| Title: | Tools for Identifying Important Nodes in Networks |
|---|---|
| Description: | Includes assorted tools for network analysis. Bridge centrality; goldbricker; MDS, PCA, & eigenmodel network plotting. |
| Authors: | Payton Jones [aut, cre] |
| Maintainer: | Payton Jones <[email protected]> |
| License: | GPL-3 |
| Version: | 1.5.2 |
| Built: | 2024-11-21 02:50:21 UTC |
| Source: | https://github.com/paytonjjones/networktools |
Checks some basic assumptions about the suitability of network analysis on your data
assumptionCheck( data, type = c("network", "impact"), percent = 20, split = c("median", "mean", "forceEqual", "cutEqual", "quartiles"), plot = FALSE, binary.data = FALSE, na.rm = TRUE )assumptionCheck( data, type = c("network", "impact"), percent = 20, split = c("median", "mean", "forceEqual", "cutEqual", "quartiles"), plot = FALSE, binary.data = FALSE, na.rm = TRUE )
data |
dataframe or matrix of observational data (rows: observations, columns: nodes) |
type |
which assumptions to check? "network" tests the suitability for network analysis in general. "impact" tests the suitability for analyzing impact |
percent |
percent difference from grand mean that is acceptable when comparing variances. |
split |
if type="impact", specifies the type of split to utilize |
plot |
logical. Should histograms each variable be plotted? |
binary.data |
logical. Defaults to FALSE |
na.rm |
logical. Should missing values be removed? |
Network analysis rests on several assumptions. Among these: - Variance of each node is (roughly) equal - Distributions are (roughly) normal
Comparing networks in impact rests on additional assumptions including: - Overall variances are (roughly) equal in each half
This function checks these assumptions and notifies any violations. This function is not intended as a substitute for careful data visualization and independent assumption checks.
See citations in the references section for further details.
Terluin, B., de Boer, M. R., & de Vet, H. C. W. (2016). Differences in Connection Strength between Mental Symptoms Might Be Explained by Differences in Variance: Reanalysis of Network Data Did Not Confirm Staging. PLOS ONE, 11(11), e0155205. Retrieved from https://doi.org/10.1371/journal.pone.0155205
Calculates bridge centrality metrics (bridge strength, bridge betweenness, bridge closeness, and bridge expected influence) given a network and a prespecified set of communities.
bridge( network, communities = NULL, useCommunities = "all", directed = NULL, nodes = NULL, normalize = FALSE )bridge( network, communities = NULL, useCommunities = "all", directed = NULL, nodes = NULL, normalize = FALSE )
network |
a network of class "igraph", "qgraph", or an adjacency matrix representing a network |
communities |
an object of class "communities" (igraph) OR a character vector of community assignments for each node (e.g., c("Comm1", "Comm1", "Comm2", "Comm2)). The ordering of this vector should correspond to the vector from argument "nodes". Can also be in list format (e.g., list("Comm1"=c(1:10), "Comm2"=c(11:20))) |
useCommunities |
character vector specifying which communities should be included. Default set to "all" |
directed |
logical. Directedness is automatically detected if set to "NULL" (the default). Symmetric adjacency matrices will be undirected, asymmetric matrices will be directed |
nodes |
a vector containing the names of the nodes. If set to "NULL", this vector will be automatically detected in the order extracted |
normalize |
logical. Bridge centralities are divided by their highest possible value (assuming max edge strength=1) in order to normalize by different community sizes |
To plot the results, first save as an object, and then use plot() (see ?plot.bridge)
Centrality metrics (strength, betweenness, etc.) illuminate how nodes are interconnected among the entire network. However, sometimes we are interested in the connectivity between specific communities in a larger network. Nodes that are important in communication between communities can be conceptualized as bridge nodes.
Bridge centrality statistics aim to identify bridge nodes. Bridge centralities
can be calculated across all communities, or between a specific subset of communities (as
identified by the useCommunities argument)
The bridge() function currently returns 5 centrality metrics: 1) bridge strength, 2) bridge betweenness, 3) bridge closeness, 4) bridge expected influence (1-step), and 5) bridge expected influence (2-step)
See ?plot.bridge for plotting details.
Bridge strength is defined as the sum of the absolute value of all edges that exist between a node A and all nodes that are not in the same community as node A. In a directed network, bridge strength can be separated into bridge in-degree and bridge out-degree.
Bridge betweenness is defined as the number of times a node B lies on the shortest path between nodes A and C, where nodes A and C come from different communities.
