Package 'EGAnet'

Description

Implements the Exploratory Graph Analysis (EGA) framework for dimensionality and psychometric assessment. EGA estimates the number of dimensions in psychological data using network estimation methods and community detection algorithms. A bootstrap method is provided to assess the stability of dimensions and items. Fit is evaluated using the Entropy Fit family of indices. Unique Variable Analysis evaluates the extent to which items are locally dependent (or redundant). Network loadings provide similar information to factor loadings and can be used to compute network scores. A bootstrap and permutation approach are available to assess configural and metric invariance. Hierarchical structures can be detected using Hierarchical EGA. Time series and intensive longitudinal data can be analyzed using Dynamic EGA, supporting individual, group, and population level assessments.

Author(s)

Hudson Golino <[email protected]> and Alexander P. Christensen <[email protected]>

References

Christensen, A. P. (2023). Unidimensional community detection: A Monte Carlo simulation, grid search, and comparison. PsyArXiv.
# Related functions: community.unidimensional

Christensen, A. P., Garrido, L. E., & Golino, H. (2023). Unique variable analysis: A network psychometrics method to detect local dependence. Multivariate Behavioral Research.
# Related functions: UVA

Christensen, A. P., Garrido, L. E., Guerra-Pena, K., & Golino, H. (2023). Comparing community detection algorithms in psychometric networks: A Monte Carlo simulation. Behavior Research Methods.
# Related functions: EGA

Christensen, A. P., & Golino, H. (2021a). Estimating the stability of the number of factors via Bootstrap Exploratory Graph Analysis: A tutorial. Psych, 3(3), 479-500.
# Related functions: bootEGA, dimensionStability, # and itemStability

Christensen, A. P., & Golino, H. (2021b). Factor or network model? Predictions from neural networks. Journal of Behavioral Data Science, 1(1), 85-126.
# Related functions: LCT

Christensen, A. P., & Golino, H. (2021c). On the equivalency of factor and network loadings. Behavior Research Methods, 53, 1563-1580.
# Related functions: LCT and net.loads

Christensen, A. P., Golino, H., & Silvia, P. J. (2020). A psychometric network perspective on the validity and validation of personality trait questionnaires. European Journal of Personality, 34, 1095-1108.
# Related functions: bootEGA, dimensionStability, # EGA, itemStability, and UVA

Christensen, A. P., Gross, G. M., Golino, H., Silvia, P. J., & Kwapil, T. R. (2019). Exploratory graph analysis of the Multidimensional Schizotypy Scale. Schizophrenia Research, 206, 43-51. # Related functions: CFA and EGA

Golino, H., Christensen, A. P., Moulder, R., Kim, S., & Boker, S. M. (2021). Modeling latent topics in social media using Dynamic Exploratory Graph Analysis: The case of the right-wing and left-wing trolls in the 2016 US elections. Psychometrika.
# Related functions: dynEGA and simDFM

Golino, H., & Demetriou, A. (2017). Estimating the dimensionality of intelligence like data using Exploratory Graph Analysis. Intelligence, 62, 54-70.
# Related functions: EGA

Golino, H., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLoS ONE, 12, e0174035.
# Related functions: CFA, EGA, and bootEGA

Golino, H., Moulder, R., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Nesselroade, J., Sadana, R., Thiyagarajan, J. A., & Boker, S. M. (2020). Entropy fit indices: New fit measures for assessing the structure and dimensionality of multiple latent variables. Multivariate Behavioral Research.
# Related functions: entropyFit, tefi, and vn.entropy

Golino, H., Nesselroade, J. R., & Christensen, A. P. (2022). Towards a psychology of individuals: The ergodicity information index and a bottom-up approach for finding generalizations. PsyArXiv.
# Related functions: boot.ergoInfo, ergoInfo, jsd, and infoCluster

Golino, H., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., Thiyagarajan, J. A., & Martinez-Molina, A. (2020). Investigating the performance of exploratory graph analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25, 292-320.
# Related functions: EGA

Golino, H., Thiyagarajan, J. A., Sadana, M., Teles, M., Christensen, A. P., & Boker, S. M. (2020). Investigating the broad domains of intrinsic capacity, functional ability, and environment: An exploratory graph analysis approach for improving analytical methodologies for measuring healthy aging. PsyArXiv.
# Related functions: EGA.fit and tefi

Jamison, L., Christensen, A. P., & Golino, H. (2021). Optimizing Walktrap's community detection in networks using the Total Entropy Fit Index. PsyArXiv.
# Related functions: EGA.fit and tefi

Jamison, L., Golino, H., & Christensen, A. P. (2023). Metric invariance in exploratory graph analysis via permutation testing. PsyArXiv.
# Related functions: invariance

Shi, D., Christensen, A. P., Day, E., Golino, H., & Garrido, L. E. (2023). A Bayesian approach for dimensionality assessment in psychological networks. PsyArXiv
# Related functions: EGA

See Also

Useful links:

• https://r-ega.net

• Report bugs at https://github.com/hfgolino/EGAnet/issues

Description

This wrapper is similar to cor_auto. There are some minor adjustments that make this function simpler and to function within EGAnet. NA values are not treated as categories (this behavior differs from cor_auto)

Usage

auto.correlate(
  data,
  corr = c("cosine", "kendall", "pearson", "spearman"),
  ordinal.categories = 7,
  forcePD = TRUE,
  na.data = c("pairwise", "listwise"),
  empty.method = c("none", "zero", "all"),
  empty.value = c("none", "point_five", "one_over"),
  verbose = FALSE,
  ...
)

Arguments

Author(s)

Alexander P. Christensen <[email protected]>

Examples

# Load data
wmt <- wmt2[,7:24]

# Obtain correlations
wmt_corr <- auto.correlate(wmt)

Description

Tests the Ergodicity Information Index obtained in the empirical sample with a distribution of EII obtained by a variant of bootstrap sampling (see Details for the procedure)

Usage

boot.ergoInfo(
  dynEGA.object,
  EII,
  use = c("edge.list", "unweighted", "weighted"),
  shuffles = 5000,
  iter = 100,
  ncores,
  verbose = TRUE
)

Arguments

Details

In traditional bootstrap sampling, individual participants are resampled with replacement from the empirical sample. This process is time consuming when carried out across v number of variables, n number of participants, t number of time points, and i number of iterations. Instead, boot.ergoInfo uses the premise of an ergodic process to establish more efficient test that works directly on the sample's networks.

With an ergodic process, the expectation is that all individuals will have a systematic relationship with the population. Destroying this relationship should result in a significant loss of information. Following this conjecture, boot.ergoInfo shuffles a random subset of edges that exist in the population that is equal to the number of shared edges it has with an individual. An individual's unique edges remain the same, controlling for their unique information. The result is a replicate individual that contains the same total number of edges as the actual individual but its shared information with the population has been scrambled.

This process is repeated over each individual to create a replicate sample and is repeated for X iterations (e.g., 100). This approach creates a sampling distribution that represents the expected information between the population and individuals when a random process generates the shared information between them. If the shared information between the population and individuals in the empirical sample is sufficiently meaningful, then this process should result in significant information loss.

How to interpret the results: the result of boot.ergoInfo is a sampling distribution of EII values that would be expected if the process was random (null distribution). If the empirical EII value is greater than or not significantly different from the null distribution, then the empirical data can be expected to be generated from an nonergodic process and the population structure is not sufficient to describe all individuals. If the empirical EII value is significantly lower than the null distribution, then the empirical data can be described by the population structure – the population structure is sufficient to describe all individuals.

