Title:	Exploratory Graph Analysis – a Framework for Estimating the Number of Dimensions in Multivariate Data using Network Psychometrics
Version:	2.3.0
Date:	2025-04-09
Maintainer:	Hudson Golino <hfg9s@virginia.edu>
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.
Depends:	R (≥ 3.5.0)
License:	AGPL (≥ 3.0)
Encoding:	UTF-8
LazyData:	true
Imports:	dendextend, fungible, future, future.apply, GGally, ggplot2, ggpubr, glasso, glassoFast, GPArotation, igraph (≥ 1.3.0), lavaan, Matrix, methods, network, progressr, qgraph, semPlot, sna, stats
Suggests:	DEoptim, fitdistrplus, gridExtra, knitr, markdown, pbapply, progress, psych, pwr, RColorBrewer
URL:	https://r-ega.net
BugReports:	https://github.com/hfgolino/EGAnet/issues
RoxygenNote:	7.3.2
NeedsCompilation:	yes
Packaged:	2025-04-09 17:23:43 UTC; alextops
Author:	Hudson Golino [aut, cre], Alexander Christensen [aut], Robert Moulder [ctb], Luis E. Garrido [ctb], Laura Jamison [ctb], Dingjing Shi [ctb]
Repository:	CRAN
Date/Publication:	2025-04-09 23:10:15 UTC

EGAnet-package

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 <hfg9s@virginia.edu> and Alexander P. Christensen <alexpaulchristensen@gmail.com>

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

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)

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,
  fast = FALSE,
  returnAllResults = FALSE,
  penalizeMatrix = NULL,
  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]

# Fast
fast <- EBICglasso.qgraph(wmt)

# Regular
regular <- EBICglasso.qgraph(wmt, fast = FALSE)

# Difference between fast and regular
sum(abs(fast - regular))

# 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)

Exploratory Graph Analysis

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 <alexpaulchristensen@gmail.com>

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)

S3 Plot Methods for EGAnet

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, ...)

plot.TEFI.compare(x, base.name, comparison.name, base.color, comparison.color, ...)

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

• base.name — Character (length = 1). A string to label the base structure in the plot. Defaults to "Base"

• comparison.name — Character (length = 1). A string to label the comparison structure in the plot. Defaults to "Comparison"

• base.color — Character (length = 1). A string to specifying the color of the base structure in the plot. Hex codes can be used. Defaults to "blue"

• comparison.color — Character (length = 1). A string to specifying the color of the comparison structure in the plot. Hex codes can be used. Defaults to "red"

• ... — 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"
)

Exploratory Graph Model

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", "logLik", "SRMR"),
  constrain.structure = TRUE,
  constrain.zeros = TRUE,
  verbose = TRUE,
  ...
)

Arguments

Author(s)

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

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,
  constrain.structure = FALSE,
  constrain.zeros = FALSE,
  rotation = "geominQ",
  ...
)

Arguments

Author(s)

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

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)

Time-delay Embedding

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 <alexpaulchristensen@gmail.com>

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)

Loadings Comparison Test

Description

An algorithm to identify whether data were generated from a factor or network model using factor and network loadings. The algorithm uses heuristics based on theory and simulation. These heuristics were then submitted to several deep learning neural networks with 240,000 samples per model with varying parameters.

Usage

LCT(
  data,
  n = NULL,
  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"),
  iter = 100,
  seed = NULL,
  verbose = TRUE,
  ...
)

Arguments

Value

Returns a list containing:

Author(s)

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

References

Model training and validation
Christensen, A. P., & Golino, H. (2021). Factor or network model? Predictions from neural networks. Journal of Behavioral Data Science, 1(1), 85-126.