Bridge closeness is defined as the inverse of the average length of the path from a node A to all nodes that are not in the same community as node A.
Bridge expected influence (1-step) is defined as the sum of the value (+ or -) of all edges that exist between a node A and all nodes that are not in the same community as node A. In a directed network, expected influence only considers edges extending from the given node (e.g., out-degree)
Bridge expected influence (2-step) is similar to 1-step, but also considers the indirect effect that a node A may have on other communities through other nodes (e.g, an indirect effect on node C as in A -> B -> C). Indirect effects are weighted by the first edge weight (e.g., A -> B), and then added to the 1-step expected influence. Indirect effects back on node A's own community (A -> B -> A) are not counted.
If negative edges exist, bridge expected influence should be used. Bridge closeness and bridge betweenness are only defined for positive edge weights, thus negative edges, if present, are deleted in the calculation of these metrics. Bridge strength uses the absolute value of edge weights.
bridge returns a list of class bridge which contains:
$'Bridge Strength'
$'Bridge Betweenness'
$'Bridge Closeness'
$'Bridge Expected Influence (1-step)'
$'Bridge Expected Influence (2-step)'
Each of these contains a vector of named centrality values
$'communities' is also returned, which returns the communities in vector format. If communities were supplied as a list or igraph object, it is advised that one check the accuracy of this vector.
graph1 <- qgraph::qgraph(cor(depression)) b <- bridge(graph1, communities=c('1','1','2','2','2','2','1','2','1')) bgraph1 <- qgraph::qgraph(cor(depression)) b <- bridge(graph1, communities=c('1','1','2','2','2','2','1','2','1')) b
Takes an object of type "qgraph", "igraph", or an adjacency matrix (or data.frame) and outputs an adjacency matrix
coerce_to_adjacency(input, directed = NULL)coerce_to_adjacency(input, directed = NULL)
input |
a network of class "igraph", "qgraph", or an adjacency matrix representing a network |
directed |
logical. is the network directed? If set to NULL, auto-detection is used |
This simulated dataset contains severity ratings for 9 symptoms of major depressive disorder in 1000 individuals. Symptom ratings are assumed to be self-reported on a 100 point sliding scale.
depressiondepression
a dataframe. Columns represent symptoms and rows represent individuals
head(depression)head(depression)
Convenience function for converting a qgraph object to an eigenmodel layout
EIGENnet( qgraph_net, EIGENadj = NULL, S = 1000, burn = 200, seed = 1, repulse = F, repulsion = 1, eigenmodelArgs = list(), ... )EIGENnet( qgraph_net, EIGENadj = NULL, S = 1000, burn = 200, seed = 1, repulse = F, repulsion = 1, eigenmodelArgs = list(), ... )
qgraph_net |
an object of type |
EIGENadj |
to use a base matrix for the eigenmodel other than the adjacency matrix
stored in |
S |
number of samples from the Markov chain |
burn |
number of initial scans of the Markov chain to be dropped |
seed |
a random seed |
repulse |
logical. Add a small repulsion force with wordcloud package to avoid node overlap? |
repulsion |
scalar for the repulsion force (if repulse=T). Larger values add more repulsion |
eigenmodelArgs |
additional arguments in list format passed to |
... |
additional arguments passed to |
An eigenmodel can be interpreted based on coordinate placement of each node. A node in the top right corner scored high on both the first and second latent components
Jones, P. J., Mair, P., & McNally, R. J. (2018). Visualizing psychological networks: A tutorial in R. Frontiers in Psychology, 9, 1742. https://doi.org/10.3389/fpsyg.2018.01742
Calculates the one-step and two-step expected influence of each node.
expectedInf(network, step = c("both", 1, 2), directed = FALSE)expectedInf(network, step = c("both", 1, 2), directed = FALSE)
network |
an object of type |
step |
compute 1-step expected influence, 2-step expected influence, or both |
directed |
logical. Specifies if edges are directed, defaults to FALSE |
When a network contains both positive and negative edges, traditional centrality measures such as strength centrality may not accurately predict node influence on the network. Robinaugh, Millner, & McNally (2016) showed that in these cases, expected influence is a more appropriate measure.
One-step expected influence is defined as the sum of all edges extending from a given node (where the sign of each edge is maintained).
Two-step expected influence, as the name implies, measures connectivity up to two edges away from the node. It is defined as the sum of the (weighted) expected influences of each node connected to the initial node plus the one-step expected influence of the initial node. Weights are determined by the edge strength between the initial node and each "second step" node.
