Hierarchical Structure of the Entrepreneurial Career Competency Instrument: Evidence from Frequentist and Bayesian Bifactor Structural Equation Modelling

Abstract

Robust measurement of entrepreneurial competencies (ECs) is crucial for entrepreneurship education, yet their internal structure remains theoretically contested and empirically underexamined. This study examined whether the four-factor Entrepreneurial Career Competency Instrument (ECCI) exhibits a hierarchical (bifactor) structure among South African entrepreneurs. Using two non-probability samples (N = 1305; N = 280), we analysed competing models, including a bifactor exploratory structural equation model (ESEM). The selected 56-item bifactor ESEM solution was examined for conceptual replicability in the smaller sample using Bayesian structural equation modelling (BSEM) with informative priors and sensitivity analyses to address small-sample uncertainty. Our findings revealed a theoretically supported hierarchical structure with a strong general factor and distinct specific factors: entrepreneurial career mindset, innovativeness, motivation, and implementation, enhancing the interpretation of scores. This study guides ECCI usage by suggesting total scores for broad assessments and domain scores for diagnostic feedback. Methodologically, the findings demonstrate that combining frequentist and Bayesian approaches across samples strengthened structural validity and provided insights into evaluating imprecise responses to self-report measures and addressing sampling constraints. Overall, this work contributes a robust structural model of the ECCI and enriches the EC literature, serving as a framework for refining, testing and applying attribute-based EC measures in diverse contexts.

1. Introduction

Entrepreneurship education has been recognised as a distinct field since the 1940s. It plays a vital role in fostering entrepreneurial intention and mindset, as well as in boosting economic growth through job creation. In entrepreneurship education, entrepreneurial competencies (ECs) are developed, which enhance opportunity-driven motivations, entrepreneurial behaviour (Man et al., 2002; Man et al., 2008), start-up activity (Morris et al., 2013), business performance (J. Sánchez, 2012), and success (Bird, 2019; Mitchelmore & Rowley, 2010). Evidence-based EC frameworks inform the design and evaluation of entrepreneurship education, thereby strengthening its effectiveness and impact. Consequently, identifying and developing ECs has become a global research agenda for scholars (Man et al., 2002, 2008; Morris et al., 2013; J. C. Sánchez, 2011). ECs, the collective term for individual attributes, knowledge, and skills, are considered to represent the full range of an entrepreneur’s capabilities to successfully carry out fundamental duties and activities (Man et al., 2002, 2008; Morris et al., 2013). While knowledge and skills are oriented towards performance and outcomes, individual attributes function as foundational inputs required for competent performance (Vargas-Halabí et al., 2017). Measuring these attribute-based ECs, which include inherent personality traits, abilities, attitudes, values, and motivations that drive entrepreneurial behaviours (Mai & Thai, 2024), forms the central focus of this study.

Despite extensive work in the field, no universally accepted EC framework has emerged, largely because theories and measures vary across contexts and regions (González-López et al., 2021; Tittel & Terzidis, 2020). In a recent review, Mai and Thai (2024) noted persistent fragmentation in EC frameworks and called for greater synergy across studies. Even so, influential contributions, such as those by Man et al. (2008) and Mitchelmore and Rowley (2010), have helped establish key attribute-based competencies, including opportunity recognition, problem-solving, and resilience. In this study, we aimed to decrease ambivalence in the EC framework debate by offering a theoretically sound structural framework and methodological foundation for improving, testing, and applying attribute-based EC measures across various study contexts and regions.

Calls to expand EC measurements across different contexts and regions have increased over the past decade (Mai & Thai, 2024; Mitchelmore & Rowley, 2010). EC research primarily focuses on the Global North, while the Global South remains largely overlooked (Mai & Thai, 2024) and may not reflect regional cultural and socio-economic conditions, as seen in South Africa (Ncube & Matlala, 2025). In South Africa, evaluating and promoting entrepreneurial competencies within its culturally diverse society, marked by significant socio-economic and structural inequalities (Mbatha, 2024), is essential: 55% of small businesses fail within a year, and the Total Entrepreneurship Activity (TEA) index was only 11.1% in 2024, substantially below the global average of 20% (Bowmaker-Falconer et al., 2023; Hechavarría et al., 2024). Nel and Botha (2025) responded to the call in South Africa by developing an attribute-based EC (AC) framework and an English self-report measure covering 14 ECs. (i.e., autonomy, action orientation, calculated risk-taking, curiosity, growth mindset, innovation, leadership, opportunity recognition and assessment, problem-solving, resilience, self-efficacy, value creation, and value-driven behaviour). Their factor-analytic findings grouped 57 items into four theoretically supported, correlated career-related factors: entrepreneurial career mindset, entrepreneurial career innovativeness, entrepreneurial career motivation, and entrepreneurial career implementation (Nel & Botha, 2025). Nonetheless, it remains uncertain whether these correlated first-order dimensions represent a broader underlying construct of entrepreneurial career competency, a crucial differentiating factor that influences the interpretation and application of a measure (Rodriguez et al., 2016a).

Although there is increasing consensus that entrepreneurial competencies are multidimensional constructs (Man et al., 2002; Mitchelmore & Rowley, 2010; Morris et al., 2013), substantial shared variance among competencies has been reported in multidimensional models (Ahmad et al., 2018; Nel & Botha, 2025; Tehseen et al., 2020). This pattern indicates the presence of a theoretically grounded hierarchical structure (Boyatzis, 1982; Menke, 2018; Spencer & Spencer, 1993), comprising a general entrepreneurial competency factor alongside domain-specific competencies (Arafeh, 2016; Cárdenas-Gutiérrez et al., 2021; Man et al., 2008; Wirda et al., 2023). Clarifying this hierarchical structure within the ECCI is essential for advancing theoretical understanding and ensuring valid interpretation of competency scores (AERA et al., 2014). Accordingly, the central research question for the study was: To what extent does the ECCI capture a general entrepreneurial career competency factor alongside distinct, meaningful specific factors corresponding to the four career-related subconstructs delineated by Nel and Botha (2025)?

Addressing this knowledge gap is vital because dimensionality decisions directly influence how ECCI scores are computed, interpreted, and used in entrepreneurship education and development (AERA et al., 2014). Grounded in classical test theory (Lord & Novick, 1968) and factor-analytic methods (Bollen, 1989), this study employs bifactor modelling to examine the hierarchical structure of the ECCI and assess conceptual replication across two independent samples (N = 1305 and N = 280) (Zwaan et al., 2018). Bifactor modelling is regarded as an effective psychometric tool for assessing hierarchical structures (Rodriguez et al., 2016a). More specifically, we used bifactor exploratory structural equation modelling (ESEM) for the larger sample and bifactor Bayesian structural equation modelling (BSEM) for the smaller sample. ESEM and BSEM overcome the limitations of conventional exploratory factor analysis (EFA) and confirmatory factor analysis (CFA), which are often too restrictive for modelling such complex structures (Alamer, 2022; Swami et al., 2023). Because direct comparisons across frequentist and Bayesian paradigms were not feasible, bifactor auxiliary diagnostics and factor-loading analyses were used to assess factor strength and conceptual replicability (Lorenzo-Seva & Berge, 2006; Petras & Meiser, 2024; Rodriguez et al., 2016b).

The research purpose and objectives of this study aligned with the research question and were guided by a substantive-methodological synergy approach (Marsh & Hau, 2007), which suggests that advanced statistical models should better reflect theoretical models of complex human attributes, thereby yielding new insights (Hofmans et al., 2021). The purpose of this study was to evaluate the hierarchical structure of the ECCI using bifactor analysis and to clarify its implications for scoring and application. Specifically, to meet the purpose of the study, we:

(a)

Examined competing measurement representations of the ECCI (Swami et al., 2023), including bifactor models (Rodriguez et al., 2016a) grounded in the four sub-constructs reported by Nel and Botha (2025).

