(data = dat1, m = 6, criterion = 'BIC', method = 'glinternet')
#> Fitting model 1/5... Complete! (0.13 secs)
#> Fitting model 2/5... Complete! (0.11 secs)
#> Fitting model 3/5... Complete! (0.08 secs)
#> Fitting model 4/5... Complete! (0.07 secs)
#> Fitting model 5/5... Complete! (0.07 secs)
#> ####### Total time: 0.46 secs
mfit1 <- fitNetwork(data = dat1, moderators = 6, type = vars1)
mfit2 <- fitNetwork(data = dat1, moderators = 6, type = 'varSelect', criterion = 'BIC')
predictNet(mfit1, mfit2)
#> Variable R2 adjR2 MSE RMSE
#> 1 V1 0 0 0 0
#> 2 V2 0 0 0 0
#> 3 V3 0 0 0 0
#> 4 V4 0 0 0 0
#> 5 V5 0 0 0 0
# Again, we see that both methods produce the same model
# Creating the 'vars1' object separately can be useful when we wish
# to analyze the results from the variable selection process; plot outputs, obtain coefficients, etc.
# Also, all moderated networks use 'glinternet' as the selection method, and so it does not need to be specified
mfit2 <- fitNetwork(data = dat1, moderators = 6, type = 'varSelect', criterion = 'CV', seed = 1)
# We can use cross-validation with the glinternet algorithm as well
### ============== MODEL COMPARISON ================ ###
# Create a list of models we want to compare
fits <- list(fit0 = fit0, fit1 = fit1, fit2 = fit2,
vfit1 = vfit1, vfit2 = vfit2, vfit3 = vfit3,
mfit1 = mfit1, mfit2 = mfit2)
modTable(fits)
#> $LRT
#> net0 net1 Chisq Df pval decision
#> 1 fit0 fit1 48.7152 5 0.0000 fit1
#> 2 fit0 fit2 147.1725 25 0.0000 fit2
#> 3 vfit1 fit0 0.0178 4 1.0000 vfit1
#> 4 vfit2 fit0 22.7036 8 0.0038 fit0
#> 5 vfit3 fit0 0.0178 4 1.0000 vfit3
#> 6 fit0 mfit1 121.7265 4 0.0000 mfit1
#> 7 fit0 mfit2 140.1842 12 0.0000 mfit2
#> 8 fit1 fit2 98.4573 20 0.0000 fit2
#> 9 vfit1 fit1 48.7330 9 0.0000 fit1
#> 10 vfit2 fit1 71.4188 13 0.0000 fit1
#> 11 vfit3 fit1 48.7330 9 0.0000 fit1
#> 12 mfit1 fit1 73.0112 1 0.0000 mfit1
#> 13 fit1 mfit2 91.4690 7 0.0000 mfit2
#> 14 vfit1 fit2 147.1903 29 0.0000 fit2
#> 15 vfit2 fit2 169.8762 33 0.0000 fit2
#> 16 vfit3 fit2 147.1903 29 0.0000 fit2
#> 17 mfit1 fit2 25.4461 21 0.2284 mfit1
#> 18 mfit2 fit2 6.9883 13 0.9028 mfit2
#> 19 vfit2 vfit1 22.6858 4 0.0001 vfit1
#> 20 vfit1 vfit3 0.0000 0 1.0000 -
#> 21 vfit1 mfit1 121.7443 8 0.0000 mfit1
#> 22 vfit1 mfit2 140.2020 16 0.0000 mfit2
#> 23 vfit2 vfit3 22.6858 4 0.0001 vfit3
#> 24 vfit2 mfit1 144.4301 12 0.0000 mfit1