Examples

# Get data
data <- psych::bfi[,1:25]

## Not run: # Compute LCT
## Factor model
LCT(data)
## End(Not run)

Triangulated Maximally Filtered Graph

Description

Applies the Triangulated Maximally Filtered Graph (TMFG) filtering method (see Massara et al., 2016). The TMFG method uses a structural constraint that limits the number of zero-order correlations included in the network (3n - 6; where n is the number of variables). The TMFG algorithm begins by identifying four variables which have the largest sum of correlations to all other variables. Then, it iteratively adds each variable with the largest sum of three correlations to nodes already in the network until all variables have been added to the network. This structure can be associated with the inverse correlation matrix (i.e., precision matrix) to be turned into a GGM (i.e., partial correlation network) by using Local-Global Inversion Method (LoGo; see Barfuss et al., 2016 for more details). See Details for more information

Usage

TMFG(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  partial = FALSE,
  returnAllResults = FALSE,
  verbose = FALSE,
  ...
)

Arguments

Details

The TMFG method applies a structural constraint on the network, which restrains the network to retain a certain number of edges (3n-6, where n is the number of nodes; Massara et al., 2016). The network is also composed of 3- and 4-node cliques (i.e., sets of connected nodes; a triangle and tetrahedron, respectively). The TMFG method constructs a network using zero-order correlations and the resulting network can be associated with the inverse covariance matrix (yielding a GGM; Barfuss, Massara, Di Matteo, & Aste, 2016). Notably, the TMFG can use any association measure and thus does not assume the data is multivariate normal.

Construction begins by forming a tetrahedron of the four nodes that have the highest sum of correlations that are greater than the average correlation in the correlation matrix. Next, the algorithm iteratively identifies the node that maximizes its sum of correlations to a connected set of three nodes (triangles) already included in the network and then adds that node to the network. The process is completed once every node is connected in the network. In this process, the network automatically generates what's called a planar network. A planar network is a network that could be drawn on a sphere with no edges crossing (often, however, the networks are depicted with edges crossing; Tumminello, Aste, Di Matteo, & Mantegna, 2005).

Value

Returns a network or list containing:

Author(s)

Alexander Christensen <alexpaulchristensen@gmail.com>

References

Local-Global Inversion Method
Barfuss, W., Massara, G. P., Di Matteo, T., & Aste, T. (2016). Parsimonious modeling with information filtering networks. Physical Review E, 94, 062306.

Psychometric network introduction to TMFG
Christensen, A. P., Kenett, Y. N., Aste, T., Silvia, P. J., & Kwapil, T. R. (2018). Network structure of the Wisconsin Schizotypy Scales-Short Forms: Examining psychometric network filtering approaches. Behavior Research Methods, 50, 2531-2550.

Triangulated Maximally Filtered Graph
Massara, G. P., Di Matteo, T., & Aste, T. (2016). Network filtering for big data: Triangulated maximally filtered graph. Journal of Complex Networks, 5, 161-178.

Examples

# TMFG filtered network
TMFG(wmt2[,7:24])

# Partial correlations using the LoGo method
TMFG(wmt2[,7:24], partial = TRUE)

Unique Variable Analysis

Description

Identifies locally dependent (redundant) variables in a multivariate dataset using the EBICglasso.qgraph network estimation method and weighted topological overlap (see Christensen, Garrido, & Golino, 2023 for more details)

Usage

UVA(
  data = NULL,
  network = NULL,
  n = NULL,
  key = NULL,
  uva.method = c("MBR", "EJP"),
  cut.off = 0.25,
  reduce = TRUE,
  reduce.method = c("latent", "mean", "remove", "sum"),
  auto = TRUE,
  verbose = FALSE,
  ...
)

Arguments

References

Most recent simulation and implementation
Christensen, A. P., Garrido, L. E., & Golino, H. (2023). Unique variable analysis: A network psychometrics method to detect local dependence. Multivariate Behavioral Research.

Conceptual foundation and outdated methods
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.

Weighted topological overlap
Nowick, K., Gernat, T., Almaas, E., & Stubbs, L. (2009). Differences in human and chimpanzee gene expression patterns define an evolving network of transcription factors in brain. Proceedings of the National Academy of Sciences, 106, 22358-22363.

Selection of CFA Estimator
Rhemtulla, M., Brosseau-Liard, P. E., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17(3), 354-373.