(b)

Evaluated the strength and interpretability of the general and specific factors to support defensible scoring decisions (AERA et al., 2014; DeMars, 2013).

(c)

Assessed the conceptual replicability and robustness of the bifactor model across two independent samples using different statistical paradigms (Frequentist and Bayesian) (Zwaan et al., 2018), while matching model complexity to sample constraints (Morin et al., 2016; Zitzmann et al., 2021).

(d)

Selected analytic approaches that best align with EC theory and measurement aims, thereby yielding new insights (Hofmans et al., 2021; Marsh & Hau, 2007).

This study establishes the robustness of the hierarchical ECCI measurement model, offering new insights derived from the precise alignment of advanced statistical techniques with specific research objectives and sample constraints. We found evidence supporting the bifactor ESEM and BSEM models of the ECCI, comprising an essentially unidimensional factor and four distinct, narrow-group factors. These findings provide a framework for interpreting ECCI scores and support the development of a widely applicable attribute-based EC model in diverse contexts. This study offers both substantive and methodological insights into the ECCI by adopting a substantive-methodological synergistic approach.

2. Theoretical Framework

The following sections outline a theoretical framework consisting of the substantive (theoretical) foundations of the ECCI structure and the methodological advances used to assess plausible measurement models, followed by the positioning of the present study.

2.1. Substantive Foundations

The section provides the background to the development of the ECCI measure, followed by a discussion of the different views on the dimensionality of ECs.

2.2. Development of the EC Framework and the Four-Factor ECCI Measurement

ECs are defined and categorised in numerous ways, and scholars have struggled to reach a consensus, which is essential for entrepreneurship education programmes. Some ECs are tied to inherent personality traits (Le Deist & Winterton, 2005; Man & Lau, 2005), whereas others emerge from integrated frameworks. Foundational frameworks by Man and Lau (2000), Man et al. (2002, 2008), and Mitchelmore and Rowley (2010) classify ECs into eight general domains: relationship, analytical, opportunity, strategic, innovative, human, commitment, and operational. However, reliance on these frameworks has introduced contextual and regional biases (Tehseen et al., 2020), often neglecting the critical ECs needed for development.

More recent research has expanded these frameworks to include additional competencies, such as motivation (e.g., need for achievement), autonomy (e.g., locus of control), ethics, action orientation, leadership, growth mindset, curiosity, and social intelligence (Mitchelmore & Rowley, 2010; Morris et al., 2013; Rasmussen et al., 2011). Building on this work, Morris et al. (2013) proposed a framework of 13 entrepreneurial competencies (ECs), which Blignaut and Botha (2022) partially adopted and expanded into a 14-entrepreneurial career competencies (ECC) framework tailored for application in South Africa. The 14 ECC framework emphasises the central role of an entrepreneurial mindset in developing individual competencies and capabilities (Kouakou et al., 2019). This framework is grounded in social learning theory and the theory of entrepreneurial competence (Mishra & Zachary, 2014). Blignaut and Botha (2022) validated the framework for the region through interviews, Delphi studies, and focus group workshops, engaging a demographically diverse group of South African entrepreneurs, industry experts, academics, and students. The 14 ECC framework was tested and refined on diverse populations, including South African entrepreneurs, academics, and students in entrepreneurial education. Despite the region’s demographic and societal diversity, this initiative has yielded a robust ECC framework.

Earlier unpublished work developed 194 items aligned with the 14 ECCs described by Nel and Botha (2025). These are provided in the Supplementary Materials (Table S1). After pilot testing with 280 participants, the item pool was narrowed down to 103 items. This was achieved through an ECC item review matrix (see Supplementary Materials File S1), focusing on content relevance, clarity and minimising redundancy to maintain the construct breadth. Statistical screening using item means, skewness, kurtosis, and item communalities for each ECC was applied conservatively to avoid prematurely discarding items due to sample-specific idiosyncrasies (DeVellis, 2017). No items retained were adapted or reworded. A more rigorous item screening using comprehensive factor analysis was deferred for validation in a larger sample.

Nel and Botha (2025) reduced 103 items to 88 via item analysis in an independent sample (N = 1305) and subsequently applied principal axis factoring, yielding a 57-item ECCI with a theoretically supported four-factor structure (

Table 1. The four ECCI factors and labels.

	Factors	14 ECCs	Omega
F1	Entrepreneurial career mindset (23 items)	Resilience (R, 7-items), Autonomy (A, 4-items), Action orientation (AC, 3-items), Opportunity assessment (OA, 2 items); Opportunity recognition (OR, 1-item), Self-efficacy (SE, 5-items), and Growth mindset (GM, 1-item). Example: “I perform despite challenges” (R14).	0.94
F2	Entrepreneurial career innovativeness (10 items)	Curiosity (C, 3-items) and Calculated risk (CR, 7-items). Example: “I pursue situations in which risk is involved” (CR8).	0.92
F3	Entrepreneurial career motivation (5 items)	Value creation (VC, 2-items) and value-driven (VD, 3-items). Example: “I want to uplift the community” (VD5).	0.88
F4	Entrepreneurial career implementation (19 items)	Innovation (6-items), Leadership (L, 1-item), Opportunity recognition (OR, 4-items), Problem-solving (PS, 4-items), Self-efficacy (SE, 1-item), Value creation (VC, 2-items), and Value-driven (VDA, 1-item) Example: “I turn my imaginative ideas into reality” (I6).	0.94

Source: Adapted from Nel and Botha (2025).

). Rather than dividing the sample into separate exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) subsamples, which introduces its own limitations, the authors used the full sample to enhance estimation stability. They embedded the exploratory solution within an ESEM framework, which can diagnose misspecification more precisely than EFA and improve replicability (Alamer, 2022; Swami et al., 2023).

The ECCI four-factor structure reflects core personal attributes expressed as broader psychological (Shaver et al., 2019) and social/management competencies (Davis et al., 2016). Nel and Botha (2025) identified four factors: (Factor 1) entrepreneurial career mindset, an adaptable orientation that helps individuals innovate in dynamic environments (Davis et al., 2016; Shaver et al., 2019); (Factor 2) entrepreneurial career innovativeness, a tendency to pursue novel ideas and engage in calculated risk-taking, supported by curiosity and comfort with uncertainty (Gören, 2017; Nel & Botha, 2025); (Factor 3) entrepreneurial career motivation, a value-driven, ethically and socially responsible intent aimed at creating opportunities for societal upliftment (Kraus et al., 2017; Littlewood & Holt, 2015; Nel & Botha, 2025); and (Factor 4) entrepreneurial career implementation, the enactment of new ideas through problem-solving, opportunity seizing, and value creation (Geum et al., 2020; Nel & Botha, 2025; Shane & Venkataraman, 2000) (See Appendix A: ECCI Factors for a more detailed description of each factor). Nel and Botha (2025) suggest that ECCI can be categorised into psychological (Factor 1), social (Factor 3), and management (Factors 2 and 4) competencies, consistent with Santos et al. (2010).

2.3. The Dimensionality of ECs

Theories of entrepreneurial competencies (ECs) often adopt hierarchical frameworks with multiple layers and dimensions (Mai & Thai, 2024; Menke, 2018), drawing on earlier models such as Spencer’s Iceberg Model (Spencer & Spencer, 1993) and Boyatzis’s Onion Model (Boyatzis, 1982). These frameworks reflect the idea that foundational competencies (e.g., general traits and motives) combine into a broader disposition while still allowing for distinct elements, such as specific attitudes and abilities, that shape entrepreneurial intent, performance, and success.