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> & Alexander P. Christensen <alexander.christensen at Vanderbilt.Edu>

References

Original Implementation
Golino, H., Nesselroade, J. R., & Christensen, A. P. (2022). Toward a psychology of individuals: The ergodicity information index and a bottom-up approach for finding generalizations. PsyArXiv.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Obtain simulated data
sim.data <- sim.dynEGA

## Not run: 
# Dynamic EGA individual and population structures
dyn1 <- dynEGA.ind.pop(
  data = sim.dynEGA[,-26], n.embed = 5, tau = 1,
  delta = 1, id = 25, use.derivatives = 1,
  model = "glasso", ncores = 2, corr = "pearson"
)

# Empirical Ergodicity Information Index
eii1 <- ergoInfo(dynEGA.object = dyn1, use = "unweighted")

# Bootstrap Test for Ergodicity Information Index
testing.ergoinfo <- boot.ergoInfo(
  dynEGA.object = dyn1, EII = eii1,
  ncores = 2, use = "unweighted"
)

# Plot result
plot(testing.ergoinfo)

# Example using `dynEGA`
dyn2 <- dynEGA(
  data = sim.dynEGA, n.embed = 5, tau = 1,
  delta = 1, use.derivatives = 1, ncores = 2,
  level = c("individual", "population")
)

# Empirical Ergodicity Information Index
eii2 <- ergoInfo(dynEGA.object = dyn2, use = "unweighted")

# Bootstrap Test for Ergodicity Information Index
testing.ergoinfo2 <- boot.ergoInfo(
  dynEGA.object = dyn2, EII = eii2,
  ncores = 2
)

# Plot result
plot(testing.ergoinfo2)
## End(Not run)

bootEGA Results of wmt2Data

Description

bootEGA results from boot.wmt <- bootEGA(wmt2[,7:24], seed = 1234)

Usage

data(boot.wmt)

Format

A list with 12 objects (see Value in bootEGA)

Examples

data("boot.wmt")

Description

bootEGA Estimates the number of dimensions of iter bootstraps using the empirical zero-order correlation matrix ("parametric") or "resampling" from the empirical dataset (non-parametric). bootEGA estimates a typical median network structure, which is formed by the median or mean pairwise (partial) correlations over the iter bootstraps (see Details for information about the typical median network structure).

Usage

bootEGA(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  uni.method = c("expand", "LE", "louvain"),
  iter = 500,
  type = c("parametric", "resampling"),
  ncores,
  EGA.type = c("EGA", "EGA.fit", "hierEGA", "riEGA"),
  plot.itemStability = TRUE,
  typicalStructure = FALSE,
  plot.typicalStructure = FALSE,
  seed = NULL,
  verbose = TRUE,
  ...
)

Arguments

Details

The typical network structure is derived from the median (or mean) value of each pairwise relationship. These values tend to reflect the "typical" value taken by an edge across the bootstrap networks. Afterward, the same community detection algorithm is applied to the typical network as the bootstrap networks.

Because the community detection algorithm is applied to the typical network structure, there is a possibility that the community algorithm determines a different number of dimensions than the median number derived from the bootstraps. The typical network structure (and number of dimensions) may not match the empirical EGA number of dimensions or the median number of dimensions from the bootstrap. This result is known and not a bug.

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Original implementation of bootEGA
Christensen, A. P., & Golino, H. (2021). Estimating the stability of the number of factors via Bootstrap Exploratory Graph Analysis: A tutorial. Psych, 3(3), 479-500.

See Also

itemStability to estimate the stability of the variables in the empirical dimensions and dimensionStability to estimate the stability of the dimensions (structural consistency)

Examples

# Load data
wmt <- wmt2[,7:24]

## Not run: 
# Standard EGA parametric example
boot.wmt <- bootEGA(
  data = wmt, iter = 500,
  type = "parametric", ncores = 2
)

# Standard resampling example
boot.wmt <- bootEGA(
  data = wmt, iter = 500,
  type = "resampling", ncores = 2
)

# Example using {igraph} `cluster_*` function
boot.wmt.spinglass <- bootEGA(
  data = wmt, iter = 500,
  algorithm = igraph::cluster_spinglass,
  # use any function from {igraph}
  type = "parametric", ncores = 2
)

# EGA fit example
boot.wmt.fit <- bootEGA(
  data = wmt, iter = 500,
  EGA.type = "EGA.fit",
  type = "parametric", ncores = 2
)

# Hierarchical EGA example
boot.wmt.hier <- bootEGA(
  data = wmt, iter = 500,
  EGA.type = "hierEGA",
  type = "parametric", ncores = 2
)

# Random-intercept EGA example
boot.wmt.ri <- bootEGA(
  data = wmt, iter = 500,
  EGA.type = "riEGA",
  type = "parametric", ncores = 2
)
## End(Not run)

CFA Fit of EGA or hierEGA Structure

Description

Verifies the fit of the structure suggested by EGA or by hierEGA using confirmatory factor analysis

Usage

CFA(ega.obj, data, estimator, plot.CFA = TRUE, layout = "spring", ...)

Arguments

Value

Returns a list containing:

Author(s)

Hudson F. Golino <hfg9s at virginia.edu>

References

Demonstrative use
Christensen, A. P., Gross, G. M., Golino, H., Silvia, P. J., & Kwapil, T. R. (2019). Exploratory graph analysis of the Multidimensional Schizotypy Scale. Schizophrenia Research, 206, 43-51.

Initial implementation
Golino, H., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLoS ONE, 12, e0174035.

Examples

# Load data
wmt <- wmt2[,7:24]

## Not run: 
# Estimate EGA
ega.wmt <- EGA(
  data = wmt,
  plot.EGA = FALSE # No plot for CRAN checks
)

# Fit CFA model to EGA results
cfa.wmt <- CFA(
  ega.obj = ega.wmt, estimator = "WLSMV",
  plot.CFA = FALSE, # No plot for CRAN checks
  data = wmt
)

# Additional fit measures
lavaan::fitMeasures(cfa.wmt$fit, fit.measures = "all")
## End(Not run)

EGA Color Palettes

Description

Color palettes for plotting ggnet2 EGA network plots

Usage

color_palette_EGA(
  name = c("polychrome", "blue.ridge1", "blue.ridge2", "rainbow", "rio", "itacare",
    "grayscale"),
  wc,
  sorted = FALSE
)

Arguments

Value

Vector of colors for community memberships

Author(s)

Hudson Golino <hfg9s at virginia.edu>, Alexander P. Christensen <alexpaulchristensen at gmail.com>

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Default
color_palette_EGA(name = "polychrome", wc = ega.wmt$wc)

# Blue Ridge Moutains 1
color_palette_EGA(name = "blue.ridge1", wc = ega.wmt$wc)

# Custom
color_palette_EGA(name = c("#7FD1B9", "#24547e"), wc = ega.wmt$wc)

Description

A permutation implementation to determine statistical significance of whether the community comparison measure is different from zero

Usage

community.compare(
  base,
  comparison,
  method = c("vi", "nmi", "split.join", "rand", "adjusted.rand"),
  iter = 1000,
  shuffle.base = TRUE,
  verbose = TRUE,
  seed = NULL
)

Arguments

Value

Returns data frame containing method used (Method), empirical or observed value (Empirical), and p-value based on the permutation test (p.value)

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Implementation of Permutation Test
Qannari, E. M., Courcoux, P., & Faye, P. (2014). Significance test of the adjusted Rand index. Application to the free sorting task. Food Quality and Preference, 32, 93–97.

Variation of Information
Meila, M. (2003, August). Comparing clusterings by the variation of information. In Learning Theory and Kernel Machines: 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003, Washington, DC, USA, August 24-27, 2003. Proceedings (pp. 173-187). Berlin, DE: Springer Berlin Heidelberg.

Normalized Mutual Information
Danon, L., Diaz-Guilera, A., Duch, J., & Arenas, A. (2005). Comparing community structure identification. Journal of Statistical Mechanics: Theory and Experiment, 2005(09), P09008.

Split-join Distance
Dongen, S. (2000). Performance criteria for graph clustering and Markov cluster experiments. CWI (Centre for Mathematics and Computer Science).

Rand Index
Rand, W. M. (1971). Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association, 66(336), 846-850.

Adjusted Rand Index
Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2, 193-218.

Steinley, D. (2004). Properties of the Hubert-Arabie adjusted rand index. Psychological Methods, 9(3), 386.