Examples

# Perform UVA
uva.wmt <- UVA(wmt2[,7:24])

# Show summary
summary(uva.wmt)

Automatic correlations

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 <alexpaulchristensen@gmail.com>

Examples

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

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

Bootstrap Test for the Ergodicity Information Index

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")

Bootstrap Exploratory Graph Analysis

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 <alexpaulchristensen@gmail.com>

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)

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)

Compares Community Detection Solutions Using Permutation

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 <alexpaulchristensen@gmail.com>

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)

Applies the Consensus Clustering Method (Louvain only)

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 <alexpaulchristensen@gmail.com>

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
)

Apply a Community Detection Algorithm

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 <alexpaulchristensen@gmail.com>

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"
)

Homogenize Community Memberships

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 <alexpaulchristensen@gmail.com>

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)

Approaches to Detect Unidimensional Communities

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 <alexpaulchristensen@gmail.com>

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")

Visually Compare Two or More EGAnet plots

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 <alexpaulchristensen@gmail.com>

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"
)

Convert networks to igraph

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)

Convert networks to tidygraph

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)

Cosine similarity

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 <alexpaulchristensen@gmail.com>

Examples

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

# Obtain cosines
wmt_cosine <- cosine(wmt)

Depression Data

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 <alexpaulchristensen@gmail.com>

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)

Loadings Comparison Test Deep Learning Neural Network Weights

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")

Dynamic Exploratory Graph Analysis

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 <alexpaulchristensen@gmail.com>

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)

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")

Entropy Fit Index

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 <alexpaulchristensen@gmail.com> and Robert Moulder <rgm4fd@virginia.edu>

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)

Ergodicity Information Index

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 <alexpaulchristensen@gmail.com>

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)

Frobenius Norm (Similarity)

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

Generalized Total Entropy Fit Index using Von Neumman's entropy (Quantum Information Theory) for correlation matrices

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 <alexpaulchristensen@gmail.com>

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)

Generalized Local Linear Approximation

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 <fjose.abad@uam.es>, Eduardo Garcia-Garzon <egarcia@ucjc.edu>, Hudson Golino <hfg9s@virginia.edu>, Alexander P. Christensen <alexpaulchristensen@gmail.com>, and Luis Eduardo Garrido <luisgarrido@pucmm.edu.do>

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")

Convert network to matrix

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)

Information Theory Metrics

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 <alexpaulchristensen@gmail.com>

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")

Intelligence Data

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 <lj5yn@virginia.edu>, Hudson F. Golino <hfg9s at virginia.edu>, and Alexander P. Christensen <alexpaulchristensen@gmail.com>,

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)

Diagnostics Analysis for Low Stability Items

Description

Computes the between- and within-community strength of each variable for each community

Usage

itemDiagnostics(data, ...)

Arguments

Value

Returns a list containing:

Author(s)

Alexander P. Christensen <alexpaulchristensen@gmail.com>, Hudson Golino <hfg9s at virginia.edu>, and Luis Eduardo Garrido <garrido.luiseduardo@gmail.com>

Examples

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

## Not run: 
# Obtain diagnostics
diagnostics <- itemDiagnostics(wmt, ncores = 2)
## 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, ...)

Arguments

Value

Returns a list containing:

Author(s)

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

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.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

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

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

# Standard item stability
wmt.is <- itemStability(boot.wmt)

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

# EGA fit item stability
wmt.is.fit <- itemStability(boot.wmt.fit)

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

# Hierarchical EGA item stability
wmt.is.hier <- itemStability(boot.wmt.hier)

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

# Random-intercept EGA item stability
wmt.is.ri <- itemStability(boot.wmt.ri)
## End(Not run)

Jensen-Shannon Distance

Description

Computes the Jensen-Shannon Distance between two networks

Usage

jsd(network1, network2, method = c("kld", "spectral"), signed = TRUE)

Arguments

Value

Returns Jensen-Shannon Distance

Author(s)

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

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)

# Spectral JSD
jsd(glas1, glas2)
# 0.1595893

# Spectral JSS (similarity)
1 - jsd(glas1, glas2)
# 0.8404107

# Jensen-Shannon Divergence
jsd(glas1, glas2, method = "kld")
# 0.1393621

Computes the (Signed) Modularity Statistic

Description

Computes (signed) modularity statistic given a network and community structure. Allows the resolution parameter to be set

Usage

modularity(network, memberships, resolution = 1, signed = FALSE)

Arguments

Value

Returns the modularity statistic

Author(s)

Alexander P. Christensen <alexpaulchristensen@gmail.com> with assistance from GPT-4

References

Gomez, S., Jensen, P., & Arenas, A. (2009). Analysis of community structure in networks of correlated data. Physical Review E, 80(1), 016114.