Early factor-analytic research described ECs primarily as first-order multidimensional constructs (e.g., risk-taking, opportunity recognition, and self-efficacy) (Arafeh, 2016; Boyatzis, 1982; Man et al., 2002; Mitchelmore & Rowley, 2010; Morris et al., 2013). Later studies extended this work by proposing higher-order structures, including second-order and general-factor models (Ahmad et al., 2018; Arafeh, 2016; Cárdenas-Gutiérrez et al., 2021; Tehseen et al., 2020; Wirda et al., 2023; Zhensheng & Liu, 2019). This shift aligns with the view that ECs operate at a higher level of abstraction, comprising heterogeneous yet related indicators, consistent with both essential unidimensionality and specific dimensions (Man et al., 2008; Tehseen et al., 2020). Overall, the literature suggests that ECs include both a dominant general factor and meaningful specific factors, although the relative contribution of each is uncertain. Moderately correlated dimensions may therefore signal multidimensionality alongside a substantial general factor (Reise et al., 2014), and adding more indicators can further strengthen the general factor as a shared, latent source, regardless of the indicators’ dimensionality (Rodriguez et al., 2016a).

Overall, ECs can be conceptualised as a hierarchical bifactor structure comprising general and specific competencies. This framework provides a nuanced understanding of its structure and enhances its applicability in research and practice.

Based on this theoretical discussion, we hypothesise the following:

Hypothesis 1.

The Entrepreneurial Career Competency Instrument (ECCI) is hierarchically structured, consisting of an essential unidimensional (broad) factor and four distinct (narrow) group factors.

The following section discusses methodological advances that enable effective psychometric analyses of complex hierarchical measurement models, which are often plagued by imprecise human responses.

2.4. Methodological Advances

In the following sections, we briefly examine the limitations of the measurement model in traditional CFA and present more flexible, robust alternatives utilised in this study to model complex, multidimensional constructs. This includes the application of BSEM in the conceptual replication study with the smaller sample. (A comprehensive discussion of methodological advances is provided in Supplementary Material Text S2).

2.5. Measurement Model Issues and Contemporary Solutions

Conventional independent cluster confirmatory factor analysis (ICM-CFA) is often misspecified for self-report instruments because its restrictive assumptions, namely, zero cross-loadings and uncorrelated residuals, disregard systematic sources of measurement error arising from imperfect human responses (Xiao et al., 2019). As a result, factor correlations may be inflated and factor loadings distorted, thereby weakening the construct validity (Asparouhov et al., 2015; Marsh et al., 2014; Morin et al., 2016; Zhang et al., 2023). In addition, correlated first-order factor models can obscure the presence of a dominant general factor underlying specific factors. This masking effect is frequently overlooked and is sometimes misinterpreted as evidence of true multidimensionality (Rodriguez et al., 2016a).

Contemporary bifactor approaches address these issues. Specifically, bifactor ESEM and bifactor BSEM models accommodate minor cross-loadings and correlated residuals while partitioning the variance attributable to a general factor from the variance specific to subconstructs. Consequently, these models provide a more realistic representation of multidimensional item structures (Rodriguez et al., 2016a; Zhang et al., 2023).

2.6. The Need for BSEM and ESEM for Testing Complex Models and Sample Size Sensitivity

Frequentist and Bayesian inferential paradigms in SEM complement each other by providing a framework for the conceptual replication of imperfect measurement models. In frequentist SEM, parameters are typically estimated from the observed data, often using maximum likelihood (ML) or related estimators, yielding point estimates and confidence intervals. In contrast, Bayesian SEM (BSEM) estimates posterior distributions by combining prior information with sample data, usually via Monte Carlo sampling, and summarises parameter uncertainty using credible intervals (van de Schoot et al., 2014). This framework also allows prior information from earlier studies to be incorporated in a principled manner (van de Schoot et al., 2014). For example, based on evidence from previous studies, a prior denoted as N(0.5, 0.10) indicates that a primary factor loading with a mean of approximately 0.50 and a variance of 0.10 can be expected, yielding a normally distributed 95% credibility interval (CI) of ±0.62 (CI = $\sqrt{0.10} \times 1.96$). Therefore, the expected primary factor loading range is −0.12 to 1.11. Similarly, factor cross-loadings from previous studies suggest that a prior N(0, 0.01) represents a mean cross-loading of 0 and a variance of 0.01, yielding a normally distributed 95% CI of ±0.20 and an expected loading range of −0.20 to +0.20.

With carefully selected informative priors, BSEM can regularise small cross-loadings and correlated residuals. In other words, it allows for near-zero “wiggle room” (e.g., −0.20 to +0.20) to account for minor systematic error or white noise arising from human imprecision in responding to questionnaire items. This often improves the estimation stability and helps mitigate overfitting or non-identifiability in complex models, particularly when using relatively small samples. Sensitivity analyses were used to evaluate the choice and influence of the priors on the model’s parameter estimates (Hoijtink & van de Schoot, 2018; B. Muthén & Asparouhov, 2012; Smid et al., 2020; Zitzmann et al., 2021).

In parallel, exploratory structural equation modelling (ESEM) provides a frequentist approach for relaxing the strict zero-crossing loading constraint. When estimated in large samples using targeted rotation, ESEM can offer an empirically grounded basis for specifying BSEM priors in subsequent conceptual replication studies with smaller samples (Alamer, 2022; Hsu et al., 2014; Swami et al., 2023; Uanhoro & Soyoye, 2025; Zhang et al., 2023).

2.7. Testing Complex Models with Hierarchical Structures

Hierarchical constructs can be modelled using either second-order or bifactor structures. Whereas second-order models represent general factors indirectly through lower-order factors, bifactor models specify a general factor that loads directly onto indicators alongside orthogonal specific factors. This formulation is advantageous when the proportionality constraints inherent in second-order models are implausible, particularly when the primary aim is to disentangle the variance attributable to a general factor from the variance specific to subconstructs (Brunner et al., 2012; Mansolf & Reise, 2017; Markon, 2019; Reise, 2012).

Model interpretation should consider both overall fit and bifactor auxiliary indices, such as omega subscale (ωS) and omega hierarchical subscale (ωHS) reliability (Rodriguez et al., 2016a, 2016b). The ωS reflects variance in a subscore attributable to general and specific factors. ωHS estimates the proportion of variance in a subscale solely due to its specific factor, after accounting for the general factor. A higher ωHS (e.g., ωHS = 0.50) indicates a distinct narrow construct beyond the general factor, provided that ωS is acceptable (e.g., ωS = 0.70). Dueber and Toland (2023) revised conventional interpretive cutoffs by demonstrating that the criterion of ωHS ≥ 0.50 is overly strict, as ωHS is moderated by ωS (Reise et al., 2013). Similarly, the explained common variance for the specific factor (ECVss) measures the proportion of subscale common variance attributable to the specific factor after removing the general factor. Like ωHS, it assesses subscale uniqueness and is moderated by ωS.

To assess the stability and generalisability of sparse, specific-factor solutions, Petras and Meiser (2024) introduced the sum of squared factor loadings (SS_λ) as a measure of total variance within a factor. This functions as an indicator of subfactor stability and generalisability in bifactor models. When SS_λ equals 1, the factor accounts for as much variance as a single indicator and can be interpreted similarly to a PCA eigenvalue of 1 when considering factor retention.

Factor determinacy (FD) measures how accurately factor scores represent the latent factor. A higher FD (e.g., FD ≥ 0.90) suggests that factor scores can reliably act as proxies for the true latent trait. The percentage of uncontaminated correlations (PUC) indicates the proportion of inter-item correlations that are “pure” indicators of the general factor. A higher PUC (e.g., PUC ≥ 0.70) signifies a dominant factor, supporting an essentially unidimensional interpretation, even if some multidimensionality exists.