See citations in the references section for further details.
Robinaugh, D. J., Millner, A. J., & McNally, R. J. (2016). Identifying highly influential nodes in the complicated grief network. Journal of abnormal psychology, 125, 747.
out1 <- expectedInf(cor(depression[,1:5])) out1$step1 out1$step2 plot(out1) plot(out1, order="value", zscore=TRUE) igraph_obj <- igraph::graph_from_adjacency_matrix(cor(depression)) out_igraph <- expectedInf(igraph_obj) qgraph_obj <- qgraph::qgraph(cor(depression), DoNotPlot=TRUE) out_qgraph <- expectedInf(qgraph_obj)out1 <- expectedInf(cor(depression[,1:5])) out1$step1 out1$step2 plot(out1) plot(out1, order="value", zscore=TRUE) igraph_obj <- igraph::graph_from_adjacency_matrix(cor(depression)) out_igraph <- expectedInf(igraph_obj) qgraph_obj <- qgraph::qgraph(cor(depression), DoNotPlot=TRUE) out_qgraph <- expectedInf(qgraph_obj)
This function compares correlations in a psychometric network in order to identify nodes which most likely measure the same underlying construct (i.e., are colinear)
goldbricker( data, p = 0.05, method = "hittner2003", threshold = 0.25, corMin = 0.5, progressbar = TRUE )goldbricker( data, p = 0.05, method = "hittner2003", threshold = 0.25, corMin = 0.5, progressbar = TRUE )
data |
a data frame consisting of n rows (participants) and j columns (variables) |
p |
a p-value threshold for determining if correlation pairs are "significantly different" |
method |
method for comparing correlations. See ?cocor.dep.groups.overlap for a full list |
threshold |
variable pairs which have less than the threshold proportion of significantly different correlations will be considered "bad pairs" |
corMin |
the minimum zero-order correlation between two items to be considered "bad pairs". Items that are uncorrelated are unlikely to represent the same underlying construct |
progressbar |
logical. prints a progress bar in the console |
In a given psychometric network, two nodes may be redundantly measuring the same underlying construct. If this is the case, the correlations between those two variables and all other variables should be highly similar. That is, they should correlate to the same degree with other variables.
The cocor package uses a p-value threshold to determine whether a pair of correlations to a third variable are significantly different from each other. Goldbricker wraps the cocor package to compare every possible combination of correlations in a psychometric network. It calculates the proportion of correlations which are significantly different for each different pair of nodes.
Using the threshold argument, one can set the proportion of correlations which is deemed "too low". All pairs of nodes which fall below this threshold are returned as defined "bad pairs".
Pairs can then be combined using the net_reduce function
Note: to quickly change the threshold, one may simply enter an object of class "goldbricker" in the data argument, and change the threshold. The p-value cannot be modified in the same fashion, as re-computation is necessary.
goldbricker returns a list of class goldbricker which contains:
$proportion_matrix - a j x j matrix of proportions. Each proportion signifies the amount of significantly
different correlations between the given node pair (j x j)
$suggested_reductions - a vector of "bad pairs" (names) and their proportions (values)
$p - p value from input
$threshold - threshold from input
gb_depression <- goldbricker(depression, threshold=0.5) reduced_depression <- net_reduce(data=depression, badpairs=gb_depression) ## Set a new threshold quickly gb_depression_60 <- goldbricker(data=gb_depression, threshold=0.6)gb_depression <- goldbricker(depression, threshold=0.5) reduced_depression <- net_reduce(data=depression, badpairs=gb_depression) ## Set a new threshold quickly gb_depression_60 <- goldbricker(data=gb_depression, threshold=0.6)
Convenience function for converting a qgraph object to a layout determined by multidimensional scaling
MDSnet( qgraph_net, type = c("ordinal", "interval", "ratio", "mspline"), MDSadj = NULL, stressTxt = F, repulse = F, repulsion = 1, mdsArgs = list(), ... )MDSnet( qgraph_net, type = c("ordinal", "interval", "ratio", "mspline"), MDSadj = NULL, stressTxt = F, repulse = F, repulsion = 1, mdsArgs = list(), ... )
qgraph_net |
an object of type |
type |
transformation function for MDS, defaults to "ordinal" |
MDSadj |
to use a proximities matrix other than the adjacency matrix
stored in |
stressTxt |
logical. Print the stress value in the lower left corner of the plot? |
repulse |
logical. Add a small repulsion force with wordcloud package to avoid node overlap? |
repulsion |
scalar for the repulsion force. Larger values add more repulsion |
mdsArgs |
additional arguments in list format passed to |
... |
additional arguments passed to |
A network plotted with multidimensional scaling can be interpreted based on the distances between nodes. Nodes close together represent closely associated nodes, whereas nodes that are far apart represent unassociated or negatively associated nodes.