Examples

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

# Estimate EGA
ega.wmt <- EGA(wmt, model = "glasso")

# Compute standard (absolute values) modularity
modularity(
  network = ega.wmt$network,
  memberships = ega.wmt$wc,
  signed = FALSE
)
# 0.1697952

# Compute signed modularity
modularity(
  network = ega.wmt$network,
  memberships = ega.wmt$wc,
  signed = TRUE
)
# 0.1701946

Network Loadings

Description

Computes the between- and within-community strength of each variable for each community

Usage

net.loads(
  A,
  wc,
  loading.method = c("original", "revised"),
  scaling = 2,
  rotation = NULL,
  ...
)

Arguments

Details

Simulation studies have demonstrated that a node's strength centrality is roughly equivalent to factor loadings (Christensen & Golino, 2021; Hallquist, Wright, & Molenaar, 2019). Hallquist and colleagues (2019) found that node strength represented a combination of dominant and cross-factor loadings. This function computes each node's strength within each specified dimension, providing a rough equivalent to factor loadings (including cross-loadings; Christensen & Golino, 2021).

Value

Returns a list containing:

Author(s)

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

References

Original implementation and simulation
Christensen, A. P., & Golino, H. (2021). On the equivalency of factor and network loadings. Behavior Research Methods, 53, 1563-1580.

Demonstration of node strength similarity to CFA loadings
Hallquist, M., Wright, A. C. G., & Molenaar, P. C. M. (2019). Problems with centrality measures in psychopathology symptom networks: Why network psychometrics cannot escape psychometric theory. Multivariate Behavioral Research, 1-25.

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

Examples

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

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

# Network loadings
net.loads(ega.wmt)

Network Scores

Description

This function computes network scores computed based on each node's strength within each community in the network (see net.loads). These values are used as "network loadings" for the weights of each variable.

Network scores are computed as a formative composite rather than a reflective factor. This composite representation is consistent with no latent factors that psychometric network theory proposes.

Scores can be computed as a "simple" structure, which is equivalent to a weighted sum scores or as a "full" structure, which is equivalent to an EFA approach. Conservatively, the "simple" structure approach is recommended until further validation

Usage

net.scores(
  data,
  A,
  wc,
  loading.method = c("original", "revised"),
  rotation = NULL,
  scores = c("Anderson", "Bartlett", "components", "Harman", "network", "tenBerge",
    "Thurstone"),
  loading.structure = c("simple", "full"),
  impute = c("mean", "median", "none"),
  ...
)

Arguments

Value

Returns a list containing:

Author(s)

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

References

Original implementation and simulation for loadings
Christensen, A. P., & Golino, H. (2021). On the equivalency of factor and network loadings. Behavior Research Methods, 53, 1563-1580.

Preliminary simulation for scores
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.

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

Examples

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

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

# Network scores
net.scores(data = wmt, A = ega.wmt)

Compares Network Structures Using Permutation

Description

A permutation implementation to determine statistical significance of whether the network structures are different from one another

Usage

network.compare(
  base,
  comparison,
  corr = c("auto", "cor_auto", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  iter = 1000,
  ncores,
  verbose = TRUE,
  seed = NULL,
  ...
)

Arguments

Value

Returns a list:

Author(s)

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

References

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

Jensen-Shannon Similarity (1 - Distance)
De Domenico, M., Nicosia, V., Arenas, A., & Latora, V. (2015). Structural reducibility of multilayer networks. Nature Communications, 6(1), 1–9.

Total Network Strength
van Borkulo, C. D., van Bork, R., Boschloo, L., Kossakowski, J. J., Tio, P., Schoevers, R. A., Borsboom, D., & Waldorp, L. J. (2023). Comparing network structures on three aspects: A permutation test. Psychological Methods, 28(6), 1273–1285.

Examples

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

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

# Groups
group1 <- wmt[groups == 1,]
group2 <- wmt[groups == 2,]

## Not run: # Perform comparison
results <- network.compare(group1, group2)

# Print results
print(results)

# Plot edge differences
plot(results)
## End(Not run)

Apply a Network Estimation Method

Description

General function to apply network estimation methods in EGAnet

Usage

network.estimation(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("BGGM", "glasso", "TMFG"),
  network.only = TRUE,
  verbose = FALSE,
  ...
)

Arguments

Value

Returns a matrix populated with a network from the input data

Author(s)

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

References

Graphical Least Absolute Shrinkage and Selection Operator (GLASSO)
Friedman, J., Hastie, T., & Tibshirani, R. (2008). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 432–441.

