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The general workflow of Exploratory Graph Analysis (EGA; Golino & Epskamp, 2017; Golino et al., 2020) should at minimum take the following order of analysis:

  • determine redundancies (using UVA)

  • perform EGA

  • check stability of EGA (using bootEGA)

To demonstrate this workflow, we’ll use the bfi dataset from the {psych} package.

About the Dataset

25 personality self report items taken from the International Personality Item Pool ( were included as part of the Synthetic Aperture Personality Assessment (SAPA) web based personality assessment project. The data from 2800 subjects are included here as a demonstration set for scale construction, factor analysis, and Item Response Theory analysis. Three additional demographic variables (sex, education, and age) are also included.

Description was taken from ?psychTools::bfi

Determine Redundancies

# Load packages
library(EGAnet); library(psychTools)

# Perform Unique Variable Analysis
bfi_uva <- UVA(
  data = bfi[,1:25],
  key = as.character(bfi.dictionary$Item[1:25])
  # Optional: provide item descriptions

# Print results
Variable pairs with wTO > 0.30 (large-to-very large redundancy)

            node_i                node_j   wto
 Get angry easily. Get irritated easily. 0.431


Variable pairs with wTO > 0.25 (moderate-to-large redundancy)


Variable pairs with wTO > 0.20 (small-to-moderate redundancy)

                         Don't talk a lot.
                   Am exacting in my work.
 Am indifferent to the feelings of others.
           Do things in a half-way manner.
               Know how to comfort others.
                         Get angry easily.
                Have frequent mood swings.
         Inquire about others' well-being.
                                node_j   wto
 Find it difficult to approach others. 0.226
 Continue until everything is perfect. 0.225
     Inquire about others' well-being. 0.219
                        Waste my time. 0.209
             Make people feel at ease. 0.207
            Have frequent mood swings. 0.205
                      Often feel blue. 0.204
           Know how to comfort others. 0.203

Unique Variable Analysis (Christensen, Garrido, & Golino, 2023) uses the weighted topological overlap measure (Nowick et al., 2009; see ?wto) on an estimated network. Values greater than 0.25 are determined to have considerable local dependence (i.e., redundancy) that should be handled.

Based on the output above, there is one pair of variables that are above this cut-off (and quite substantially): Get angry easily. and Get irritated easily. (\(\omega\) = 0.431). By default, the UVA will remove all redundant variables (\(\omega \ge\) 0.25) except for one based on the following rules:

  • doublets (two variables): The variable with the lowest maximum weighted topological overlap to all other variables (other than the one it is redundant with) is retained and the other is removed

  • triplets (three or more variables): The variable with the highest mean weighted topological overlap to all other variables that are redundant with one another is retained and all others are removed

The variables that were removed in this automated process can be viewed using:

[1] "Get irritated easily."

[1] "Get angry easily."

Moving forward, we’ll work with the reduced dataset obtained from the UVA function.

Perform EGA

With redundancies handled, EGA is ready to be applied to the data:

bfi_ega <- EGA(data = bfi_uva$reduced_data)

With the reduced data, five dimensions are recovered from the bfi dataset (consistent with the five factor model of personality). We can obtain a summary of this output:

Model: GLASSO (EBIC with gamma = 0.5)
Correlations: auto
Lambda: 0.0597096451199323 (n = 100, ratio = 0.1)

Number of nodes: 24
Number of edges: 125
Edge density: 0.453

Non-zero edge weights: 
     M    SD    Min   Max
 0.041 0.112 -0.270 0.396


Algorithm:  Walktrap

Number of communities:  5

A1 A2 A3 A4 A5 C1 C2 C3 C4 C5 E1 E2 E3 E4 E5 N2 N3 N4 N5 O1 O2 O3 O4 O5 
 1  1  1  1  1  2  2  2  2  2  3  3  3  3  3  4  4  4  4  5  5  5  5  5 


Unidimensional Method: Louvain
Unidimensional: No


TEFI: -24.989

The summary contains several things of interest. First, it tells us what model was used to estimate the network ("glasso") and what parameters were used for that model such as gamma (\(\gamma = 0.5\)) and lambda (\(\lambda = 0.0597\)). Second, there are descriptives about the network such as the number of nodes, edges, edge density, and descriptive statistics about the edges. Third, it tells us what community detection algorithm was used, the number of communities (dimensions), and each variable’s membership. Fourth, the unidimensional method and check (No meaning it was not unidimensional). Finally, the Total Entropy Fit Index (or tefi) is provided, which can be used for model comparison (see Golino et al., 2021).

To change the appearance of the EGA plot, see Plotting

Check Stability of EGA

# Perform Bootstrap EGA
bfi_boot <- bootEGA(
  data = bfi_uva$reduced_data,
  seed = 1 # set seed for reproducibility

Bootstrap EGA (Christensen & Golino, 2021) performs a parametric (default) or resampling procedure to determine the robustness of the empirical EGA analysis (using 500 iterations by default). The plot output by bootEGA is the median network structure representing the median value of each pairwise partial correlation across the bootstraps. After obtaining the median value for each pairwise partial correlation, a community detection algorithm is applied ("walktrap" by default).

In this example, the median structure matches our empirical structure:

bfi_compare <- compare.EGA.plots(
  bfi_ega, bfi_boot,
  labels = c("Empirical", "Bootstrap")

Although this result is common, it is by no means necessary. Because a community detection algorithm is applied adhoc to the median network structure, it is possible that the number and content of the communities do not match the empirical structure. This possibility happens from time-to-time and does not mean there is anything wrong with your analysis but instead might hint at some instability in the structure.

Following through on some basic descriptive statistics about the bootstrap analysis is often more informative:

Correlations: auto
Algorithm:  Walktrap
Unidimensional Method:  Louvain


EGA Type: EGA 
Bootstrap Samples: 500 (Parametric)
                4     5
Frequency:  0.046 0.954

Median dimensions: 5 [4.59, 5.41] 95% CI

Much like the empirical procedure, the first information is about the estimation methods and algorithms used. After, there is information about the bootstrap procedure including how frequent each number of communities were observed and the median number of communities (with 95% confidence intervals). In this example, the structure is quite stable and can be taken as preliminary evidence of a robust structure.

The frequency of the number of communities should not be used as the main evidence of robustness. Instead, dimension and item stability should be obtained to better understand the details.

EGA Type: EGA 
Bootstrap Samples: 500 (Parametric)

Proportion Replicated in Dimensions:

   A1    A2    A3    A4    A5    C1    C2    C3    C4    C5    E1    E2    E3 
1.000 1.000 1.000 0.998 1.000 1.000 1.000 1.000 1.000 1.000 0.998 0.998 0.998 
   E4    E5    N2    N3    N4    N5    O1    O2    O3    O4    O5 
0.998 0.952 1.000 1.000 1.000 1.000 0.956 0.956 0.956 0.956 0.956 


Structural Consistency:

    1     2     3     4     5 
0.998 1.000 0.958 1.000 0.956 

The output of dimensionStability produces a plot of how often each variable is replicating in their empirical structure across bootstraps. The summary statistics produced also relay this information as well as structural consistency. Structural consistency is defined as the extent to which each empirically derived dimension is exactly (i.e., identical variable composition) recovered from the replicate bootstrap samples (Christensen, Golino, & Silvia, 2020). In general, values of structural consistency and item stability greater than 0.70-0.75 reflect sufficient stability (Christensen & Golino, 2021). Our results demonstrate that the five dimension structure we’ve identified is quite robust.