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 released version of the package from CRAN, or the development version from GitHub with:
# Install the package from CRAN install.packages('modnets') # Or install the development version from GitHub # 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) #> | | | 0% | | | 1% | |= | 1% | |= | 2% | |== | 2% | |== | 3% | |=== | 4% | |=== | 5% | |==== | 5% | |==== | 6% | |===== | 7% | |===== | 8% | |====== | 8% | |====== | 9% | |======= | 9% | |======= | 10% | |======= | 11% | |======== | 11% | |======== | 12% | |========= | 12% | |========= | 13% | |========== | 14% | |========== | 15% | |=========== | 15% | |=========== | 16% | |============ | 17% | |============ | 18% | |============= | 18% | |============= | 19% | |============== | 19% | |============== | 20% | |============== | 21% | |=============== | 21% | |=============== | 22% | |================ | 22% | |================ | 23% | |================= | 24% | |================= | 25% | |================== | 25% | |================== | 26% | |=================== | 27% | |=================== | 28% | |==================== | 28% | |==================== | 29% | |===================== | 29% | |===================== | 30% | |===================== | 31% | |====================== | 31% | |====================== | 32% | |======================= | 32% | |======================= | 33% | |======================== | 34% | |======================== | 35% | |========================= | 35% | |========================= | 36% | |========================== | 37% | |========================== | 38% | |=========================== | 38% | |=========================== | 39% | |============================ | 39% | |============================ | 40% | |============================ | 41% | |============================= | 41% | |============================= | 42% | |============================== | 42% | |============================== | 43% | |=============================== | 44% | |=============================== | 45% | |================================ | 45% | |================================ | 46% | |================================= | 47% | |================================= | 48% | |================================== | 48% | |================================== | 49% | |=================================== | 49% | |=================================== | 50% | |=================================== | 51% | |==================================== | 51% | |==================================== | 52% | |===================================== | 52% | |===================================== | 53% | |====================================== | 54% | |====================================== | 55% | |======================================= | 55% | |======================================= | 56% | |======================================== | 57% | |======================================== | 58% | |========================================= | 58% | |========================================= | 59% | |========================================== | 59% | |========================================== | 60% | |========================================== | 61% | |=========================================== | 61% | |=========================================== | 62% | |============================================ | 62% | |============================================ | 63% | |============================================= | 64% | |============================================= | 65% | |============================================== | 65% | |============================================== | 66% | |=============================================== | 67% | |=============================================== | 68% | |================================================ | 68% | |================================================ | 69% | |================================================= | 69% | |================================================= | 70% | |================================================= | 71% | |================================================== | 71% | |================================================== | 72% | |=================================================== | 72% | |=================================================== | 73% | |==================================================== | 74% | |==================================================== | 75% | |===================================================== | 75% | |===================================================== | 76% | |====================================================== | 77% | |====================================================== | 78% | |======================================================= | 78% | |======================================================= | 79% | |======================================================== | 79% | |======================================================== | 80% | |======================================================== | 81% | |========================================================= | 81% | |========================================================= | 82% | |========================================================== | 82% | |========================================================== | 83% | |=========================================================== | 84% | |=========================================================== | 85% | |============================================================ | 85% | |============================================================ | 86% | |============================================================= | 87% | |============================================================= | 88% | |============================================================== | 88% | |============================================================== | 89% | |=============================================================== | 89% | |=============================================================== | 90% | |=============================================================== | 91% | |================================================================ | 91% | |================================================================ | 92% | |================================================================= | 92% | |================================================================= | 93% | |================================================================== | 94% | |================================================================== | 95% | |=================================================================== | 95% | |=================================================================== | 96% | |==================================================================== | 97% | |==================================================================== | 98% | |===================================================================== | 98% | |===================================================================== | 99% | |======================================================================| 99% | |======================================================================| 100% #> Time difference of 17.60832 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 17.6081564426422 #> ..- 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! (0.11 secs) #> Fitting model 2/5... Complete! (0.09 secs) #> Fitting model 3/5... Complete! (0.06 secs) #> Fitting model 4/5... Complete! (0.05 secs) #> Fitting model 5/5... Complete! (0.06 secs) #> ####### Total time: 0.38 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 trevorswanson222@gmail.com with any questions.