GLASSO with Extended Bayesian Information Criterion (EBICglasso)
Epskamp, S., & Fried, E. I. (2018). A tutorial on regularized partial correlation networks. Psychological Methods, 23(4), 617–634.

Bayesian Gaussian Graphical Model (BGGM)
Williams, D. R. (2021). Bayesian estimation for Gaussian graphical models: Structure learning, predictability, and network comparisons. Multivariate Behavioral Research, 56(2), 336–352.

Triangulated Maximally Filtered Graph (TMFG)
Massara, G. P., Di Matteo, T., & Aste, T. (2016). Network filtering for big data: Triangulated maximally filtered graph. Journal of Complex Networks, 5, 161-178.

Examples

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

# EBICglasso (default for EGA functions)
glasso_network <- network.estimation(
  data = wmt, model = "glasso"
)

# TMFG
tmfg_network <- network.estimation(
  data = wmt, model = "TMFG"
)

GLASSO with Non-convex Penalties

Description

The graphical least absolute shrinkage and selection operator with a non-convex regularization penalties

Usage

network.nonconvex(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  penalty = c("iPOT", "LGP", "POP", "SPOT"),
  gamma = NULL,
  lambda = NULL,
  nlambda = 50,
  lambda.min.ratio = 0.01,
  penalize.diagonal = TRUE,
  optimize.over = c("none", "lambda", "both"),
  ic = c("AIC", "AICc", "BIC", "EBIC"),
  ebic.gamma = 0.5,
  fast = TRUE,
  verbose = FALSE,
  ...
)

Arguments

Value

A network matrix

Author(s)

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

Examples

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

# Obtain network
awe_network <- network.nonconvex(data = wmt)

Predict New Data based on Network

Description

General function to compute a network's predictive power on new data, following Haslbeck and Waldorp (2018) and Williams and Rodriguez (2022)

This implementation is different from the predictability in the mgm package (Haslbeck), which is based on (regularized) regression. This implementation uses the network directly, converting the partial correlations into an implied precision (inverse covariance) matrix. See Details for more information

Usage

network.predictability(network, original.data, newdata, ordinal.categories = 7)

Arguments

Details

This implementation of network predictability proceeds in several steps with important assumptions:

1. Network was estimated using (partial) correlations (not regression like the mgm package!)

2. Original data that was used to estimate the network in 1. is necessary to apply the original scaling to the new data

3. (Linear) regression-like coefficients are obtained by reserve engineering the inverse covariance matrix using the network's partial correlations (i.e., by setting the diagonal of the network to -1 and computing the inverse of the opposite signed partial correlation matrix; see EGAnet:::pcor2inv)

4. Predicted values are obtained by matrix multiplying the new data with these coefficients

5. Dichotomous and polytomous data are given categorical values based on the original data's thresholds and these thresholds are used to convert the continuous predicted values into their corresponding categorical values

6. Evaluation metrics:

• dichotomous — "Accuracy" or the percent correctly predicted for the 0s and 1s and "Kappa" or Cohen's Kappa (see cite)

• polytomous — "Linear Kappa" or linearly weighted Kappa and "Krippendorff's alpha" (see cite)

• continuous — R-squared ("R2") and root mean square error ("RMSE")

Value

Returns a list containing:

Author(s)

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

References

Original Implementation of Node Predictability
Haslbeck, J. M., & Waldorp, L. J. (2018). How well do network models predict observations? On the importance of predictability in network models. Behavior Research Methods, 50(2), 853–861.

Derivation of Regression Coefficients Used (Formula 3)
Williams, D. R., & Rodriguez, J. E. (2022). Why overfitting is not (usually) a problem in partial correlation networks. Psychological Methods, 27(5), 822–840.

Cohen's Kappa
Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20(1), 37-46.

Cohen, J. (1968). Weighted kappa: nominal scale agreement provision for scaled disagreement or partial credit. Psychological Bulletin, 70(4), 213-220.