Examples

# Load data
wmt <- wmt2[,7:24]

# Estimate network
network <- EBICglasso.qgraph(data = wmt)

# Compute Edge Betweenness
edge_between <- community.detection(network, algorithm = "edge_betweenness")

# Compute Fast Greedy
fast_greedy <- community.detection(network, algorithm = "fast_greedy")

# Perform permutation test
community.compare(edge_between, fast_greedy)

Description

Applies the consensus clustering method introduced by (Lancichinetti & Fortunato, 2012). The original implementation of this method applies a community detection algorithm repeatedly to the same network. With stochastic networks, the algorithm is likely to identify different community solutions with many repeated applications.

Usage

community.consensus(
  network,
  order = c("lower", "higher"),
  resolution = 1,
  consensus.method = c("highest_modularity", "iterative", "most_common", "lowest_tefi"),
  consensus.iter = 1000,
  correlation.matrix = NULL,
  allow.singleton = FALSE,
  membership.only = TRUE,
  ...
)

Arguments

Details

The goal of the consensus clustering method is to identify a stable solution across algorithm applications to derive a "consensus" clustering. The standard or "iterative" approach is to apply the community detection algorithm N times. Then, a co-occurrence matrix is created representing how often each pair of nodes co-occurred across the applications. Based on some cut-off value (e.g., 0.30), co-occurrences below this value are set to zero, forming a "new" sparse network. The procedure proceeds until all nodes co-occur with all other nodes in their community (or a proportion of 1.00).

Variations of this procedure are also available in this package but are experimental. Use these experimental procedures with caution. More work is necessary before these experimental procedures are validated

At this time, seed setting for consensus clustering is not supported

Value

Returns either a vector with the selected solution or a list when membership.only = FALSE:

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Louvain algorithm
Blondel, V. D., Guillaume, J.-L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008.

Consensus clustering
Lancichinetti, A., & Fortunato, S. (2012). Consensus clustering in complex networks. Scientific Reports, 2(1), 1–7.

Entropy fit indices
Golino, H., Moulder, R. G., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Nesselroade, J., Sadana, R., Thiyagarajan, J. A., & Boker, S. M. (2020). Entropy fit indices: New fit measures for assessing the structure and dimensionality of multiple latent variables. Multivariate Behavioral Research.

Examples

# Load data
wmt <- wmt2[,7:24]

# Estimate correlation matrix
correlation.matrix <- auto.correlate(wmt)

# Estimate network
network <- EBICglasso.qgraph(data = wmt)

# Compute standard Louvain with highest modularity approach
community.consensus(
  network,
  consensus.method = "highest_modularity"
)

# Compute standard Louvain with iterative (original) approach
community.consensus(
  network,
  consensus.method = "iterative"
)

# Compute standard Louvain with most common approach
community.consensus(
  network,
  consensus.method = "most_common"
)

# Compute standard Louvain with lowest TEFI approach
community.consensus(
  network,
  consensus.method = "lowest_tefi",
  correlation.matrix = correlation.matrix
)

Description

General function to apply community detection algorithms available in igraph. Follows the EGAnet approach of setting singleton and disconnected nodes to missing (NA)

Usage

community.detection(
  network,
  algorithm = c("edge_betweenness", "fast_greedy", "fluid", "infomap", "label_prop",
    "leading_eigen", "leiden", "louvain", "optimal", "spinglass", "walktrap"),
  allow.singleton = FALSE,
  membership.only = TRUE,
  ...
)

Arguments

Value

Returns memberships from a community detection algorithm

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Csardi, G., & Nepusz, T. (2006). The igraph software package for complex network research. InterJournal, Complex Systems, 1695.

Examples

# Load data
wmt <- wmt2[,7:24]

# Estimate network
network <- EBICglasso.qgraph(data = wmt)

# Compute Edge Betweenness
community.detection(network, algorithm = "edge_betweenness")

# Compute Fast Greedy
community.detection(network, algorithm = "fast_greedy")

# Compute Fluid
community.detection(
  network, algorithm = "fluid",
  no.of.communities = 2 # needs to be set
)

# Compute Infomap
community.detection(network, algorithm = "infomap")

# Compute Label Propagation
community.detection(network, algorithm = "label_prop")

# Compute Leading Eigenvector
community.detection(network, algorithm = "leading_eigen")

# Compute Leiden (with modularity)
community.detection(
  network, algorithm = "leiden",
  objective_function = "modularity"
)

# Compute Leiden (with CPM)
community.detection(
  network, algorithm = "leiden",
  objective_function = "CPM",
  resolution_parameter = 0.05 # "edge density"
)

# Compute Louvain
community.detection(network, algorithm = "louvain")

# Compute Optimal (identifies maximum modularity solution)
community.detection(network, algorithm = "optimal")

# Compute Spinglass
community.detection(network, algorithm = "spinglass")

# Compute Walktrap
community.detection(network, algorithm = "walktrap")

# Example with {igraph} network
community.detection(
  convert2igraph(network), algorithm = "walktrap"
)

Description

Memberships from community detection algorithms do not always align numerically. This function seeks to homogenize community memberships between a target membership (the membership to homogenize toward) and one or more other memberships. This function is the core of the dimensionStability and itemStability functions

Usage

community.homogenize(target.membership, convert.membership)

Arguments

Value

Returns a vector or matrix the length or size of convert.membership with memberships homogenized toward target.membership

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Original implementation of bootEGA
Christensen, A. P., & Golino, H. (2021). Estimating the stability of the number of factors via Bootstrap Exploratory Graph Analysis: A tutorial. Psych, 3(3), 479-500.

Examples

# Get network
network <- network.estimation(wmt2[,7:24])

# Apply Walktrap
network_walktrap <- community.detection(
  network, algorithm = "walktrap"
)

# Apply Louvain
network_louvain <- community.detection(
  network, algorithm = "louvain"
)

# Homogenize toward Walktrap
community.homogenize(network_walktrap, network_louvain)

Description

A function to apply several approaches to detect a unidimensional community in networks. There have many different approaches recently such as expanding the correlation matrix to have orthogonal correlations ("expand"), applying the Leading Eigenvalue community detection algorithm cluster_leading_eigen to the correlation matrix ("LE"), and applying the Louvain community detection algorithm cluster_louvain to the correlation matrix ("louvain"). Not necessarily intended for individual use – it's better to use EGA

Usage

community.unidimensional(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  uni.method = c("expand", "LE", "louvain"),
  verbose = FALSE,
  ...
)

Arguments

Value

Returns the memberships of the community detection algorithm. The memberships will output regardless of whether the network is unidimensional

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Expand approach
Golino, H., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., Thiyagarajan, J. A., & Martinez-Molina, A. (2020). Investigating the performance of exploratory graph analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25, 292-320.

Leading Eigenvector approach
Christensen, A. P., Garrido, L. E., Guerra-Pena, K., & Golino, H. (2023). Comparing community detection algorithms in psychometric networks: A Monte Carlo simulation. Behavior Research Methods.

Louvain approach
Christensen, A. P. (2023). Unidimensional community detection: A Monte Carlo simulation, grid search, and comparison. PsyArXiv.

