Hierarchical EGA

Some constructs aren’t just multidimensional — they’re multidimensional and organized under a broader, more general factor. hierEGA estimates that kind of structure directly: a lower-order EGA on the items themselves, and a higher-order EGA on the dimensions that emerge from it. genTEFI then gives a single fit statistic across both levels at once.

hierEGA is still an experimental part of {EGAnet} — the function and its output may continue to change as it’s validated further. Treat the interpretation below as illustrative of the method rather than a finished analysis.

We’ll use the optimism dataset: 10 items from the Revised Life Orientation Test (LOT-R), a scale that mixes optimistically- and pessimistically-worded items and is a well-known candidate for this kind of layered structure.

# Load {EGAnet}
library(EGAnet)

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

# Print results
summary(opt_hier)

Lower Order

Model: GLASSO (EBIC with gamma = 0.5)
Correlations: auto
Lambda: 0.0815338053487632 (n = 100, ratio = 0.1)

Number of nodes: 10
Number of edges: 32
Edge density: 0.711

Non-zero edge weights: 
     M    SD    Min   Max
 0.072 0.190 -0.238 0.568

----

Consensus Method: Most Common (1000 iterations)
Algorithm: Louvain
Order: Lower

Number of communities:  4

 O1  O2  O3  O4  O5  O6  O7  O8  O9 O10 
  1   2   3   4   2   4   3   2   3   1 

----

Unidimensional Method: Louvain (Most Common for 1000 iterations)
Unidimensional: No

----

TEFI: -2.852

------------

Higher Order

Model: GLASSO (EBIC with gamma = 0.5)
Correlations: auto
Lambda: 0.0605080059973183 (n = 100, ratio = 0.1)

Number of nodes: 4
Number of edges: 4
Edge density: 0.667

Non-zero edge weights: 
     M    SD    Min   Max
 0.012 0.337 -0.301 0.443

----

Algorithm:  Louvain

Number of communities:  1

1 2 3 4 
1 1 1 1 

----

Unidimensional Method: Louvain
Unidimensional: Yes

----

TEFI: -8.829

----

Generalized TEFI: -11.681

----

Interpretation: Based on lower (-2.852) and higher (-8.829) TEFI, there is better fit for a bifactor structure than correlated lower order factor structure

Two Levels, Two Structures

The lower-order EGA splits the 10 LOT-R items into four small dimensions (TEFI = -2.852). The higher-order EGA then takes those four dimensions as its own “items” and finds that all four collapse into a single higher-order dimension (TEFI = -8.829) — consistent with the LOT-R’s usual reading as one general optimism–pessimism factor sitting above a handful of narrower item clusters.

plot(opt_hier, plot.type = "multilevel")

Generalized TEFI

genTEFI combines both levels into one number, which is what makes hierEGA solutions comparable to a single-level EGA on the same items:

genTEFI(opt_hier)

  VN.Entropy.Fit Level_1_VN Level_2_VN
1      -11.68105  -2.852031  -8.829023

The comparison that matters is between the two levels’ own TEFI values: the higher-order TEFI (-8.829) is lower (more negative, better fit) than the lower-order TEFI (-2.852). That ordering — higher-order fit beating lower-order fit — is what favors a bifactor-like structure, where a general factor sits above the specific item clusters, over treating those four lower-order clusters as independent, uncorrelated dimensions. genTEFI’s combined value (-11.681) is what makes this whole hierEGA solution comparable to a flat, single-level EGA on the same items; it’s not itself the basis for the bifactor-vs-correlated-factors call. hierEGA’s built-in interpretation reports the higher-vs-lower comparison directly:

attr(opt_hier, "methods")$interpretation

[1] "Based on lower (-2.852) and higher (-8.829) TEFI, there is better fit for a bifactor structure than correlated lower order factor structure"