#> 25 vfit2 mfit2 162.8878 20 0.0000 mfit2
#> 26 vfit3 mfit1 121.7443 8 0.0000 mfit1
#> 27 vfit3 mfit2 140.2020 16 0.0000 mfit2
#> 28 mfit1 mfit2 18.4577 8 0.0180 mfit2
#>
#> $omnibus
#> LL df AIC BIC LRT
#> mfit2 -3400.600 38 6877.199 7098.513 7
#> mfit1 -3409.829 30 6879.657 7054.379 6
#> fit2 -3397.106 51 6896.211 7193.237 5
#> fit1 -3446.334 31 6954.668 7135.214 4
#> vfit1 -3470.701 22 6985.401 7113.530 2
#> vfit3 -3470.701 22 6985.401 7113.530 2
#> fit0 -3470.692 26 6993.384 7144.809 1
#> vfit2 -3482.044 18 7000.087 7104.920 0
#>
#> attr(,"alpha")
#> [1] 0.05
# Performs likelihood ratio tests comparing each model with every other
modTable(fits)$omnibus
#> LL df AIC BIC LRT
#> mfit2 -3400.600 38 6877.199 7098.513 7
#> mfit1 -3409.829 30 6879.657 7054.379 6
#> fit2 -3397.106 51 6896.211 7193.237 5
#> fit1 -3446.334 31 6954.668 7135.214 4
#> vfit1 -3470.701 22 6985.401 7113.530 2
#> vfit3 -3470.701 22 6985.401 7113.530 2
#> fit0 -3470.692 26 6993.384 7144.809 1
#> vfit2 -3482.044 18 7000.087 7104.920 0
# This shows us the final results. The 'LRT' column indicates
# the total number of times each model was selected across all tests
# We can see that 'fit2' (the saturated MNM) was selected across all tests
# The second-most selected was 'mfit2', which used glinternet with CV selection
modTable(fits, nodes = TRUE)
#> $nodes
#> $nodes$V1
#> LL df AIC BIC
#> fit0 -733.9535 495 1479.907 1505.195
#> fit1 -720.1321 494 1454.264 1483.767
#> fit2 -709.7404 490 1441.481 1487.841
#> vfit1 -733.9565 496 1477.913 1498.986
#> vfit2 -734.2404 497 1476.481 1493.339
#> vfit3 -733.9565 496 1477.913 1498.986
#> mfit1 -710.8920 494 1435.784 1465.286
#> mfit2 -710.8920 494 1435.784 1465.286
#>
#> $nodes$V2
#> LL df AIC BIC
#> fit0 -748.9500 495 1509.900 1535.188
#> fit1 -724.3260 494 1462.652 1492.154
#> fit2 -721.4508 490 1464.902 1511.262
#> vfit1 -748.9514 496 1507.903 1528.976
#> vfit2 -749.2353 497 1506.471 1523.329
#> vfit3 -748.9514 496 1507.903 1528.976
#> mfit1 -724.7573 496 1459.515 1480.588
#> mfit2 -721.8251 493 1459.650 1493.367
#>
#> $nodes$V3
#> LL df AIC BIC
#> fit0 -737.0920 495 1486.184 1511.472
#> fit1 -736.8972 494 1487.794 1517.297
#> fit2 -718.8669 490 1459.734 1506.094
#> vfit1 -737.0920 495 1486.184 1511.472
#> vfit2 -737.0920 495 1486.184 1511.472
#> vfit3 -737.0920 495 1486.184 1511.472
#> mfit1 -720.3461 492 1458.692 1496.624