Examples

# Load data
wmt <- wmt2[,7:24]

# Louvain with Consensus Clustering (default)
community.unidimensional(wmt)

# Leading Eigenvector
community.unidimensional(wmt, uni.method = "LE")

# Expand
community.unidimensional(wmt, uni.method = "expand")

Description

Organizes EGA plots for comparison. Ensures that nodes are placed in the same layout to maximize comparison

Usage

compare.EGA.plots(
  ...,
  input.list = NULL,
  base = 1,
  labels = NULL,
  rows = NULL,
  columns = NULL,
  plot.all = TRUE
)

Arguments

Value

Visual comparison of EGAnet objects

Author(s)

Alexander Christensen <[email protected]>

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Obtain WMT-2 data
wmt <- wmt2[,7:24]

# Draw random samples of 300 cases
sample1 <- wmt[sample(1:nrow(wmt), 300),]
sample2 <- wmt[sample(1:nrow(wmt), 300),]

# Estimate EGAs
ega1 <- EGA(sample1)
ega2 <- EGA(sample2)


# Compare EGAs via plot
compare.EGA.plots(
  ega1, ega2,
  base = 1, # use "ega1" as base for comparison
  labels = c("Sample 1", "Sample 2"),
  rows = 1, columns = 2
)

# Change layout to circle plots
compare.EGA.plots(
  ega1, ega2,
  labels = c("Sample 1", "Sample 2"),
  mode = "circle"
)

Description

Converts networks to igraph format

Usage

convert2igraph(A, diagonal = 0)

Arguments

Value

Returns a network in the igraph format

Author(s)

Hudson Golino <hfg9s at virginia.edu> & Alexander P. Christensen <alexander.christensen at Vanderbilt.Edu>

Examples

convert2igraph(ega.wmt$network)

Description

Converts networks to tidygraph format

Usage

convert2tidygraph(EGA.object)

Arguments

Value

Returns a network in the tidygraph format

Author(s)

Dominique Makowski, Hudson Golino <hfg9s at virginia.edu>, & Alexander P. Christensen <alexander.christensen at Vanderbilt.Edu>

Examples

convert2tidygraph(ega.wmt)

Description

Computes cosine similarity

Usage

cosine(x, y = NULL, ...)

Arguments

Details

On missing values: 0 will be used to replace missing values. When using (matrix) multiplication, the 0 value cancels out the product rendering the missing value as "not counting" in the sums

Author(s)

Alexander P. Christensen <[email protected]>

Examples

# Load data
wmt <- wmt2[,7:24]

# Obtain cosines
wmt_cosine <- cosine(wmt)

Description

A response matrix (n = 574) of the Beck Depression Inventory, Beck Anxiety Inventory, and the Athens Insomnia Scale.

Usage

data(depression)

Format

A 574x78 response matrix

Examples

data("depression")

Dimension Stability Statistics from bootEGA

Description

Based on the bootEGA results, this function computes the stability of dimensions. Stability is computed by assessing the proportion of times the original dimension is exactly replicated in across bootstrap samples

Usage

dimensionStability(bootega.obj, IS.plot = TRUE, structure = NULL, ...)

Arguments

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Original implementation of bootEGA
Christensen, A. P., & Golino, H. (2021). Estimating the stability of the number of factors via Bootstrap Exploratory Graph Analysis: A tutorial. Psych, 3(3), 479-500.

Conceptual introduction
Christensen, A. P., Golino, H., & Silvia, P. J. (2020). A psychometric network perspective on the validity and validation of personality trait questionnaires. European Journal of Personality, 34(6), 1095-1108.

Examples

# Load data
wmt <- wmt2[,7:24]

## Not run: 
# Estimate bootstrap EGA
boot.wmt <- bootEGA(
  data = wmt, iter = 500,
  type = "parametric", ncores = 2
)
## End(Not run)

# Estimate stability statistics
dimensionStability(boot.wmt)

Description

A list of weights from four different neural network models: random vs. non-random model (r_nr_weights), low correlation factor vs. network model (lf_n_weights), high correlation with variables less than or equal to factors vs. network model (hlf_n_weights), and high correlation with variables greater than factors vs. network model (hgf_n_weights)

Usage

data(dnn.weights)

Format

A list of with a length of 4

Examples

data("dnn.weights")

Description

Estimates dynamic communities in multivariate time series (e.g., panel data, longitudinal data, intensive longitudinal data) at multiple time scales and at different levels of analysis: individuals (intraindividual structure), groups, and population (interindividual structure)

Usage

dynEGA(
  data,
  id = NULL,
  group = NULL,
  n.embed = 5,
  tau = 1,
  delta = 1,
  use.derivatives = 1,
  level = c("individual", "group", "population"),
  corr = c("auto", "cor_auto", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  uni.method = c("expand", "LE", "louvain"),
  ncores,
  verbose = TRUE,
  ...
)

Arguments

Details

Derivatives for each variable's time series for each participant are estimated using generalized local linear approximation (see glla). EGA is then applied to these derivatives to model how variables are changing together over time. Variables that change together over time are detected as communities

Value

A list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Generalized local linear approximation
Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2010) Generalized local linear approximation of derivatives from time series. In S.-M. Chow, E. Ferrer, & F. Hsieh (Eds.), The Notre Dame series on quantitative methodology. Statistical methods for modeling human dynamics: An interdisciplinary dialogue, (p. 161-178). Routledge/Taylor & Francis Group.

Deboeck, P. R., Montpetit, M. A., Bergeman, C. S., & Boker, S. M. (2009) Using derivative estimates to describe intraindividual variability at multiple time scales. Psychological Methods, 14(4), 367-386.

Original dynamic EGA implementation
Golino, H., Christensen, A. P., Moulder, R. G., Kim, S., & Boker, S. M. (2021). Modeling latent topics in social media using Dynamic Exploratory Graph Analysis: The case of the right-wing and left-wing trolls in the 2016 US elections. Psychometrika.

Time delay embedding procedure
Savitzky, A., & Golay, M. J. (1964). Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36(8), 1627-1639.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Population structure
simulated_population <- dynEGA(
  data = sim.dynEGA, level = "population"
  # uses simulated data in package
  # useful to understand how data should be structured
)

# Group structure
simulated_group <- dynEGA(
  data = sim.dynEGA, level = "group"
  # uses simulated data in package
  # useful to understand how data should be structured
)

## Not run: 
# Individual structure
simulated_individual <- dynEGA(
  data = sim.dynEGA, level = "individual",
  ncores = 2, # use more for quicker results
  verbose = TRUE # progress bar
)

# Population, group, and individual structure
simulated_all <- dynEGA(
  data = sim.dynEGA,
  level = c("individual", "group", "population"),
  ncores = 2, # use more for quicker results
  verbose = TRUE # progress bar
)

# Plot population
plot(simulated_all$dynEGA$population)

# Plot groups
plot(simulated_all$dynEGA$group)

# Plot individual
plot(simulated_all$dynEGA$individual, id = 1)

# Step through all plots
# Unless `id` is specified, 4 random IDs
# will be drawn from individuals
plot(simulated_all)
## End(Not run)

Intra- and Inter-individual dynEGA

Description

A wrapper function to estimate both intraindividiual (level = "individual") and interindividual (level = "population") structures using dynEGA

Usage

dynEGA.ind.pop(
  data,
  id = NULL,
  n.embed = 5,
  tau = 1,
  delta = 1,
  use.derivatives = 1,
  corr = c("auto", "cor_auto", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  uni.method = c("expand", "LE", "louvain"),
  ncores,
  verbose = TRUE,
  ...
)

Arguments

Value

Same output as EGAnet{dynEGA} returning list objects for level = "individual" and level = "population"

Author(s)

Hudson Golino <hfg9s at virginia.edu>

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Obtain data
sim.dynEGA <- sim.dynEGA # bypasses CRAN checks

## Not run: 
# Dynamic EGA individual and population structure
dyn.ega1 <- dynEGA.ind.pop(
  data = sim.dynEGA, n.embed = 5, tau = 1,
  delta = 1, id = 25, use.derivatives = 1,
  ncores = 2, corr = "pearson"
)
## End(Not run)

EBICglasso from qgraph 1.4.4

Description

This function uses the glasso package (Friedman, Hastie and Tibshirani, 2011) to compute a sparse gaussian graphical model with the graphical lasso (Friedman, Hastie & Tibshirani, 2008). The tuning parameter is chosen using the Extended Bayesian Information criterion (EBIC) described by Foygel & Drton (2010).

Usage

EBICglasso.qgraph(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  gamma = 0.5,
  penalize.diagonal = FALSE,
  nlambda = 100,
  lambda.min.ratio = 0.1,
  returnAllResults = FALSE,
  penalizeMatrix,
  countDiagonal = FALSE,
  refit = FALSE,
  model.selection = c("EBIC", "JSD"),
  verbose = FALSE,
  ...
)

Arguments

Details

The glasso is run for 100 values of the tuning parameter logarithmically spaced between the maximal value of the tuning parameter at which all edges are zero, lambda_max, and lambda_max/100. For each of these graphs the EBIC is computed and the graph with the best EBIC is selected. The partial correlation matrix is computed using wi2net and returned.