Jones, P. J., Mair, P., & McNally, R. J. (2018). Visualizing psychological networks: A tutorial in R. Frontiers in Psychology, 9, 1742. https://doi.org/10.3389/fpsyg.2018.01742
This function takes predefined pairs of colinear variables in a dataset and a) combines them via PCA or b) picks the "better" variable and eliminates the other variable
net_reduce(data, badpairs, method = c("PCA", "best_goldbricker"))net_reduce(data, badpairs, method = c("PCA", "best_goldbricker"))
data |
a data frame consisting of n rows (participants) and j columns (variables) |
badpairs |
pairs of variables to be combined. Input may consist of: -an object of class "goldbricker" (all bad pairs are combined) -a vector of item names, each consecutive pair will be considered a bad pair -a matrix with 2 columns where each bad pair takes up 1 row |
method |
method for combining variables. PCA takes the first principal component of the two variables and defines it as a new variable. best_goldbricker requires that the input of "badpairs" be an object of class "goldbricker" it selects the more unique variable, and eliminates the other variable in the pair. |
In a given psychometric network, two nodes may be redundantly measuring the same underlying construct. If this is the case, both variables should not appear in the same network, or network properties will be inaccurate. These variable pairs can be reduced by combining them, or by eliminating one of them. net_reduce automates this process when given a list of "bad pairs"
If the same variable appears in multiple "bad pairs" (e.g., "x" and "y" is a bad pair, and so is "x" and "z"), only the first of these pairs which appears in the badpairs argument will be reduced by the function.
goldbricker returns a dataframe of n rows (participants) and j - x columns,
where j is the number of variables in the original dataframe, and x is the number of bad pairs to reduce.
gb_depression <- goldbricker(depression, threshold=0.5) reduced_depression_PCA <- net_reduce(data=depression, badpairs=gb_depression) reduced_depression_best <- net_reduce(data=depression, badpairs=gb_depression, method="best_goldbricker")gb_depression <- goldbricker(depression, threshold=0.5) reduced_depression_PCA <- net_reduce(data=depression, badpairs=gb_depression) reduced_depression_best <- net_reduce(data=depression, badpairs=gb_depression, method="best_goldbricker")
Convenience function for converting a qgraph object to a layout determined by principal components analysis
PCAnet( qgraph_net, cormat, varTxt = F, repulse = F, repulsion = 1, principalArgs = list(), ... )PCAnet( qgraph_net, cormat, varTxt = F, repulse = F, repulsion = 1, principalArgs = list(), ... )
qgraph_net |
an object of type |
cormat |
the correlation matrix of the relevant data. If this argument is missing,
the function will assume that the adjacency matrix from |
varTxt |
logical. Print the variance accounted for by the PCA in the lower left corner of the plot |
repulse |
logical. Add a small repulsion force with wordcloud package to avoid node overlap? |
repulsion |
scalar for the repulsion force (if repulse=T). Larger values add more repulsion |
principalArgs |
additional arguments in list format passed to |
... |
additional arguments passed to |
A network plotted with PCA can be interpreted based on coordinate placement of each node. A node in the top right corner scored high on both the first and second principal components
Jones, P. J., Mair, P., & McNally, R. J. (2018). Visualizing psychological networks: A tutorial in R. Frontiers in Psychology, 9, 1742. https://doi.org/10.3389/fpsyg.2018.01742
Convenience function for plotting bridge centrality
## S3 method for class 'bridge' plot( x, order = c("given", "alphabetical", "value"), zscore = FALSE, include, color = FALSE, colpalette = "Dark2", plotNA = FALSE, ... )## S3 method for class 'bridge' plot( x, order = c("given", "alphabetical", "value"), zscore = FALSE, include, color = FALSE, colpalette = "Dark2", plotNA = FALSE, ... )
x |
an output object from |
order |
"alphabetical" orders nodes alphabetically, "value" orders nodes from highest to lowest centrality values |
zscore |
logical. Converts raw impact statistics to z-scores for plotting |
include |
a vector of centrality measures to include ("Bridge Strength", "Bridge Betweenness", "Bridge Closeness", "Bridge Expected Influence (1-step)", "Bridge Expected Influence (2-step)"), if missing all available measures will be plotted |
color |
logical. Color each community separately in the plot? |
colpalette |
A palette name from RColorBrewer, for coloring of axis labels |
plotNA |
should nodes with NA values be included on the y axis? |
... |
other plotting specifications in ggplot2 (aes) |
Inputting an object of class bridge
will return a line plot that shows the bridge centrality
values of each node
b <- bridge(cor(depression)) plot(b) plot(b, order="value", zscore=TRUE,include=c("Bridge Strength", "Bridge Betweenness"))b <- bridge(cor(depression)) plot(b) plot(b, order="value", zscore=TRUE,include=c("Bridge Strength", "Bridge Betweenness"))
Convenience function for plotting expected influence
## S3 method for class 'expectedInf' plot(x, order = c("given", "alphabetical", "value"), zscore = TRUE, ...)## S3 method for class 'expectedInf' plot(x, order = c("given", "alphabetical", "value"), zscore = TRUE, ...)