#> mfit2 -718.8669 490 1459.734 1506.094
#>
#> $nodes$V4
#> LL df AIC BIC
#> fit0 -696.3325 495 1404.665 1429.953
#> fit1 -696.0762 494 1406.152 1435.655
#> fit2 -692.7979 490 1407.596 1453.957
#> vfit1 -696.3371 497 1400.674 1417.533
#> vfit2 -696.3371 497 1400.674 1417.533
#> vfit3 -696.3371 497 1400.674 1417.533
#> mfit1 -696.3371 497 1400.674 1417.533
#> mfit2 -693.5546 495 1399.109 1424.397
#>
#> $nodes$V5
#> LL df AIC BIC
#> fit0 -744.4335 495 1500.867 1526.155
#> fit1 -744.4163 494 1502.833 1532.335
#> fit2 -728.9414 490 1479.883 1526.244
#> vfit1 -744.4335 495 1500.867 1526.155
#> vfit2 -749.8211 497 1507.642 1524.501
#> vfit3 -744.4335 495 1500.867 1526.155
#> mfit1 -729.0802 492 1476.160 1514.092
#> mfit2 -728.9428 491 1477.886 1520.032
#>
#>
#> $LRT
#> $LRT$LL_diff2
#> net0 net1 | V1 V2 V3 V4 V5
#> 1 fit0 fit1 | 27.642732993 49.248007033 0.3895996 0.512704268 0.034506600
#> 2 fit0 fit2 | 48.426212747 54.998357118 36.4501942 7.069194569 30.984132425
#> 3 vfit1 fit0 | 0.005980198 0.002913092 0.0000000 0.009184894 0.000000000
#> 4 vfit2 fit0 | 0.573754166 0.570687060 0.0000000 0.009184894 10.775144944
#> 5 vfit3 fit0 | 0.005980198 0.002913092 0.0000000 0.009184894 0.000000000
#> 6 fit0 mfit1 | 46.122928240 48.385466247 33.4917773 0.009184894 30.706638845
#> 7 fit0 mfit2 | 46.122928240 54.249832678 36.4501942 5.555794961 30.981365617
#> 8 fit1 fit2 | 20.783479754 5.750350084 36.0605946 6.556490301 30.949625826
#> 9 vfit1 fit1 | 27.648713191 49.250920125 0.3895996 0.521889162 0.034506600
#> 10 vfit2 fit1 | 28.216487159 49.818694093 0.3895996 0.521889162 10.809651544
#> 11 vfit3 fit1 | 27.648713191 49.250920125 0.3895996 0.521889162 0.034506600
#> 12 mfit1 fit1 | 18.480195247 0.862540787 33.1021777 0.521889162 30.672132246
#> 13 fit1 mfit2 | 18.480195247 5.001825644 36.0605946 5.043090693 30.946859017
#> 14 vfit1 fit2 | 48.432192945 55.001270210 36.4501942 7.078379463 30.984132425
#> 15 vfit2 fit2 | 48.999966913 55.569044177 36.4501942 7.078379463 41.759277369
#> 16 vfit3 fit2 | 48.432192945 55.001270210 36.4501942 7.078379463 30.984132425
#> 17 mfit1 fit2 | 2.303284507 6.612890871 2.9584169 7.078379463 0.277493580
#> 18 mfit2 fit2 | 2.303284507 0.748524440 0.0000000 1.513399608 0.002766809
#> 19 vfit2 vfit1 | 0.567773968 0.567773968 0.0000000 0.000000000 10.775144944
#> 20 vfit1 vfit3 | 0.000000000 0.000000000 0.0000000 0.000000000 0.000000000