Value

A partial correlation matrix

Author(s)

Sacha Epskamp; for maintanence, Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <alexpaulchristensen at gmail.com>

References

Instantiation of GLASSO
Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9, 432-441.

glasso + EBIC
Foygel, R., & Drton, M. (2010). Extended Bayesian information criteria for Gaussian graphical models. In Advances in neural information processing systems (pp. 604-612).

glasso package
Friedman, J., Hastie, T., & Tibshirani, R. (2011). glasso: Graphical lasso-estimation of Gaussian graphical models. R package version 1.7.

Tutorial on EBICglasso
Epskamp, S., & Fried, E. I. (2018). A tutorial on regularized partial correlation networks. Psychological Methods, 23(4), 617–634.

Examples

# Obtain data
wmt <- wmt2[,7:24]

# Compute graph with tuning = 0 (BIC)
BICgraph <- EBICglasso.qgraph(data = wmt, gamma = 0)

# Compute graph with tuning = 0.5 (EBIC)
EBICgraph <- EBICglasso.qgraph(data = wmt, gamma = 0.5)

Description

Estimates the number of communities (dimensions) of a dataset or correlation matrix using a network estimation method (Golino & Epskamp, 2017; Golino et al., 2020). After, a community detection algorithm is applied (Christensen et al., 2023) for multidimensional data. A unidimensional check is also applied based on findings from Golino et al. (2020) and Christensen (2023)

Usage

EGA(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  uni.method = c("expand", "LE", "louvain"),
  plot.EGA = TRUE,
  verbose = FALSE,
  ...
)

Arguments

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu>, Alexander P. Christensen <alexpaulchristensen at gmail.com>, Maria Dolores Nieto <acinodam at gmail.com> and Luis E. Garrido <garrido.luiseduardo at gmail.com>

References

Original simulation and implementation of EGA
Golino, H. F., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLoS ONE, 12, e0174035.

Current implementation of EGA, introduced unidimensional checks, continuous and dichotomous data
Golino, H., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., & Thiyagarajan, J. A. (2020). Investigating the performance of Exploratory Graph Analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25, 292-320.

Compared all igraph community detection algorithms, introduced Louvain algorithm, simulation with continuous and polytomous data
Also implements the Leading Eigenvalue unidimensional method
Christensen, A. P., Garrido, L. E., Pena, K. G., & Golino, H. (2023). Comparing community detection algorithms in psychological data: A Monte Carlo simulation. Behavior Research Methods.

Comprehensive unidimensionality simulation
Christensen, A. P. (2023). Unidimensional community detection: A Monte Carlo simulation, grid search, and comparison. PsyArXiv.

Compared all igraph community detection algorithms, simulation with continuous and polytomous data
Christensen, A. P., Garrido, L. E., Guerra-Pena, K., & Golino, H. (2023). Comparing community detection algorithms in psychometric networks: A Monte Carlo simulation. Behavior Research Methods.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Obtain data
wmt <- wmt2[,7:24]

# Estimate EGA
ega.wmt <- EGA(
  data = wmt,
  plot.EGA = FALSE # No plot for CRAN checks
)

# Print results
print(ega.wmt)

# Estimate EGAtmfg
ega.wmt.tmfg <- EGA(
  data = wmt, model = "TMFG",
  plot.EGA = FALSE # No plot for CRAN checks
)

# Estimate EGA with Louvain algorithm
ega.wmt.louvain <- EGA(
  data = wmt, algorithm = "louvain",
  plot.EGA = FALSE # No plot for CRAN checks
)

# Estimate EGA with an {igraph} function (Fast-greedy)
ega.wmt.greedy <- EGA(
  data = wmt,
  algorithm = igraph::cluster_fast_greedy,
  plot.EGA = FALSE # No plot for CRAN checks
)

Estimates EGA for Multidimensional Structures

Description

A basic function to estimate EGA for multidimensional structures. This function does not include the unidimensional check and it does not plot the results. This function can be used as a streamlined approach for quick EGA estimation when unidimensionality or visualization is not a priority

Usage

EGA.estimate(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  verbose = FALSE,
  ...
)

Arguments

Value

Returns a list containing:

Author(s)

Alexander P. Christensen <alexpaulchristensen at gmail.com> and Hudson Golino <hfg9s at virginia.edu>

References

Original simulation and implementation of EGA
Golino, H. F., & Epskamp, S. (2017). Exploratory graph analysis: A new approach for estimating the number of dimensions in psychological research. PLoS ONE, 12, e0174035.

Introduced unidimensional checks, simulation with continuous and dichotomous data
Golino, H., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Sadana, R., & Thiyagarajan, J. A. (2020). Investigating the performance of Exploratory Graph Analysis and traditional techniques to identify the number of latent factors: A simulation and tutorial. Psychological Methods, 25, 292-320.

Compared all igraph community detection algorithms, simulation with continuous and polytomous data
Christensen, A. P., Garrido, L. E., Guerra-Pena, K., & Golino, H. (2023). Comparing community detection algorithms in psychometric networks: A Monte Carlo simulation. Behavior Research Methods.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Obtain data
wmt <- wmt2[,7:24]

# Estimate EGA
ega.wmt <- EGA.estimate(data = wmt)

# Estimate EGA with TMFG
ega.wmt.tmfg <- EGA.estimate(data = wmt, model = "TMFG")

# Estimate EGA with an {igraph} function (Fast-greedy)
ega.wmt.greedy <- EGA.estimate(
  data = wmt,
  algorithm = igraph::cluster_fast_greedy
)

EGA Optimal Model Fit using the Total Entropy Fit Index (tefi)

Description

Estimates the best fitting model using EGA. The number of steps in the cluster_walktrap detection algorithm is varied and unique community solutions are compared using tefi.

Usage

EGA.fit(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  plot.EGA = TRUE,
  verbose = FALSE,
  ...
)

Arguments

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Entropy fit measures
Golino, H., Moulder, R. G., Shi, D., Christensen, A. P., Garrido, L. E., Neito, M. D., Nesselroade, J., Sadana, R., Thiyagarajan, J. A., & Boker, S. M. (in press). Entropy fit indices: New fit measures for assessing the structure and dimensionality of multiple latent variables. Multivariate Behavioral Research.

Simulation for EGA.fit
Jamison, L., Christensen, A. P., & Golino, H. (under review). Optimizing Walktrap's community detection in networks using the Total Entropy Fit Index. PsyArXiv.

Leiden algorithm
Traag, V. A., Waltman, L., & Van Eck, N. J. (2019). From Louvain to Leiden: guaranteeing well-connected communities. Scientific Reports, 9(1), 1-12.

Louvain algorithm
Blondel, V. D., Guillaume, J. L., Lambiotte, R., & Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of Statistical Mechanics: Theory and Experiment, 2008(10), P10008.

Walktrap algorithm
Pons, P., & Latapy, M. (2006). Computing communities in large networks using random walks. Journal of Graph Algorithms and Applications, 10, 191-218.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Load data
wmt <- wmt2[,7:24]

# Estimate optimal EGA with Walktrap
fit.walktrap <- EGA.fit(
  data = wmt, algorithm = "walktrap",
  steps = 3:8, # default
  plot.EGA = FALSE # no plot for CRAN checks
)

# Estimate optimal EGA with Leiden and CPM
fit.leiden <- EGA.fit(
  data = wmt, algorithm = "leiden",
  objective_function = "CPM", # default
  # resolution_parameter = seq.int(0, max(abs(network)), 0.01),
  # For CPM, the default max resolution parameter
  # is set to the largest absolute edge in the network
  plot.EGA = FALSE # no plot for CRAN checks
)

# Estimate optimal EGA with Leiden and modularity
fit.leiden <- EGA.fit(
  data = wmt, algorithm = "leiden",
  objective_function = "modularity",
  resolution_parameter = seq.int(0, 2, 0.05),
  # default for modularity
  plot.EGA = FALSE # no plot for CRAN checks
)

## Not run: 
# Estimate optimal EGA with Louvain
fit.louvain <- EGA.fit(
  data = wmt, algorithm = "louvain",
  resolution_parameter = seq.int(0, 2, 0.05), # default
  plot.EGA = FALSE # no plot for CRAN checks
)
## End(Not run)

EGA Network of wmt2Data

Description

EGA results from ega.wmt <- EGA(wmt2[,7:24]) for the Wiener Matrizen-Test (WMT-2)

Usage

data(ega.wmt)

Format

A list with 8 objects (see Value in EGA)

Examples

data("ega.wmt")

Description

General usage for plots created by EGAnet's S3 methods. Plots across the EGAnet package leverage GGally's ggnet2 and ggplot2's ggplot.