Krippendorff's alpha
Krippendorff, K. (2013). Content analysis: An introduction to its methodology (3rd ed.). Thousand Oaks, CA: Sage.

Examples

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

# Set seed (to reproduce results)
set.seed(42)

# Split data
training <- sample(
  1:nrow(wmt), round(nrow(wmt) * 0.80) # 80/20 split
)

# Set splits
wmt_train <- wmt[training,]
wmt_test <- wmt[-training,]

# EBICglasso (default for EGA functions)
glasso_network <- network.estimation(
  data = wmt_train, model = "glasso"
)

# Check predictability
network.predictability(
  network = glasso_network, original.data = wmt_train,
  newdata = wmt_test
)

Optimism Data

Description

A response matrix (n = 282) containing responses to 10 items of the Revised Life Orientation Test (LOT-R), developed by Scheier, Carver, & Bridges (1994).

Usage

data(optimism)

Format

A 282x10 response matrix

References

Scheier, M. F., Carver, C. S., & Bridges, M. W. (1994). Distinguishing optimism from neuroticism (and trait anxiety, self-mastery, and self-esteem): a reevaluation of the Life Orientation Test. Journal of Personality and Social Psychology, 67, 1063-1078.

Examples

data("optimism")

Computes Polychoric Correlations

Description

A fast implementation of polychoric correlations in C. Uses the Beasley-Springer-Moro algorithm (Boro & Springer, 1977; Moro, 1995) to estimate the inverse univariate normal CDF, the Drezner-Wesolosky approximation (Drezner & Wesolosky, 1990) to estimate the bivariate normal CDF, and Brent's method (Brent, 2013) for optimization of rho

Usage

polychoric.matrix(
  data,
  na.data = c("pairwise", "listwise"),
  empty.method = c("none", "zero", "all"),
  empty.value = c("none", "point_five", "one_over"),
  ...
)

Arguments

Value

Returns a polychoric correlation matrix

Author(s)

Alexander P. Christensen <alexpaulchristensen@gmail.com> with assistance from GPT-4

References

Beasley-Moro-Springer algorithm
Beasley, J. D., & Springer, S. G. (1977). Algorithm AS 111: The percentage points of the normal distribution. Journal of the Royal Statistical Society. Series C (Applied Statistics), 26(1), 118-121.

Moro, B. (1995). The full monte. Risk 8 (February), 57-58.

Brent optimization
Brent, R. P. (2013). Algorithms for minimization without derivatives. Mineola, NY: Dover Publications, Inc.

Drezner-Wesolowsky bivariate normal approximation
Drezner, Z., & Wesolowsky, G. O. (1990). On the computation of the bivariate normal integral. Journal of Statistical Computation and Simulation, 35(1-2), 101-107.

Examples

# Load data (ensure matrix for missing data example)
wmt <- as.matrix(wmt2[,7:24])

# Compute polychoric correlation matrix
correlations <- polychoric.matrix(wmt)

# Randomly assign missing data
wmt[sample(1:length(wmt), 1000)] <- NA

# Compute polychoric correlation matrix
# with pairwise missing
pairwise_correlations <- polychoric.matrix(
  wmt, na.data = "pairwise"
)

# Compute polychoric correlation matrix
# with listwise missing
pairwise_correlations <- polychoric.matrix(
  wmt, na.data = "listwise"
)

Prime Numbers through 100,000

Description

Numeric vector of primes generated from the primes package. Used in the function [EGAnet]{ergoInfo}. Not for general use

Usage

data(prime.num)

Format

A 1185x24 response matrix

Examples

data("prime.num")

Random-Intercept EGA

Description

Estimates the number of substantive dimensions after controlling for wording effects. EGA is applied to a residual correlation matrix after subtracting and random intercept factor with equal unstandardized loadings from all the regular and unrecoded reversed items in the database

Usage

riEGA(
  data,
  n = NULL,
  corr = c("auto", "cor_auto", "cosine", "pearson", "spearman"),
  na.data = c("pairwise", "listwise"),
  model = c("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)

Alejandro Garcia-Pardina <alejandrogp97@gmail.com>, Francisco J. Abad <fjose.abad@uam.es>, Alexander P. Christensen <alexpaulchristensen@gmail.com>, Hudson Golino <hfg9s at virginia.edu>, Luis Eduardo Garrido <luisgarrido@pucmm.edu.do>, and Robert Moulder <rgm4fd@virginia.edu>

References

Selection of CFA Estimator
Rhemtulla, M., Brosseau-Liard, P. E., & Savalei, V. (2012). When can categorical variables be treated as continuous? A comparison of robust continuous and categorical SEM estimation methods under suboptimal conditions. Psychological Methods, 17, 354-373.