The absolute relative parameter bias (ARPB) measures bias in item loadings when multidimensional (bifactor) data are simplified into a unidimensional model. A lower ARPB (e.g., ARPB ≤ 10%) indicates minimal bias, suggesting that a unidimensional approximation is acceptable. A low ARPB permits total-score calculations where researchers are less concerned with subscale scores. These indices and cutoff criteria are described in Supplementary Material Text S1. They help identify the strengths and contributions of the model’s factors (Bonifay et al., 2017; Dueber & Toland, 2023; Petras & Meiser, 2024; Reise et al., 2013; Rodriguez et al., 2016b).

Overall, selecting an optimal model requires balancing theoretical considerations with evidence from model fit indices, factor strength indices, and local misspecification diagnostics such as residual correlation matrices and modification indices (Alamer, 2022; Swami et al., 2023).

2.8. The Limitations of Bifactor Models

A key limitation of bifactor models is their susceptibility to overfitting, such that an excellent apparent fit may reflect sample-specific idiosyncrasies (including trivial specific factors) rather than the intended hierarchical structure, thereby undermining interpretability and generalisability (Bonifay et al., 2017; Swami et al., 2023).

The risk of overfitting can be mitigated by (i) grounding model specifications in theory, (ii) triangulating evidence from global fit, local misfit diagnostics, and bifactor strength indices (including SS_λ to gauge subfactor stability), (iii) applying BSEM regularisation with thoughtfully specified priors and sensitivity analyses, and (iv) testing conceptual replication across independent samples (Petras & Meiser, 2024; Zitzmann et al., 2021). All these methods were applied in the present study.

2.9. The Present Study

This study examines whether the ECCI’s four-factor ESEM structure is better characterised as a hierarchical (bifactor) construct comprising a general entrepreneurial career competency factor alongside four distinctly interpretable group factors (Nel & Botha, 2025). Because this hierarchical representation has not yet been formally evaluated, the analyses were theory-guided and exploratory rather than strictly confirmatory. Using the original validation dataset (Sample 1; N = 1305), we compared plausible measurement models (CFA, ESEM, bifactor-CFA, bifactor-ESEM), supplemented with local misfit diagnostics and bifactor strength indices, to enable a deeper psychometric analysis of dimensionality (Swami et al., 2023). This comparison informed the model selection by balancing parsimony and model fidelity (Alamer, 2022; Swami et al., 2023).

Building on the Nel and Botha (2025) EFA-ESEM embedded model, we aimed to develop a stable, refined, and theory-driven measurement model using a large dataset, thereby providing a sound basis for future independent replication studies. This approach diverges from the conventional split-sample EFA/CFA approach, in which the less statistically sophisticated EFA model is rarely confirmed by the more restrictive ICM-CFA model for lengthy measures (e.g., 50 items) (Alamer, 2022; Marsh et al., 2014).

We conceptually replicated the bifactor ESEM model on a smaller pilot sample (Sample 2; N = 280) using bifactor BSEM with informative and slightly informative priors anchored to large-sample results (Asparouhov et al., 2015; Zitzmann et al., 2021; Zwaan et al., 2018). Recruiting a new sample of entrepreneurs with strong English language proficiency from an eligible but socio-economically constrained pool for model replication was infeasible at the time; therefore, we reused an independent pilot dataset for the analysis.

The reuse of these datasets is warranted because, first, the study addresses a distinct question—whether the ECCI is hierarchically structured and the implications for score interpretation—rather than replicating instrument development or initial validation (Nel & Botha, 2025). Second, the original pilot and validation studies employed distinct analytic phases: item pruning in the pilot was largely content-driven, with conservative use of item-level statistics and item communalities within each ECC, whereas the four-factor structure was primarily informed by covariance-based factor-analytic evidence across ECCs from an independent validation sample. This separation reduces the risk that the pilot data shaped the target factor solution, although some residual circularity arising from within-sample item selection cannot be fully ruled out. In the pilot replication, Bayesian regularising priors and sensitivity analyses further help limit overfitting and enhance the stability of parameter estimates in the smaller sample (Asparouhov et al., 2015; Zitzmann et al., 2021).

Reusing data for secondary analysis is a well-established approach to optimising underused datasets, provided that it is reported transparently and paired with methodological advances that yield new insights (Cheng & Phillips, 2014; Kelly et al., 2024; Weston et al., 2019). In scale validation, it is increasingly accepted and aligns well with the substantive-methodological synergy approach, provided that potential biases are acknowledged and managed (Asparouhov et al., 2015; Byrne et al., 2025; B. Muthén & Asparouhov, 2012).

In this study, we found evidence supporting the hierarchical structure of the ECCI and provided substantive and methodological insights into EC measurement.

3. Materials and Methods

3.1. Study Design

We utilised cross-sectional data from two non-probability samples to evaluate the internal structure of the ECCI, contributing to the validity evidence of the ECCI.

3.2. Data Collection Process

The target population comprised South African entrepreneurs aged 18 or older, from diverse language, gender, and racial backgrounds, who were proficient in English, owned businesses, and had engaged in entrepreneurial activities in the past five years. The study used Statistics South Africa’s racial classifications—Black African, Coloured, Indian/Asian, White, and Other—along with gender, age, and language (Statistics South Africa, 2023). The Qualtrics survey platform distributed links via email to a database of over 20,000 entrepreneurs maintained by a non-profit organisation supporting entrepreneurs. The survey, conducted in English on two occasions with distinct groups, yielded 1305 and 280 valid responses for Samples 1 and 2, respectively.

3.3. Ethics Statement

Participants were prospectively recruited and completed surveys between 1 July 2021 and 31 March 2022. Sample 2 was recruited first, followed by sample 1. Participation was unpaid and voluntary. The study was approved by the Institutional Research Ethics Committee (Protocol EMS113/21) and conducted in accordance with the principles outlined in the Declaration of Helsinki. Electronic informed consent was obtained from the participants on the introductory Qualtrics page. Participants were informed that the study aimed to validate and refine the competency measure, that participation was voluntary and anonymous, that they could withdraw at any time without penalty, and that their responses would be used for research purposes only.

Consent was indicated by clicking the continue arrow after reading the statement: “By continuing, you are agreeing that (a) you have read and understood the information provided above, and (b) you give your consent to participate in the study voluntarily.”

3.4. Study Samples

Sample 1 included 1305 respondents (59.9% males, 33.7% females, and 6% undisclosed). Most (82.8%) were aged 18–65 years, and 16% were aged 66 years or older. Racial distribution: 63.9% White, 21% Black, 8% Indian, 6% Coloured, 2% undisclosed. English was the home language for 48.1% of the population, Afrikaans for 31.5%, and 20% spoke indigenous languages, mostly isiXhosa, isiZulu, Setswana, Sepedi, and Sesotho. Overall, 97.4% of the participants reported proficiency in English, ranging from good to excellent.

Sample 2 included 280 respondents (61.8% males, 31.4% females, and 6.8% undisclosed). Most (88%) were aged 18–65 years, with 12% aged 66 years or older. Racial distribution: 76.8% White, 13.7% Black, 6% Indian, 4% Coloured, and less than 1% undisclosed. English was the home language for 49.3% of the participants, Afrikaans for 36.7%, and 14% from the isiXhosa, isiZulu, Setswana, Sepedi, and Sesotho language groups. Overall, 97% of the participants reported proficiency in English, ranging from good to excellent.