Most plots allow the full usage of the gg* series functionality and therefore plotting arguments should be referenced through those packages rather than here in EGAnet.

The sections below list the functions and their usage for the S3 plot methods. The plot methods are intended to be generic and without many arguments so that nearly all arguments are passed to ggnet2 and ggplot.

There are some constraints placed on certain plots to keep the EGAnet style throughout the (network) plots in the package, so be aware that if some settings are not changing your plot output, then these settings might be fixed to maintain the EGAnet style

General Usage

plot(x, ...)

plot.dynEGA(x, base = 1, id = NULL, ...)

plot.dynEGA.Group(x, base = 1, ...)

plot.dynEGA.Individual(x, base = 1, id = NULL, ...)

plot.hierEGA(
  x, plot.type = c("multilevel", "separate"),
  color.match = FALSE, ...
)

plot.invariance(x, p_type = c("p", "p_BH"), p_value = 0.05, ...)

General Arguments

• x — EGAnet object with available S3 plot method (see full list below)

• color.palette — Character (vector). Either a character (length = 1) from the pre-defined palettes in color_palette_EGA or character (length = total number of communities) using HEX codes (see Color Palettes and Examples sections)

• layout — Character (length = 1). Layouts can be set using gplot.layout and the ending layout name; for example, gplot.layout.circle can be set in these functions using layout = "circle" or mode = "circle" (see Examples)

• base — Numeric (length = 1). Plot to be used as the base for the configuration of the networks. Uses the number of the order in which the plots are input. Defaults to 1 or the first plot

• id — Numeric index(es) or character name(s). IDs to use when plotting dynEGA level = "individual". Defaults to NULL or 4 IDs drawn at random

• plot.type — Character (length = 1). Whether hierEGA networks should plotted in a stacked, "multilevel" fashion or as "separate" plots. Defaults to "multilevel"

• color.match — Boolean (length = 1). Whether lower order community colors in the hierEGA plot should be "matched" and used as the border color for the higher order communities. Defaults to FALSE

• p_type — Character (length = 1). Type of p-value when plotting invariance. Defaults to "p" or uncorrected p-value. Set to "p_BH" for the Benjamini-Hochberg corrected p-value

• p_value — Numeric (length = 1). The p-value to use alongside p_type when plotting invariance. Defaults to 0.05

• ... — Additional arguments to pass on to ggnet2 and gplot.layout (see Examples)

*EGA Plots

bootEGA, dynEGA, EGA, EGA.estimate, EGA.fit, hierEGA, invariance, riEGA

All Available S3 Plot Methods

boot.ergoInfo, bootEGA, dynEGA, dynEGA.Group, dynEGA.Individual, dynEGA.Population, EGA, EGA.estimate, EGA.fit, hierEGA, infoCluster, invariance, itemStability, riEGA

Color Palettes

color_palette_EGA will implement some color palettes in EGAnet. The main EGAnet style palette is "polychrome". This palette currently has 40 colors but there will likely be a need to expand it further (e.g., hierEGA demands a lot of colors).

The color.palette argument will also accept HEX code colors that are the same length as the number of communities in the plot.

In any network plots, the color.palette argument can be used to select color palettes from color_palette_EGA as well as those in the color scheme of RColorBrewer

For more worked examples than below, see Plots in {EGAnet}

Examples

# Using different arguments in {GGally}'s `ggnet2`
plot(ega.wmt, node.size = 6, edge.size = 4)

# Using a different layout in {sna}'s `gplot.layout`
plot(ega.wmt, layout = "circle") # 'layout' argument
plot(ega.wmt, mode = "circle") # 'mode' argument

# Using different color palettes with `color_palette_EGA`

## Pre-defined palette
plot(ega.wmt, color.palette = "blue.ridge2")

## University of Virginia colors
plot(ega.wmt, color.palette = c("#232D4B", "#F84C1E"))

## Vanderbilt University colors
## (with additional {GGally} `ggnet2` argument)
plot(
  ega.wmt, color.palette = c("#FFFFFF", "#866D4B"),
  label.color = "#000000"
)

Description

Function to fit the Exploratory Graph Model

Usage

EGM(
  data,
  EGM.model = c("standard", "EGA"),
  communities = NULL,
  structure = NULL,
  search = FALSE,
  p.in = NULL,
  p.out = NULL,
  opt = c("AIC", "BIC", "CFI", "chisq", "logLik", "RMSEA", "SRMR", "TEFI", "TEFI.adj",
    "TLI"),
  constrained = TRUE,
  verbose = TRUE,
  ...
)

Arguments

Author(s)

Hudson F. Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

Examples

# Get depression data
data <- depression[,24:44]

# Estimate EGM (using EGA)
egm_ega <- EGM(data)

# Estimate EGM (using EGA) specifying communities
egm_ega_communities <- EGM(data, communities = 3)

# Estimate EGM (using EGA) specifying structure
egm_ega_structure <- EGM(
  data, structure = c(
    1, 1, 1, 2, 1, 1, 1,
    1, 1, 1, 3, 2, 2, 2,
    2, 3, 3, 3, 3, 3, 2
  )
)

# Estimate EGM (using standard)
egm_standard <- EGM(
  data, EGM.model = "standard",
  communities = 3, # specify number of communities
  p.in = 0.95, # probability of edges *in* each community
  p.out = 0.80 # probability of edges *between* each community
)

## Not run: 
# Estimate EGM (using EGA search)
egm_ega_search <- EGM(
  data, EGM.model = "EGA", search = TRUE
)

# Estimate EGM (using EGA search and AIC criterion)
egm_ega_search_AIC <- EGM(
  data, EGM.model = "EGA", search = TRUE, opt = "AIC"
)

# Estimate EGM (using search)
egm_search <- EGM(
  data, EGM.model = "standard", search = TRUE,
  communities = 3, # need communities or structure
  p.in = 0.95 # only need 'p.in'
)
## End(Not run)

Compare EGM with EFA

Description

Estimates an EGM based on EGA and uses the number of communities as the number of dimensions in exploratory factor analysis (EFA) using fa

Usage

EGM.compare(data, constrained = FALSE, rotation = "geominQ", ...)

Arguments

Author(s)

Hudson F. Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

Examples

# Get depression data
data <- depression[,24:44]

# Compare EGM (using EGA) with EFA
## Not run: 
results <- EGM.compare(data)

# Print summary
summary(results)
## End(Not run)

Description

Reorganizes a single observed time series into an embedded matrix. The embedded matrix is constructed with replicates of an individual time series that are offset from each other in time. The function requires two parameters, one that specifies the number of observations to be used (i.e., the number of embedded dimensions) and the other that specifies the number of observations to offset successive embeddings

Usage

Embed(x, E, tau)

Arguments

Value

Returns a numeric matrix

Author(s)

Pascal Deboeck <pascal.deboeck at psych.utah.edu> and Alexander P. Christensen <[email protected]>

References

Deboeck, P. R., Montpetit, M. A., Bergeman, C. S., & Boker, S. M. (2009) Using derivative estimates to describe intraindividual variability at multiple time scales. Psychological Methods, 14, 367-386.