See Also

plot.EGAnet for plot usage in EGAnet

Examples

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

# riEGA example
riEGA(data = wmt, plot.EGA = FALSE)
# no plot for CRAN checks

sim.dynEGA Data

Description

A simulated (multivariate time series) data with 24 variables, 100 individual observations, 50 time points per individual and 2 groups of individuals

Usage

data(sim.dynEGA)

Format

A 5000 x 26 multivariate time series

Details

Data were generated using the simDFM function with the following arguments:

Group 1

simDFM( variab = 12, timep = 50, nfact = 2, error = 0.125, dfm = "DAFS", loadings = EGAnet:::runif_xoshiro( 1, min = 0.50, max = 0.70 ), autoreg = 0.80, crossreg = 0.00, var.shock = 0.36, cov.shock = 0.18 )

Group 2

simDFM( variab = 8, timep = 50, nfact = 3, error = 0.125, dfm = "DAFS", loadings = EGAnet:::runif_xoshiro( 1, min = 0.50, max = 0.70 ), autoreg = 0.80, crossreg = 0.00, var.shock = 0.36, cov.shock = 0.18 )

Examples

data("sim.dynEGA")

Simulate data following a Dynamic Factor Model

Description

Function to simulate data following a dynamic factor model (DFM). Two DFMs are currently available: the direct autoregressive factor score model (Engle & Watson, 1981; Nesselroade, McArdle, Aggen, and Meyers, 2002) and the dynamic factor model with random walk factor scores.

Usage

simDFM(
  variab,
  timep,
  nfact,
  error,
  dfm = c("DAFS", "RandomWalk"),
  loadings,
  autoreg,
  crossreg,
  var.shock,
  cov.shock,
  burnin = 1000
)

Arguments

Author(s)

Hudson F. Golino <hfg9s at virginia.edu>

References

Engle, R., & Watson, M. (1981). A one-factor multivariate time series model of metropolitan wage rates. Journal of the American Statistical Association, 76(376), 774-781.

Nesselroade, J. R., McArdle, J. J., Aggen, S. H., & Meyers, J. M. (2002). Dynamic factor analysis models for representing process in multivariate time-series. In D. S. Moskowitz & S. L. Hershberger (Eds.), Multivariate applications book series. Modeling intraindividual variability with repeated measures data: Methods and applications, 235-265.

Examples

## Not run: 
# Estimate EGA network
data1 <- simDFM(variab = 5, timep = 50, nfact = 3, error = 0.05,
dfm = "DAFS", loadings = 0.7, autoreg = 0.8,
crossreg = 0.1, var.shock = 0.36,
cov.shock = 0.18, burnin = 1000)
## End(Not run)

Simulate data following a Exploratory Graph Model (EGM)

Description

Function to simulate data based on EGM

Usage

simEGM(
  communities,
  variables,
  loadings,
  cross.loadings = 0.02,
  correlations,
  sample.size,
  max.iterations = 1000
)

Arguments

Author(s)

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

Examples

simulated <- simEGM(
  communities = 2, variables = 6,
  loadings = 0.55, # use standard factor loading sizes
  correlations = 0.30,
  sample.size = 1000
)

Total Entropy Fit Index using Von Neumman's entropy (Quantum Information Theory) for correlation matrices

Description

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

Usage

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

Arguments

Value

Returns a data frame with columns:

Non-hierarchical Structure

Hierarchical Structure

Author(s)

Hudson Golino <hfg9s at virginia.edu>, Alexander P. Christensen <alexpaulchristensen@gmail.com>, and Robert Moulder <rgm4fd@virginia.edu>

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]

# Estimate EGA model
ega.wmt <- EGA(
  data = wmt, model = "glasso",
  plot.EGA = FALSE # no plot for CRAN checks
)

# Compute entropy indices for empirical EGA
tefi(ega.wmt)

# User-defined structure (with `EGA` object)
tefi(ega.wmt, structure = c(rep(1, 5), rep(2, 5), rep(3, 8)))

Compare Total Entropy Fit Index (tefi) Between Two Structures

Description

This function computes the tefi values for two different structures using bootstrapped correlation matrices from bootEGA and compares them using a non-parametric bootstrap test. It also visualizes the distributions of tefi values for both structures.