Both samples reported good-to-excellent English proficiency, enabling them to complete the questionnaires and supporting the evaluation of the ECCI measurement model. However, because this was a non-probability, email-based survey requiring voluntary participation with no incentives, the sample did not mirror South Africa’s 2022 population profile (81% Black, 7.3% White, 8.2% Coloured, and 2.7% Indian). Socio-economic and structural inequalities restrict digital access and English proficiency among many Black entrepreneurs, who comprise approximately 89% of the informal sector (Mbatha, 2024; Statistics South Africa, 2023, 2025). Consequently, the survey likely attracted wealthier, English-proficient entrepreneurs who were disproportionately White and more active in the formal sector (Makgetla & Moshikaro, 2025). Accordingly, English proficiency was prioritised over representativeness at the time to establish a reliable English ECCI version for South African entrepreneurs, which would support later validation across diverse subgroups.

3.5. Measure

The ECCI (Table 1) comprises 57 self-reported items rated on a five-point Likert scale (1 = strongly disagree to 5 = strongly agree). Nel and Botha (2025) four-factor model groups items into entrepreneurial career mindset (F1, 23 items), entrepreneurial career innovativeness (F2, 10 items), entrepreneurial career motivation (F3, 5 items), and entrepreneurial career implementation (F4, 19 items). The internal consistency was acceptable (α = 0.90, 0.92, 0.88, and 0.94, respectively).

3.6. Statistical Analysis

3.6.1. Correlational Analysis for Sample Circular Effects

We examined how item statistics and communalities for each EC dimension, shown in the item review matrix (Supplementary Materials File S2), affected pruning decisions during piloting using Spearman correlation analysis. This helped evaluate the risk of circularity when reusing the pilot sample as Sample 2 to replicate the factor model derived from the independent Sample 1.

3.6.2. Descriptive Statistics

The data distribution and normality were assessed using descriptive statistics, including the mean, skewness, and kurtosis. The Mahalanobis distance test was used to identify influential outliers in the data, and the sensitivity of the selected models was assessed.

3.6.3. Analytic Strategy for Model Assessments

We adopted a theory-guided, multi-stage analytic strategy to examine the bifactor hierarchical model and proceeded sequentially across samples and statistical paradigms to minimise circularity. First, we applied frequentist estimation to a large validation sample to evaluate competing structural models, including the bifactor ESEM model (see Figure 1A–E). Second, the selected bifactor and one-factor models were examined for conceptual replicability in the independent pilot sample using bifactor BSEM (see Figure 2F–H) and informative priors. For the Bayesian model, we used parameter regularisation and sensitivity testing for complex models and small-sample conditions. Model evaluation emphasised global fit, local misspecification diagnostics, factor strength indices, and the theoretical interpretability of factor structures, rather than relying solely on fit indices.

3.6.4. ML SEM Analysis for Testing the Hypothesis

We conducted SEM in Mplus 8.10 (L. K. Muthén & Muthén, 2023) using robust maximum likelihood estimation (MLR) with 1305 participants. Missing data were handled using full-information maximum likelihood (FIML) estimation under the missing-at-random (MAR) assumption. Following Swami et al. (2023), we tested first-order four-factor CFA and ESEM, bifactor CFA and ESEM, and one-factor CFA (Figure 1A–E). Model selection used standard fit thresholds for the Comparative Fit Index (CFI ≥ 0.90), Tucker–Lewis Index (TLI ≥ 0.90), Root Mean Square Error of Approximation (RMSEA ≤ 0.08) and Standardised Root Mean Square Residual (SRMR ≤ 0.05) and the inspection of parameters, including loadings, cross-loadings, factor correlations, and correlated residuals. In addition, bifactor indices (ωS, ωHS, FD, ECV, ECVss, PUC, ARPB, VAR_ECV, and SS_λ) were computed using Dueber (2017)’s calculator.

We used Jrule for Mplus expected parameter change (EPC) indicator to evaluate misspecifications in correlated residuals, a key source of model misfit (Oberski, 2009). The EPC should fall within −0.10 to 0.10 to be considered irrelevant misspecification. Misspecifications outside this range require further consideration (Saris et al., 2009). We used the modification index (MI) and the EPC indicator to assess model misspecifications based on overall model fit.

In the bifactor ESEM, we used a 0.40 cut-off for primary loadings on the general factor. Specific factors may not meet this criterion after accounting for the general factor’s variance. Primary loadings below this threshold were considered distinct if they were higher than other cross-loadings (Bostwick et al., 2025; Morin et al., 2016). Loadings under 0.20 were considered non-substantive (Asparouhov et al., 2015). In the bifactor model, item loadings were satisfactory if they met the 0.40 cut-off for the general factor, even if they did not exceed 0.20 for the specific factor (Morin et al., 2016).

We conducted a bifactor analysis to assess both the common and unique item variances. To evaluate essential unidimensionality, we considered ECV, PUC, and ωH, requiring a minimum of 0.70 for each measure. The PUC moderates the ECV, and together they guide the assessment of unidimensionality. We followed the thresholds from Reise et al. (2013) and Rodriguez et al. (2016b): if PUC ≥ 0.80, ECV should be above 0.50; if PUC < 0.80, then ECV should be at least 0.60, and ωH must be ≥0.70. Additionally, the FD should be ≥0.90, and an average ARPB below 0.10 to 0.15 indicates no significant factor score bias (B. Muthén et al., 1987).

The authors used a value-added ratio (VAR) cutoff of ≥1.1 to indicate added value beyond the general factor. The VAR ≥ 1.1 threshold is estimated from ωS, ωHS, or ECVss using regression equations, with cut-offs based on factor numbers, as provided in Dueber and Toland (Dueber & Toland, 2023, pp. 228–229), (See Supplementary Materials Text S1, Table A). The ωHS and ECVss cut-offs are moderated by ωS (the ωS calculation includes general and specific factor variance). We used cut-offs for a four-factor model with ωS values between 0.85 and 0.95.

When ωS ≈ 0.85, the cut-offs are ωHS ≥ 0.17 and ECVss ≥ 0.20. For ωS ≈ 0.90, cut-offs are ωHS ≥ 0.11 and ECVss ≥ 0.15. At ωS ≈ 0.95, thresholds decrease to ωHS ≥ 0.00 and ECVss ≥ 0.05. As ωS increases, ωHS and ECVss become less significant in determining added value. To better illustrate factor distinction, we calculated the value-added ratio for ECVss (VAR_ECV) using the regression formula (See Supplementary Materials Text S1, Equation (S1)) from Dueber and Toland (Dueber & Toland, 2023, p. 228). Although VAR_ECV is less optimal, it is sufficiently accurate for evaluating the added value of models with four or more specific factors.

We used an SS_λ cutoff of ≥1, a strength indicator such as the PCA eigenvalue, to ensure that the residual factors were generalisable (Petras & Meiser, 2024). Well-fitting bifactor models often have weak residual factors, requiring additional strength measurements (Petras & Meiser, 2024).

3.6.5. Bayesian SEM Analysis for Testing the Hypothesis

We used Mplus 8.10 (L. K. Muthén & Muthén, 2023) and BSEM to replicate the ECCI model in the pilot sample (N = 280) using priors from bifactor ML-ESEM analyses in the larger sample. Missing data were handled using full-information Bayesian estimation. The models were estimated using four MCMC chains with a Gibbs sampler. Convergence was assessed using the potential scale reduction factor (PSRF) and inspection of trace and posterior density plots. PSRF values < 1.05 indicate convergence. We ran 40,000 iterations with thinning set to 2 and then increased the number of iterations to 80,000 to confirm convergence. Analyses used standardised variables, with factor variances fixed at 1, and the results are reported for the standardised model.

We tested three BSEM models. First, we estimated a bifactor BSEM model with informative (small-variance) priors for primary and cross-loadings (Figure 2F). Second, we added tiny (near-zero-variance) priors on correlated residuals to the bifactor model (Figure 2G). Third, we estimated a one-factor BSEM model with informative priors for primary loadings and tiny priors for correlated residuals (Figure 2H).