Examples

# A time series with 8 time points
time_series <- 49:56

# Time series embedding
Embed(time_series, E = 5, tau = 1)

Description

Computes the fit of a dimensionality structure using empirical entropy. Lower values suggest better fit of a structure to the data.

Usage

entropyFit(data, structure)

Arguments

Value

Returns a list containing:

Author(s)

Hudson F. Golino <hfg9s at virginia.edu>, Alexander P. Christensen <[email protected]> and Robert Moulder <[email protected]>

References

Initial formalization and simulation
Golino, H., Moulder, R. G., Shi, D., Christensen, A. P., Garrido, L. E., Nieto, M. D., Nesselroade, J., Sadana, R., Thiyagarajan, J. A., & Boker, S. M. (2020). Entropy fit indices: New fit measures for assessing the structure and dimensionality of multiple latent variables. Multivariate Behavioral Research.

Examples

# Load data
wmt <- wmt2[,7:24]

## Not run: 
# Estimate EGA model
ega.wmt <- EGA(data = wmt)
## End(Not run)

# Compute entropy indices
entropyFit(data = wmt, structure = ega.wmt$wc)

Description

Computes the Ergodicity Information Index

Usage

ergoInfo(
  dynEGA.object,
  use = c("edge.list", "unweighted", "weighted"),
  shuffles = 5000
)

Arguments

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander Christensen <[email protected]>

References

Original Implementation
Golino, H., Nesselroade, J. R., & Christensen, A. P. (2022). Toward a psychology of individuals: The ergodicity information index and a bottom-up approach for finding generalizations. PsyArXiv.

Examples

# Obtain data
sim.dynEGA <- sim.dynEGA # bypasses CRAN checks

## Not run: 
# Dynamic EGA individual and population structure
dyn.ega1 <- dynEGA.ind.pop(
  data = sim.dynEGA[,-26], n.embed = 5, tau = 1,
  delta = 1, id = 25, use.derivatives = 1,
  ncores = 2, corr = "pearson"
)

# Compute empirical ergodicity information index
eii <- ergoInfo(dyn.ega1)
## End(Not run)

Description

Computes the Frobenius Norm (Ulitzsch et al., 2023)

Usage

frobenius(network1, network2)

Arguments

Value

Returns Frobenius Norm

Author(s)

Hudson Golino <hfg9s at virginia.edu> & Alexander P. Christensen <alexander.christensen at Vanderbilt.Edu>

References

Simulation Study
Ulitzsch, E., Khanna, S., Rhemtulla, M., & Domingue, B. W. (2023). A graph theory based similarity metric enables comparison of subpopulation psychometric networks Psychological Methods.

Examples

# Obtain wmt2 data
wmt <- wmt2[,7:24]

# Set seed (for reproducibility)
set.seed(1234)

# Split data
split1 <- sample(
  1:nrow(wmt), floor(nrow(wmt) / 2)
)
split2 <- setdiff(1:nrow(wmt), split1)

# Obtain split data
data1 <- wmt[split1,]
data2 <- wmt[split2,]

# Perform EBICglasso
glas1 <- EBICglasso.qgraph(data1)
glas2 <- EBICglasso.qgraph(data2)

# Frobenius norm
frobenius(glas1, glas2)
# 0.7070395

Description

Computes the fit (Generalized TEFI) of a hierarchical or correlated bifactor dimensionality structure (or hierEGA objects) using Von Neumman's entropy when the input is a correlation matrix. Lower values suggest better fit of a structure to the data

Usage

genTEFI(data, structure = NULL, verbose = TRUE)

Arguments

Value

Returns a three-column data frame of the Generalized Total Entropy Fit Index using Von Neumman's entropy (VN.Entropy.Fit) (first column), as well as Lower.Order.VN - TEFI for the first-order factors (second column), and Higher.Order.VN, the equivalent for the second-order factors.

Author(s)

Hudson Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

Examples

# Example using network scores
opt.hier <- hierEGA(
  data = optimism, scores = "network",
  plot.EGA = FALSE # No plot for CRAN checks
)

# Compute the Generalized Total Entropy Fit Index
genTEFI(opt.hier)

Description

Estimates the derivatives of a time series using generalized local linear approximation (GLLA). GLLA is a filtering method for estimating derivatives from data that uses time delay embedding and a variant of Savitzky-Golay filtering to accomplish the task.

Usage

glla(x, n.embed, tau, delta, order)

Arguments

Value

Returns a matrix containing n columns in which n is one plus the maximum order of the derivatives to be estimated via generalized local linear approximation

Author(s)

Hudson Golino <hfg9s at virginia.edu>

References

GLLA implementation
Boker, S. M., Deboeck, P. R., Edler, C., & Keel, P. K. (2010) Generalized local linear approximation of derivatives from time series. In S.-M. Chow, E. Ferrer, & F. Hsieh (Eds.), The Notre Dame series on quantitative methodology. Statistical methods for modeling human dynamics: An interdisciplinary dialogue, (p. 161-178). Routledge/Taylor & Francis Group.

Deboeck, P. R., Montpetit, M. A., Bergeman, C. S., & Boker, S. M. (2009) Using derivative estimates to describe intraindividual variability at multiple time scales. Psychological Methods, 14(4), 367-386.

Filtering procedure
Savitzky, A., & Golay, M. J. (1964). Smoothing and differentiation of data by simplified least squares procedures. Analytical Chemistry, 36(8), 1627-1639.

Examples

# A time series with 8 time points
tseries <- 49:56
deriv.tseries <- glla(tseries, n.embed = 4, tau = 1, delta = 1, order = 2)

Hierarchical EGA

Description

Estimates EGA using the lower-order solution of the Louvain algorithm (cluster_louvain)to identify the lower-order dimensions and then uses factor or network loadings to estimate factor or network scores, which are used to estimate the higher-order dimensions (for more details, see Jiménez et al., 2023)

Usage

hierEGA(
  data,
  loading.method = c("original", "revised"),
  rotation = NULL,
  scores = c("factor", "network"),
  loading.structure = c("simple", "full"),
  impute = c("mean", "median", "none"),
  corr = c("auto", "cor_auto", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  lower.algorithm = "louvain",
  higher.algorithm = c("leiden", "louvain", "walktrap"),
  uni.method = c("expand", "LE", "louvain"),
  plot.EGA = TRUE,
  verbose = FALSE,
  ...
)

Arguments

Value

Returns a list of lists containing:

Author(s)

Marcos Jiménez <marcosjnezhquez@gmailcom>, Francisco J. Abad <[email protected]>, Eduardo Garcia-Garzon <[email protected]>, Hudson Golino <[email protected]>, Alexander P. Christensen <[email protected]>, and Luis Eduardo Garrido <[email protected]>

References

Hierarchical EGA simulation
Jiménez, M., Abad, F. J., Garcia-Garzon, E., Golino, H., Christensen, A. P., & Garrido, L. E. (2023). Dimensionality assessment in bifactor structures with multiple general factors: A network psychometrics approach. Psychological Methods.

3+ level hierarchical EGA
Samo, A., Christensen, A. P., Abad, F. J., Garrido, L. E., Garcia-Garzon, E., Golino, H. & McAbee, S. T. (2023). Building the structure of personality from the bottom-up using Hierarchical Exploratory Graph Analysis. PsyArXiv.

Conceptual implementation
Golino, H., Thiyagarajan, J. A., Sadana, R., Teles, M., Christensen, A. P., & Boker, S. M. (2020). Investigating the broad domains of intrinsic capacity, functional ability and environment: An exploratory graph analysis approach for improving analytical methodologies for measuring healthy aging. PsyArXiv.

Revised network loadings
Christensen, A. P., Golino, H., Abad, F. J., & Garrido, L. E. (2024). Revised network loadings. PsyArXiv.