#> 21 vfit1 mfit1 | 46.128908438 48.388379339 33.4917773 0.000000000 30.706638845
#> 22 vfit1 mfit2 | 46.128908438 54.252745770 36.4501942 5.564979855 30.981365617
#> 23 vfit2 vfit3 | 0.567773968 0.567773968 0.0000000 0.000000000 10.775144944
#> 24 vfit2 mfit1 | 46.696682406 48.956153307 33.4917773 0.000000000 41.481783789
#> 25 vfit2 mfit2 | 46.696682406 54.820519737 36.4501942 5.564979855 41.756510561
#> 26 vfit3 mfit1 | 46.128908438 48.388379339 33.4917773 0.000000000 30.706638845
#> 27 vfit3 mfit2 | 46.128908438 54.252745770 36.4501942 5.564979855 30.981365617
#> 28 mfit1 mfit2 | 0.000000000 5.864366431 2.9584169 5.564979855 0.274726771
#>
#> $LRT$Df_diff
#> net0 net1 | V1 V2 V3 V4 V5
#> 1 fit0 fit1 | 1 1 1 1 1
#> 2 fit0 fit2 | 5 5 5 5 5
#> 3 vfit1 fit0 | 1 1 0 2 0
#> 4 vfit2 fit0 | 2 2 0 2 2
#> 5 vfit3 fit0 | 1 1 0 2 0
#> 6 fit0 mfit1 | 1 1 3 2 3
#> 7 fit0 mfit2 | 1 2 5 0 4
#> 8 fit1 fit2 | 4 4 4 4 4
#> 9 vfit1 fit1 | 2 2 1 3 1
#> 10 vfit2 fit1 | 3 3 1 3 3
#> 11 vfit3 fit1 | 2 2 1 3 1
#> 12 mfit1 fit1 | 0 2 2 3 2
#> 13 fit1 mfit2 | 0 1 4 1 3
#> 14 vfit1 fit2 | 6 6 5 7 5
#> 15 vfit2 fit2 | 7 7 5 7 7
#> 16 vfit3 fit2 | 6 6 5 7 5
#> 17 mfit1 fit2 | 4 6 2 7 2
#> 18 mfit2 fit2 | 4 3 0 5 1
#> 19 vfit2 vfit1 | 1 1 0 0 2
#> 20 vfit1 vfit3 | 0 0 0 0 0
#> 21 vfit1 mfit1 | 2 0 3 0 3
#> 22 vfit1 mfit2 | 2 3 5 2 4
#> 23 vfit2 vfit3 | 1 1 0 0 2
#> 24 vfit2 mfit1 | 3 1 3 0 5
#> 25 vfit2 mfit2 | 3 4 5 2 6
#> 26 vfit3 mfit1 | 2 0 3 0 3
#> 27 vfit3 mfit2 | 2 3 5 2 4
#> 28 mfit1 mfit2 | 0 3 2 2 1
#>
#> $LRT$pval
#> net0 net1 | V1 V2 V3 V4 V5
#> 1 fit0 fit1 | 0.0000 0.0000 0.5325 0.4740 0.8526
#> 2 fit0 fit2 | 0.0000 0.0000 0.0000 0.2155 0.0000
#> 3 vfit1 fit0 | 0.9384 0.9570 1.0000 0.9954 1.0000
#> 4 vfit2 fit0 | 0.7506 0.7518 1.0000 0.9954 0.0046
#> 5 vfit3 fit0 | 0.9384 0.9570 1.0000 0.9954 1.0000
#> 6 fit0 mfit1 | 0.0000 0.0000 0.0000 0.9954 0.0000
#> 7 fit0 mfit2 | 0.0000 0.0000 0.0000 0.0000 0.0000
#> 8 fit1 fit2 | 0.0003 0.2186 0.0000 0.1613 0.0000
#> 9 vfit1 fit1 | 0.0000 0.0000 0.5325 0.9141 0.8526
#> 10 vfit2 fit1 | 0.0000 0.0000 0.5325 0.9141 0.0128
#> 11 vfit3 fit1 | 0.0000 0.0000 0.5325 0.9141 0.8526
#> 12 mfit1 fit1 | 0.0000 0.6497 0.0000 0.9141 0.0000
#> 13 fit1 mfit2 | 0.0000 0.0253 0.0000 0.0247 0.0000
#> 14 vfit1 fit2 | 0.0000 0.0000 0.0000 0.4208 0.0000
#> 15 vfit2 fit2 | 0.0000 0.0000 0.0000 0.4208 0.0000