x |
an output object from an |
order |
"alphabetical" orders nodes alphabetically, "value" orders nodes from highest to lowest impact value |
zscore |
logical. Converts raw impact statistics to z-scores for plotting |
... |
other plotting specifications (ggplot2) |
Inputting an object of class expectedInf
will return a line plot that shows the relative one-step and/or two-step
expected influence of each node.
myNetwork <- cor(depression[,1:5]) out1 <- expectedInf(myNetwork) plot(out1$step1) plot(out1, order="value", zscore=TRUE)myNetwork <- cor(depression[,1:5]) out1 <- expectedInf(myNetwork) plot(out1$step1) plot(out1, order="value", zscore=TRUE)
Convenience function for simultaneously plotting two networks containing the same nodes.
PROCRUSTESnet( qgraph_net1, qgraph_net2, type1 = c("ordinal", "interval", "ratio", "mspline"), type2 = type1, MDSadj1 = NULL, MDSadj2 = NULL, stressTxt = F, congCoef = F, repulse = F, repulsion = 1, mdsArgs = list(), ... )PROCRUSTESnet( qgraph_net1, qgraph_net2, type1 = c("ordinal", "interval", "ratio", "mspline"), type2 = type1, MDSadj1 = NULL, MDSadj2 = NULL, stressTxt = F, congCoef = F, repulse = F, repulsion = 1, mdsArgs = list(), ... )
qgraph_net1 |
an object of type |
qgraph_net2 |
an object of type |
type1 |
transformation function for first MDS, defaults to "ordinal" |
type2 |
transformation function for second MDS, defaults to the same as |
MDSadj1 |
to use a proximities matrix other than the adjacency matrix
stored in |
MDSadj2 |
to use a proximities matrix other than the adjacency matrix
stored in |
stressTxt |
logical. Print the stress value in the lower left corner of the plots? |
congCoef |
logical. Print the congruence coefficient for the two layouts? |
repulse |
logical. Add a small repulsion force with wordcloud package to avoid node overlap? |
repulsion |
scalar for the repulsion force. Larger values add more repulsion |
mdsArgs |
additional arguments in list format passed to |
... |
additional arguments passed to |
Each network's layout is determined by multidimensional scaling, and then the layouts are brought into a similar space by using the Procrustes algorithm.
A network plotted with multidimensional scaling can be interpreted based on the distances between nodes. Nodes close together represent closely associated nodes, whereas nodes that are far apart represent unassociated or negatively associated nodes.
The Procrustes algorithm brings the two layouts into a similar space through rotations and dilations that do not impact the fit of the MDS solutions. In this implementation, the second network is rotated and dilated to fit the first.
Jones, P. J., Mair, P., & McNally, R. J. (2018). Visualizing psychological networks: A tutorial in R. Frontiers in Psychology, 9, 1742. https://doi.org/10.3389/fpsyg.2018.01742
Simulated Social Engagement Data
Description
This simulated dataset contains binary social engagement scores for 16 individuals. For 400 social media posts on a group forum, individuals were given a score of 1 if they engaged in group conversation regarding the post, and a score of 0 if they did not engage with the post.
Usage
Format
a dataframe. Columns represent individuals (nodes) and rows represent engagement in social media group conversations
Examples