See Also

plot.EGAnet for plot usage in

Examples

# Example using network scores
opt.hier <- hierEGA(
  data = optimism, scores = "network",
  plot.EGA = FALSE # No plot for CRAN checks
)


# Plot multilevel plot
plot(opt.hier, plot.type = "multilevel")

# Plot multilevel plot with higher order
# border color matching the corresponding
# lower order color
plot(opt.hier, color.match = TRUE)

# Plot levels separately
plot(opt.hier, plot.type = "separate")

Description

Converts network to matrix

Usage

igraph2matrix(igraph_network, diagonal = 0)

Arguments

Value

Returns a network in the format

Author(s)

Hudson Golino <hfg9s at virginia.edu> & Alexander P. Christensen <alexander.christensen at Vanderbilt.Edu>

Examples

# Convert network to {igraph}
igraph_network <- convert2igraph(ega.wmt$network)

# Convert network back to matrix
igraph2matrix(igraph_network)

Information Theoretic Mixture Clustering for dynEGA

Description

Performs hierarchical clustering using Jensen-Shannon distance followed by the Louvain algorithm with consensus clustering. The method iteratively identifies smaller and smaller clusters until there is no change in the clusters identified

Usage

infoCluster(dynEGA.object, plot.cluster = TRUE, ...)

Arguments

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu> & Alexander P. Christensen <alexander.christensen at Vanderbilt.Edu>

See Also

plot.EGAnet for plot usage in EGAnet

Examples

# Obtain data
sim.dynEGA <- sim.dynEGA # bypasses CRAN checks

## Not run: 
# Dynamic EGA individual and population structure
dyn.ega1 <- dynEGA.ind.pop(
  data = sim.dynEGA, n.embed = 5, tau = 1,
  delta = 1, id = 25, use.derivatives = 1,
  ncores = 2, corr = "pearson"
)

# Perform information-theoretic clustering
clust1 <- infoCluster(dynEGA.object = dyn.ega1)
## End(Not run)

Description

A general function to compute several different information theory metrics

Usage

information(
  data,
  base = 2.718282,
  bins = floor(sqrt(nrow(data)/5)),
  statistic = c("entropy", "joint.entropy", "conditional.entropy", "total.correlation",
    "dual.total.correlation", "o.information")
)

Arguments

Value

Returns list containing only requested statistic

Author(s)

Hudson F. Golino <hfg9s at virginia.edu> and Alexander P. Christensen <[email protected]>

References

Shannon's entropy
Shannon, C. E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379-423.

Formalization of total correlation
Watanabe, S. (1960). Information theoretical analysis of multivariate correlation. IBM Journal of Research and Development 4, 66-82.

Applied implementation of total correlation
Felix, L. M., Mansur-Alves, M., Teles, M., Jamison, L., & Golino, H. (2021). Longitudinal impact and effects of booster sessions in a cognitive training program for healthy older adults. Archives of Gerontology and Geriatrics, 94, 104337.

Formalization of dual total correlation
Te Sun, H. (1978). Nonnegative entropy measures of multivariate symmetric correlations. Information and Control, 36, 133-156.

Formalization of O-information
Crutchfield, J. P. (1994). The calculi of emergence: Computation, dynamics and induction. Physica D: Nonlinear Phenomena, 75(1-3), 11-54.

Applied implementation of O-information
Marinazzo, D., Van Roozendaal, J., Rosas, F. E., Stella, M., Comolatti, R., Colenbier, N., Stramaglia, S., & Rosseel, Y. (2024). An information-theoretic approach to build hypergraphs in psychometrics. Behavior Research Methods, 1-23.

Examples

# All measures
information(wmt2[,7:24])

# One measures
information(wmt2[,7:24], statistic = "joint.entropy")

Description

A response matrix (n = 1152) of the International Cognitive Ability Resource (ICAR) intelligence battery developed by Condon and Revelle (2016).

Usage

data(intelligenceBattery)

Format

A 1185x125 response matrix

Examples

data("intelligenceBattery")

Measurement Invariance of EGA Structure

Description

Estimates configural invariance using bootEGA on all data (across groups) first. After configural variance is established, then metric invariance is tested using the community structure that established configural invariance (see Details for more information on this process)

Usage

invariance(
  data,
  groups,
  structure = NULL,
  iter = 500,
  configural.threshold = 0.7,
  configural.type = c("parametric", "resampling"),
  corr = c("auto", "cor_auto", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  algorithm = c("leiden", "louvain", "walktrap"),
  uni.method = c("expand", "LE", "louvain"),
  ncores,
  seed = NULL,
  verbose = TRUE,
  ...
)

Arguments

Details

In traditional psychometrics, measurement invariance is performed in sequential testing from more flexible (more free parameters) to more rigid (fewer free parameters) structures. Measurement invariance in network psychometrics is no different.

Configural Invariance

To establish configural invariance, the data are collapsed across groups and a common sample structure is identified used bootEGA and itemStability. If some variables have a replication less than 0.70 in their assigned dimension, then they are considered unstable and therefore not invariant. These variables are removed and this process is repeated until all items are considered stable (replication values greater than 0.70) or there are no variables left. If configural invariance cannot be established, then the last run of results are returned and metric invariance is not tested (because configural invariance is not met). Importantly, if any variables are removed, then configural invariance is not met for the original structure. Any removal would suggest only partial configural invariance is met.

Metric Invariance

The variables that remain after configural invariance are submitted to metric invariance. First, each group estimates a network and then network loadings (net.loads) are computed using the assigned community memberships (determined during configural invariance). Then, the difference between the assigned loadings of the groups is computed. This difference represents the empirical values. Second, the group memberships are permutated and networks are estimated based on the these permutated groups for iter times. Then, network loadings are computed and the difference between the assigned loadings of the group is computed, resulting in a null distribution. The empirical difference is then compared against the null distribution using a two-tailed p-value based on the number of null distribution differences that are greater and less than the empirical differences for each variable. Both uncorrected and false discovery rate corrected p-values are returned in the results. Uncorrected p-values are flagged for significance along with the direction of group differences.

Three or More Groups

When there are 3 or more groups, the function performs metric invariance testing by comparing all possible pairs of groups. Specifically:

• Pairwise Comparisons: The function generates all possible unique group pairings and computes the differences in network loadings for each pair. The same community structure, derived from configural invariance or provided by the user, is used for all groups.

• Permutation Testing: For each group pair, permutation tests are conducted to assess the statistical significance of the observed differences in loadings. p-values are calculated based on the proportion of permuted differences that are greater than or equal to the observed difference.

• Result Compilation: The function compiles the results for each pair including both uncorrected (p) and FDR-corrected (Benjamini-Hochberg; p_BH) p-values, and the direction of differences. It returns a summary of the findings for all pairwise comparisons.

This approach allows for a detailed examination of metric invariance across multiple groups, ensuring that all potential differences are thoroughly assessed while maintaining the ability to identify specific group differences.

For more details, see Jamison, Golino, and Christensen (2023)

Value

Returns a list containing:

Author(s)

Laura Jamison <[email protected]>, Hudson F. Golino <hfg9s at virginia.edu>, and Alexander P. Christensen <[email protected]>,

References

Original implementation
Jamison, L., Christensen, A. P., & Golino, H. F. (2024). Metric invariance in exploratory graph analysis via permutation testing. Methodology, 20(2), 144-186.

See Also

plot.EGAnet for plot usage in

Examples

# Load data
wmt <- wmt2[-1,7:24]

# Groups
groups <- rep(1:2, each = nrow(wmt) / 2)

## Not run: 
# Measurement invariance
results <- invariance(wmt, groups, ncores = 2)

# Plot with uncorrected alpha = 0.05
plot(results, p_type = "p", p_value = 0.05)

# Plot with BH-corrected alpha = 0.10
plot(results, p_type = "p_BH", p_value = 0.10)
## End(Not run)

Item Stability Statistics from bootEGA

Description

Based on the bootEGA results, this function computes and plots the number of times an variable is estimated in the same dimension as originally estimated by an empirical EGA structure or a theoretical/input structure. The output also contains each variable's replication frequency (i.e., proportion of bootstraps that a variable appeared in each dimension

Usage

itemStability(bootega.obj, IS.plot = TRUE, structure = NULL, ...)