Primary loadings received weakly informative priors, N(0.5, 0.10), while cross-loadings were assigned small-variance priors, N(0, 0.01). This resulted in 95% credible intervals of approximately ±0.62 and ±0.20, aligning with Sample 1 estimates and classical test theory expectations of non-substantive cross-loadings (B. Muthén & Asparouhov, 2012).

Our cross-loading priors followed Liang and Cao (2023), who recommended N(0, 0.01) for non-substantive cross-loadings, with a 95% CI of ±0.20 that does not dominate the data (Asparouhov et al., 2015). In contrast, the more restrictive N(0, 0.005) gives a 95% CI of ±0.14 and barely covers observed cross-loadings (−0.16 to 0.16) in the bifactor ML-ESEM model. Priors for primary loadings, N(0.5, 0.10), were based on bifactor ML-ESEM loadings, ranging from −0.05 to 0.76. A mean of 0.50 with a 95% CI of −0.11 to 1.12 was therefore reasonable. The literature supports slightly informative priors with adequate variance for primary loadings in complex small-sample models, as they are often more accurate and less prone to convergence issues than uninformative priors (Smid et al., 2020). We balanced the prior variance against the potential loading bias, recognising that in small samples, a slightly biased but less variable estimate can be more accurate than an unbiased but highly variable estimate (Zitzmann et al., 2021).

Starting from the baseline BSEM model with a diagonal residual covariance matrix (θ), with residual correlations fixed to zero, we added tiny, small-variance priors to the residual correlations so that fixed-to-zero constraints could be treated as near-zero estimates (Asparouhov et al., 2015; Schaap et al., 2022). Small-variance priors for correlated residuals were derived using the inverse Wishart prior, θ ~ IW(Dd, d), starting from the BSEM model without misspecification. As d increases, the prior variances for residual correlations shrink toward zero, approximating the constrained ML ESEM model and driving the posterior predictive p-value (PPp) toward 0, which is analogous to a significant chi-square. We then relaxed the fixed-to-zero constraints via these priors until PPp slightly exceeded 0.05, thereby addressing minor misspecifications and allowing more salient sources of misfit to emerge (Asparouhov et al., 2015).

Models were compared using the deviance information criterion (DIC), PPp, prior-posterior predictive p-value (PPPp), comparative fit index (CFI), Tucker–Lewis index (TLI), and RMSEA. PPPp evaluates whether small-variance informative priors, N(0, 0.01), are overly restrictive. If PPPp rejected minor loadings, more lenient priors, N(0, 0.02), were considered (Asparouhov & Muthén, 2017). We interpreted PPp values above 0.05, with CFI and TLI values ≥ 0.95 and RMSEA values ≤ 0.05, as indicating a good fit.

Following the When-to-Worry-and-How-to-Avoid-the-Misuse-of-Bayesian-Statistics (WAMBS) checklist (Depaoli & Schoot, 2017) for Mplus, we conducted sensitivity analyses of the bifactor model by varying the prior variances for factor loadings, cross-loadings, and correlated residuals. We evaluated the posterior estimates using changes in the DIC, PPp, PPPp, CFI, TLI, and RMSEA. Meaningful differences were defined as ∆CFI and ∆TLI ≥ 0.01, ∆RMSEA ≥ 0.015, and ∆DIC > 3 (Cain & Zhang, 2019). DIC is suitable for comparing BSEM models because it does not penalise parameters near zero (Asparouhov et al., 2015).

We computed the absolute relative percentage bias, ARPB = (θ₂ − θ₁)/θ₁, where θ₁ is the baseline estimate, and θ₂ is the alternative estimate, for primary loadings (λ) and posterior standard deviations (σ), analogous to frequentist standard errors. Estimates were considered biased when ARPB exceeded 10% to 15% (Dueber, 2017; B. Muthén et al., 1987), although caution is required for very small parameters, such as minor cross-loadings or small σ values, as these inflate ARPB values. We computed bifactor strength indices, including ωS, ωHS, FD, ECV, ECVss, PUC, ARPB, VAR, VAR_ECV, and SS_λ to evaluate the BSEM bifactor model.

3.6.6. Model Comparability Indicators

The researchers relied on auxiliary diagnostic indices and factor loading pattern analysis to assess the conceptual replication of the ML ESEM and BSEM measurement models across samples. In addition, we used Tucker’s congruence coefficient (TCC) to evaluate the comparability of the factor structure and conceptual replication. Factors were considered congruent when TCC ≥ 0.95 and structures comparable when TCC was 0.85–0.94 (Lorenzo-Seva & Berge, 2006). We applied these lenient cut-offs to compare ML SEM and BSEM parameter estimates, as BSEM’s informative priors are likely to lead to divergence, complicating item-level comparisons. However, TCCs are influenced by the number of items in the factor, and the cut-offs are arbitrary; therefore, they should be interpreted with caution.

4. Results

The SEM results are presented by study sample, with analyses performed for each. First, the potential circularity bias effects in Sample 2 are assessed.

4.1. Potential Circularity Bias Effects for Sample 2

The correlations relevant to circularity bias are reported and discussed in more detail in Supplementary Materials Table S3. Overall, the inclusion/exclusion decisions made during pruning of the initial 194 items based on the pilot sample were only weakly associated with within-ECC communalities (r = 0.21). In addition, item communalities showed negligible associations with the descriptive statistics used in the pruning process (i.e., item means, skewness, and kurtosis; r = −0.13 to 0.22), with similarly minimal associations after the item set was reduced to 103 items (r = −0.15 to 0.21). Taken together, these results suggest that item screening was primarily content-driven and that any circularity bias introduced by relying on descriptive statistics and communalities was likely minor in the Bayesian SEM.

4.2. ML SEM Analysis for Testing the Hypothesis on Sample 1

Descriptive statistics showed a mean item score of 4.16 (range, 3.60–4.47), and a mean standard deviation of 0.50 (range, 0.14–1.50). The mean item skewness was −0.93 (range, −0.38 to −1.30), and the mean kurtosis was 0.98 (range, −0.82 to 2.31). Ninety random missing data points, comprising less than 1.5% of the sample, were identified. The results for the factor models examined are presented in

Table 2. Model fit indices for the tested SEM maximum likelihood models.

Model	Chi2	D.F.	p-Value	AIC	BIC	RMSEA	SRMR	CFI	TLI
Sample 1:
4-factor CFA	5949.53	1478	0.00	131,415.06	132,315.33	0.05 [0.05–0.05]	0.05	0.87	0.86
4-factor CFA R	5178.46	1475	0.00	130,267.87	131,183.66	0.04 [0.04–0.05]	0.05	0.89	0.88
4-factor ESEM R	4179.29	1319	0.00	129,028.24	130,751.17	0.04 [0.04–0.04]	0.02	0.91	0.90
Bifactor CFA R	454.92	1425	0.00	129,310.17	130,484.65	0.04 [0.04–0.04]	0.04	0.91	0.90
Bifactor ESEM R	3847.37	1267	0.00	128,333.45	130,325.42	0.04 [0.04–0.04]	0.03	0.92	0.91
1-factor	9915.52	1481	0.00	137,396.35	137,737.91	0.07 [0.07–0.07]	0.06	0.75	0.74

CFA, confirmatory factor analysis; D.F., degrees of freedom; CFI, comparative fit index; TLI, Tucker–Lewis index; RMSEA, root mean square error of approximation; SRMR, standardised root mean square residual; BIC, Bayesian information criterion; AIC, Akaike information criterion; ^R, three correlated residuals free; ESEM, exploratory structural equation model; [ ] CI, 90% confidence interval. Bold font = selected models.