#> 16 vfit3 fit2 | 0.0000 0.0000 0.0000 0.4208 0.0000
#> 17 mfit1 fit2 | 0.6802 0.3581 0.2278 0.4208 0.8704
#> 18 mfit2 fit2 | 0.6802 0.8617 1.0000 0.9115 0.9581
#> 19 vfit2 vfit1 | 0.4511 0.4511 1.0000 1.0000 0.0046
#> 20 vfit1 vfit3 | 1.0000 1.0000 1.0000 1.0000 1.0000
#> 21 vfit1 mfit1 | 0.0000 0.0000 0.0000 1.0000 0.0000
#> 22 vfit1 mfit2 | 0.0000 0.0000 0.0000 0.0619 0.0000
#> 23 vfit2 vfit3 | 0.4511 0.4511 1.0000 1.0000 0.0046
#> 24 vfit2 mfit1 | 0.0000 0.0000 0.0000 1.0000 0.0000
#> 25 vfit2 mfit2 | 0.0000 0.0000 0.0000 0.0619 0.0000
#> 26 vfit3 mfit1 | 0.0000 0.0000 0.0000 1.0000 0.0000
#> 27 vfit3 mfit2 | 0.0000 0.0000 0.0000 0.0619 0.0000
#> 28 mfit1 mfit2 | 1.0000 0.1184 0.2278 0.0619 0.6002
#>
#> $LRT$decision
#> net0 net1 | V1 V2 V3 V4 V5
#> 1 fit0 fit1 | fit1 fit1 fit0 fit0 fit0
#> 2 fit0 fit2 | fit2 fit2 fit2 fit0 fit2
#> 3 vfit1 fit0 | vfit1 vfit1 - vfit1 -
#> 4 vfit2 fit0 | vfit2 vfit2 - vfit2 fit0
#> 5 vfit3 fit0 | vfit3 vfit3 - vfit3 -
#> 6 fit0 mfit1 | mfit1 mfit1 mfit1 mfit1 mfit1
#> 7 fit0 mfit2 | mfit2 mfit2 mfit2 mfit2 mfit2
#> 8 fit1 fit2 | fit2 fit1 fit2 fit1 fit2
#> 9 vfit1 fit1 | fit1 fit1 vfit1 vfit1 vfit1
#> 10 vfit2 fit1 | fit1 fit1 vfit2 vfit2 fit1
#> 11 vfit3 fit1 | fit1 fit1 vfit3 vfit3 vfit3
#> 12 mfit1 fit1 | mfit1 mfit1 mfit1 mfit1 mfit1
#> 13 fit1 mfit2 | mfit2 mfit2 mfit2 mfit2 mfit2
#> 14 vfit1 fit2 | fit2 fit2 fit2 vfit1 fit2
#> 15 vfit2 fit2 | fit2 fit2 fit2 vfit2 fit2
#> 16 vfit3 fit2 | fit2 fit2 fit2 vfit3 fit2
#> 17 mfit1 fit2 | mfit1 mfit1 mfit1 mfit1 mfit1
#> 18 mfit2 fit2 | mfit2 mfit2 - mfit2 mfit2
#> 19 vfit2 vfit1 | vfit2 vfit2 - - vfit1
#> 20 vfit1 vfit3 | - - - - -
#> 21 vfit1 mfit1 | mfit1 mfit1 mfit1 - mfit1
#> 22 vfit1 mfit2 | mfit2 mfit2 mfit2 vfit1 mfit2
#> 23 vfit2 vfit3 | vfit2 vfit2 - - vfit3
#> 24 vfit2 mfit1 | mfit1 mfit1 mfit1 - mfit1
#> 25 vfit2 mfit2 | mfit2 mfit2 mfit2 vfit2 mfit2
#> 26 vfit3 mfit1 | mfit1 mfit1 mfit1 - mfit1
#> 27 vfit3 mfit2 | mfit2 mfit2 mfit2 vfit3 mfit2
#> 28 mfit1 mfit2 | - mfit1 mfit1 mfit1 mfit1
#>
#>
#> $counts
#> V1 V2 V3 V4 V5
#> fit0 0 0 1 2 2
#> fit1 4 5 0 1 1
#> fit2 5 4 5 0 5
#> vfit1 1 1 1 4 2
#> vfit2 3 3 1 4 0
#> vfit3 1 1 1 4 2
#> mfit1 6 7 7 4 7
#> mfit2 6 6 5 3 6
#>
#> attr(,"alpha")
#> [1] 0.05
# This does the same thing as above but at the nodewise level
More examples to be added soon.
Please contact [email protected] with any questions.