Usage

tefi.compare(bootega.obj, base, comparison, plot.TEFI = TRUE, ...)

Arguments

Details

The null hypothesis is that the TEFI values obtained in the bootstrapped correlation matrices for the base structure are than the TEFI values obtained in the bootstrapped correlation matrices for the comparison structure. Therefore, the p-value in this bootstrap test can be interpreted as follows:

• If the p-value less than 0.05: TEFI values for the base structure tend to be lower than the comparison structure, indicating that the former provides a better fit (lower entropy) than the latter

• If the p-value is greater than 0.05: TEFI values for the base structure are not significantly lower than the comparison structure, suggesting that both structures may provide similar fits or that comparison might fit better

Value

A list containing:

Author(s)

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

Examples

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

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

# Perform comparison
comparing_tefi <- tefi.compare(
  boot.wmt,
  base = boot.wmt$EGA$wc, # Compare Walktrap
  comparison = community.detection(
   boot.wmt$EGA$network, algorithm = "louvain"
  ) # With Louvain
)

# Plot options (UVa colors)
plot(
  comparing_tefi,
  base.name = "Walktrap", base.color = "#232D4B",
  comparison.name = "Louvain", comparison.color = "#E57200"
)

Total Correlation

Description

Computes the total correlation of a dataset

Usage

totalCor(data, base = 2.718282)

Arguments

Value

Returns a list containing:

Author(s)

Hudson F. Golino <hfg9s at virginia.edu>

References

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

Applied implementation
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.

Examples

# Compute total correlation
totalCor(wmt2[,7:24])

Total Correlation Matrix

Description

Computes the pairwise total correlation (totalCor) for a dataset

Usage

totalCorMat(data, base = 2.718282, normalized = FALSE)

Arguments

Value

Returns a symmetric matrix with pairwise total correlations

Author(s)

Hudson F. Golino <hfg9s at virginia.edu>

References

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

Applied implementation
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.

Examples

# Compute total correlation matrix
totalCorMat(wmt2[,7:24])

Entropy Fit Index using Von Neumman's entropy (Quantum Information Theory) for correlation matrices

Description

Computes the fit of a dimensionality structure using Von Neumman's entropy when the input is a correlation matrix. Lower values suggest better fit of a structure to the data

Usage

vn.entropy(data, structure)

Arguments

Value

Returns a list containing:

Author(s)

Hudson Golino <hfg9s at virginia.edu>, Alexander P. Christensen <alexpaulchristensen@gmail.com>, and Robert Moulder <rgm4fd@virginia.edu>

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

# Get EGA result
ega.wmt <- EGA(
  data = wmt2[,7:24], model = "glasso",
  plot.EGA = FALSE # no plot for CRAN checks
)

# Compute Von Neumman entropy
vn.entropy(ega.wmt$correlation, ega.wmt$wc)

WMT-2 Data

Description

A response matrix (n = 1185) of the Wiener Matrizen-Test 2 (WMT-2).

Usage

data(wmt2)

Format

A 1185x24 response matrix

Examples

data("wmt2")

Weighted Topological Overlap

Description

Computes weighted topological overlap following the Novick et al. (2009) definition

Usage

wto(network, signed = TRUE, diagonal.zero = TRUE)

Arguments

Value

A symmetric matrix of weighted topological overlap values between each pair of variables

References

Original formalization
Nowick, K., Gernat, T., Almaas, E., & Stubbs, L. (2009). Differences in human and chimpanzee gene expression patterns define an evolving network of transcription factors in brain. Proceedings of the National Academy of Sciences, 106, 22358-22363.

Examples

# Obtain network
network <- network.estimation(wmt2[,7:24], model = "glasso")

# Compute wTO
wto(network)