. The ECCI items are listed in Supplementary Materials Table S2.

Table 3. Bifactor loading summary and auxiliary indices.

	Sample 1						Sample 2
		Bifactor ESEM						Bifactor BSEM
Loadings λ:	1-Fact	Gf	F1	F2	F3	F4	1-Fact	Gf	F1	F2	F3	F4
Primary λ:
Mean	0.65	0.63	0.23	0.48	0.58	0.30	0.62	0.56	0.31	0.57	0.59	0.33
Maximum	0.77	0.76	0.39	0.65	0.66	0.47	0.77	0.75	0.48	0.69	0.66	0.53
Minimum	0.47	0.48	−0.05	0.18	0.42	0.17	0.35	0.31	0.02	0.34	0.34	0.13
Cross λ:
Mean			0.00	0.00	0.00	0.00			0.02	0.00	0.00	0.02
Maximum			−0.14	0.15	0.16	0.14			0.21	0.16	0.16	0.14
Minimum			−0.13	−0.11	−0.10	−0.15			−0.06	−0.13	−0.13	−0.09
Indices:
ARPB	0.05	-	-	-	-	-	0.13	-	-	-	-	-
PUC	-	0.70	-	-	-	-	-	0.70	-	-	-	-
FD	0.97	0.97	0.78	0.91	0.89	0.81	0.98	0.96	0.85	0.93	0.90	0.83
TCC	-	-	-	-	-	-	1.00	0.99	0.95	0.99	1.0	0.98
ωS	0.94	0.98	0.98	0.94	0.88	0.96	0.96	0.98	0.94	0.95	0.89	0.95
ECVss	-	0.75	0.15 +	0.40 +	0.56 +	0.18 +	-	0.65	0.28 +	0.51 +	0.58 +	0.24 +
ωH/ωHS	-	0.92	0.11 +	0.35 +	0.49 +	0.17 +	-	0.87	0.24 +	0.47 +	0.51 +	0.22 +
VARECV	-	-	1.16	1.42	1.66	1.19	-	-	1.26	1.61	1.71	1.23
SSλ	-	-	1.56	2.31	1.69	1.83	-	-	2.61	3.03	1.80	2.34

Fact = one-factor CFA model; Gf = entrepreneurial competency general factor; F1 = entrepreneurial career mindset; F2 = entrepreneurial career innovativeness; F3 = entrepreneurial career motivation; F4 = entrepreneurial career implementation; Cross = cross-loadings. ECVss for the proportion of common variance explained by items of the specific factor; ω = coefficient omega; ωH/ωHS = coefficient omega hierarchical; FD = factor determinacy; ARPB = absolute mean relative % parameter bias; ⁺ = VAR ≥ 1.1; VAR_ECV = value-added ratio for ECV; SS_λ = sum of squared item loadings.

summarises the structures of the one-factor CFA model and the bifactor ESEM model, along with the bifactor strength indices for Sample 1. Appendix B presents the factor structure and all factor loadings for the 4-factor ESEM, 1-factor CFA and the bifactor ESEM for Sample 1. The detailed 4-factor ESEM’s factor structure is available in File S2, and the 1-factor and bifactor models are available in File S3 of the Supplementary Materials. Influential outliers were found to have a negligible impact on the model’s fit statistics and parameter estimates of the selected bifactor ESEM model and were retained.

4.3. The 4-Factor CFA Model

Similar to Nel and Botha (2025), we tested a four-factor CFA model with cross-loadings fixed to zero and a four-factor ESEM model with cross-loadings freely estimated. Item C6 was excluded, as Nel and Botha (2025) reported a low loading (0.33) on F2. The initial CFA showed a marginal fit (RMSEA = 0.05, SRMR = 0.05, CFI = 0.87, TLI = 0.86) (Table 2). Three large, statistically significant residual correlations were identified (Figure 3), consistent with the method effects from overlapping wording. The largest effects were between R8 (“I manage my difficult feelings”) and R11 (“I control my negative emotions”), EPC = 0.24, MI = 207.87, AC9 (“I start immediately with a task”) and AC12 (“I actively start with a task”), EPC = 0.34, MI = 313.32, and OR6 (“I identify opportunities through changes in the environment”) and OR7 (“I identify opportunities related to changes in the environment”), EPC = 0.12, MI = 139.31. As Ferrando et al. (2022) noted, misspecified correlated residuals can bias loadings and may be freed when identified and theoretically justified. However, this should be done sparingly. Freeing these residuals improved the fit (ΔRMSEA = 0.01, ΔCFI = 0.02, ΔTLI = 0.02), yet the model remained marginal (RMSEA = 0.05, CFI = 0.89, TLI = 0.88). Therefore, we estimated a four-factor ESEM using targeted rotation and geomin oblique rotation.

The 4-factor ESEM model, with three correlated residuals, demonstrated an acceptable fit (RMSEA = 0.04, CFI = 0.91, TLI = 0.90), and the loadings were similar across the rotation methods. We retained a more parsimonious target rotation model as the final solution. Most loadings met the criterion (|λ| > 0.40), and omega coefficients (0.88–0.98) indicated high reliability. The model showed strong primary loadings and minimal cross-loadings across the factors (Table 3 and Appendix B). Primary loadings (λ) ranged from 0.35 to 0.95, with mean loadings of 0.58 for F1 (entrepreneurial career mindset), 0.72 for F2 (entrepreneurial career innovativeness), 0.73 for F3 (entrepreneurial career motivation), and 0.65 for F4 (entrepreneurial career implementation). Cross-loadings (λ) were small (−0.27 to 0.29), with three F1 cross-loadings exceeding 0.22 and others between −0.12 and 0.22, supporting an interpretable structure. Latent factor correlations were substantial (r = 0.41–0.78), indicating shared variance and supporting the bifactor analysis (Rodriguez et al., 2016a).

4.4. Bifactor ESEM Model Analysis

The bifactor CFA model with three correlated residuals provided an acceptable fit (Table 2). The bifactor ESEM model with target rotation fit better (∆CFI and ∆TLI > 0.01, ∆RMSEA = 0.01) and was retained (RMSEA = 0.04, CFI = 0.92, TLI = 0.91). It showed a strong general factor (ω = 0.98, PUC = 0.70, ECV = 0.75) with moderate-to-high loadings (M_λ = 0.63, range 0.47–0.77), supporting essential unidimensionality (Reise et al., 2013) (Table 3). Despite poor fit for the one-factor CFA (CFI = 0.75, TLI = 0.74), the ARPB was 0.05, suggesting minimal score bias. Specific factors were evaluated using λ loadings and bifactor indices (Table 3), applying Dueber and Toland (2023)’s criteria (SS_λ ≥ 1.0, VAR ≥ 1.10) and treating loadings < 0.20 as non-substantive. All specific factors met these thresholds, indicating their distinctiveness from the general factor.

More specifically, F2 (entrepreneurial career innovativeness) and F3 (entrepreneurial career motivation) showed moderate to high mean loadings (M_λ = 0.48 and 0.58), high reliability (ωS = 0.94 and 0.88), adequate strength (SS_λ = 2.31 and 1.70), and substantial added value (VAR = 1.42 and 1.66). F1 (entrepreneurial career mindset) and F4 (entrepreneurial career implementation) had weaker mean loadings (M_λ = 0.23 and 0.30) with high reliability (ωS = 0.98 and 0.96), acceptable strength (SS_λ = 1.56 and 1.83), and meaningful added value (VAR = 1.16 and 1.19), respectively. 21% of items had specific-factor loadings below 0.20, comparable to the 25% benchmark from bifactor meta-analyses (Petras & Meiser, 2024). As shown in Appendix B, most were from F1 (nine items), including five resilience items (R6, R7, R8, R11, R13) and four items (A5, AC8, GM7, and OA9) from different dimensions. Low-loading items were observed in F2 (C7) and F4 (OR3 and OR6). Cross-loadings were minimal (−0.15 to 0.16), supporting a simple, clear structure. F2 and F3 yielded the highest VAR values, indicating contributions to factor uniqueness and the general factor. Items from F1 and F4 contributed to factor uniqueness but loaded more strongly on the general factor than on the specific factors. Low specific-factor loadings (λ < 0.20) often coincided with high general-factor loadings (λ > 0.70), supporting the dominance of the general factor (e.g., R6).

