Child Hope Scale Exploratory Graph Analysis

Article title: Children’s Hope Scale: factor structure and norms for Australian children aged 8–18 years

Authors: Richter, S., Dorrian, J., Wicking, P., Wicking, A., & Lushington, K.

Journal: Australian Journal of Psychology

Bibliometrics: Volume 76, Number 1, pages 2322724

DOI: http://dx.doi.org/10.1080/00049530.2024.2322724

Following the publication of our article (Richter et al., 2024), a colleague suggested that we conduct Exploratory Graph Analysis (EGA) to further examine the factor structure of the Children’s Hope Scale (CHS) in our sample of 171,052 Australian children aged 8–18 years. While our original analyses, which included exploratory factor analysis (EFA), confirmatory factor analysis (CFA), and bifactor modelling, supported a unidimensional factor structure, EGA provides a complementary network psychometrics approach to assessing dimensionality (Golino & Epskamp, 2017). Unlike exploratory or confirmatory factor analysis, which rely on latent variable modelling, EGA uses community detection algorithms to identify the number of dimensions directly from item–item relationships, quantify item redundancy, and assess stability through bootstrapping. This provides an additional, visually interpretable check on the robustness of the factor structure (Golino et al., 2020).

EGA analyses

Unique variable analysis (partial correlations and weighted topological overlap [wTO]) was used to identify potential item redundancy (Christensen & Golino, 2021). Four pairs showed small-to-moderate redundancy (wTO > 0.20) but not at a magnitude warranting removal (Supplementary Table 1). EGA was performed using graphical least absolute shrinkage and selection operator (GLASSO) with the Louvain community detection algorithm. Results yielded a single community, confirmed via the Louvain Method, with consistent network loadings across items (Supplementary Figure 1). Bootstrap analysis replicated a single dimension in 100% of resamples (stability = 1.0).

Supplementary Table 1.

Exploratory Graph Analysis results for the Children’s Hope Scale

Item	Network loading	wTO redundancy (max)
CHS1: I think I am doing pretty well.	0.521	CHS1–CHS3 = 0.23
CHS2: I can think of many ways to get the things in life that are most important to me.	0.445	CHS1–CHS2 = 0.21
CHS3: I am doing just as well as other kids my age.	0.444	CHS1–CHS3 = 0.23
CHS4: When I have a problem, I can come up with lots of ways to solve it.	0.497	CHS4–CHS6 = 0.22
CHS5: I think the things I have done in the past will help me in the future.	0.455	CHS5–CHS6 = 0.21
CHS6: Even when others want to quit, I know that I can find ways to solve the problem.	0.487	CHS4–CHS6 = 0.22

Note. Network loadings = strength of node’s association with its community; wTO = weighted topological overlap. All redundancy values fell below thresholds for removal.

Supplementary Figure 1.

Summary of exploratory graph analysis (EGA) of the Children’s Hope Scale, yielding a single community. Variables (scale items) are represented as nodes, and the strength of the relationships between variables is represented by the thickness of the edges. The model specified graphical least absolute shrinkage and selection operator (GLASSO) regularisation and used the Louvain algorithm for testing unidimensionality.

Interpretation

These EGA results align with and strengthen the findings reported in our original article, further supporting the interpretation that the CHS functions as a unidimensional measure of hope in Australian children.

Impact on conclusions

These additional analyses do not change the conclusions or implications discussed in the published article.

Acknowledgment

We would like to thank Dr Michael Spezio for his feedback and drawing our attention to EGA as an alternative approach for testing dimensionality following publication of our original article. This recommendation was helpful in guiding the additional analyses reported in this addendum.