4.5. Bayesian Bifactor Analysis for Testing the Hypothesis on Sample 2

The mean item score was 4.20 (range 3.75–4.59), with a mean standard deviation of 0.45 (range 0.10–1.11), mean skewness of −0.92 (range −0.56 to −1.40), and mean kurtosis of 0.80 (range −0.46 to 3.55), indicating a slight departure from normality. Missing data were minimal (<1%; 19 points).

Model convergence was confirmed for the models assessed (Figure 2F–H,

Table 4. Model fit indices for the tested Bayesian bifactor models.

			Lower	Upper
Model	d	#	0.025	0.975	DIC	PPPp	PPp	RMSEA	CFI	TLI
			PP Limit	PP Limit
Sample 2:
N0.5,0.20 N0,0.01			920.29	1183.08	35,439.13	1.00	0.000	0.057 [0.056–0.058]	0.889	0.869
N0.5,0.15 N0,0.01			919.78	1182.31	35,438.72	1.00	0.000	0.057 [0.056–0.058]	0.889	0.869
N0.5,0.05 N0,0.01			921.34	1183.58	35,436.42	0.95	0.000	0.057 [0.056–0.058]	0.889	0.869
N0.5,0.1 N0,0.005			933.65	1195.92	35,430.07	1.00	0.000	0.057 [0.056–0.058]	0.888	0.869
N0.5,0.1 N0,0.01			919.10	1181.18	35,437.39	1.00	0.000	0.057 [0.056–0.058]	0.889	0.869
d285 N0.5,0.1 N0,0.01	285	1929	−55.44	254.97	34,920.34	1.00	0.112	0.030 [0.024–0.036]	0.979	0.963
d300 N0.5,0.1 N0,0.01	300	1929	−45.66	267.28	34,920.25	1.00	0.086	0.031 [0.025–0.036]	0.978	0.962
d315 N0.5,0.1 N0,0.01	315	1929	−34.42	284.78	34,923.91	1.00	0.060	0.032 [0.026–0.037]	0.977	0.960
d330 N0.5,0.1 N0,0.01	330	1929	−20.63	259.85	34,925.06	1.00	0.042	0.032 [0.027–0.037]	0.976	0.958
1-factor d315 N0.5,0.10	315	1708	60.56	378.55	35,008.04	1.00	0.003	0.037 [0.032–0.041]	0.968	0.945

d = degrees of freedom; # = number of free parameters; PPp = posterior predictive p-value; DIC = deviance information criterion; PPPp = prior posterior predictive p-value; [ ] = 95% credibility interval; N = normal prior with specified mean and variance; d = degrees of freedom for inverse-Wishart priors. Bold font = selected models.

), with PSR values < 1.05 and well-mixed trace plots (see Figure 4 and Figure 5 for examples). The results for the factor models examined, including models used in the sensitivity tests, are presented in Table 4. Table 3 summarises the structures of the one-factor BSEM model and the bifactor BSEM model, along with the bifactor strength indices for Sample 2. Appendix B presents the factor structures and all factor loadings for the one-factor BSEM and the bifactor BSEM for Sample 2. The detailed factor structures for the one-factor and bifactor models are available in File S4 of the Supplementary Materials. Influential outliers were found to have a negligible impact on the model’s fit statistics and parameter estimates of the selected bifactor ESEM model and were retained.

4.6. Bayesian Bifactor (BSEM) with Primary Factors and Cross-Loadings

The priors for the BSEM model were informed by the bifactor ESEM results for Sample 1 (Figure 2, Model F). Table 4 summarises the baseline specification, with slightly informative priors for primary factor loadings N(0.50, 0.10) and small-variance informative priors for cross-loadings N(0, 0.01), denoted as N^0.5,0.1N^0,0.01. The baseline model showed poor to marginal fit (PPp = 0.00, RMSEA = 0.06, CFI = 0.89, TLI = 0.87), below the acceptable threshold, although PPPp = 1 supported the informative cross-loading prior.

This model served as the baseline for sensitivity analysis. Converged sensitivity models, including N^0.5,0.20 N^0,0.01, N^0.5,0.15 N^0,0.01, N^0.5,0.05 N^0,0.01 and N^0.5,0.1 N^0,0.01, corresponding to M_λ = 0.50 and 95% CI of ±0.88, ±0.76 and ±0.44, respectively, for primary loadings and M_λ = 0 and 95% CI of ±0.20 for cross-loadings (see Table 4 and

Table 5. Prior impact on primary and cross-factor loadings and standard deviations.

Base-Line Priors		N0.5,0.1 N0,0.01		N0.5,0.1 N0,0.01		N0.5,0.10 N0,0.01
Sensitivity Priors		N0.5,0.1 N0,0.005		N0.5,0.05 N0,0.01		N0.5,0.20 N0,0.01
Factors		ARPB		ARPB		ARPB
		% λ	% σ	% λ	% σ	% λ	% σ
Gf	M	1.6	3.5	3.6	0.2	2.9	1.4
	Max	4.9	14.7	6.6	1.0	5.9	3.7
F1	M	4.0 (34.1)	2.0 (11.6)	10.0	1.0	5.3	3.6
	Max	10.7 (200.0)	3.3 (18.8)	30.4	2.1	9.3	8.2
F2	M	1.3 (31.7)	5.7 (13.7)	0.7	0.2	1.2	0.6
	Max	4.2(400)	7.7 (18.0)	1.8	2.6	4.0	2.6
F3	M	1.9 (27.0)	4.1 (13.3)	1.2	1.0	0.1	1.0
	Max	4.3 (114)	6.6 (25.9)	6.6	2.5	4.2	2.4
F4	M	4.5 (160.0)	3.3 (13.5)	8.4	4.7	5.8	3.7
	Max	14.3 (4900)	9.2 (18.5)	18.0	11.1	12.5	8.9
Mean	M	2.5 (58.8)	3.4 (13.0)	5.4	3.4	3.3	2.0

ARPB = absolute relative % bias; λ = factor loading; σ = factor loading standard deviation; M = average ARPB over all parameters estimated; Max = maximum ARPB over all parameters estimated; ( ) = factor cross-loadings; ARPB ≤ 10% = minimal bias.

) These are briefly discussed in the following section (Supplementary Materials Text S3 provides a detailed discussion). Additional boundary checks using N^0.5,0.25 N^0,0.01, weakly informative priors with mean 0 (i.e., N^0,0.25 N^0,0.01 and N^0,0.25 N^0,0.0), and the non-informative N(0, 10¹⁰), did not converge (Depaoli & Schoot, 2017; Holtmann et al., 2016), suggesting excessive model complexity and priors that were too weak for the small sample size.

4.7. Sensitivity Analysis Findings for Primary Factors and Cross-Loadings

Overall, among the converged BSEM bifactor models, results remained highly stable across plausible item-level primary-loading and cross-loading priors, with negligible model-level bias (ΔCFI and ΔTLI < 0.01; ΔRMSEA < 0.015). Accordingly, the baseline priors N(0.50, 0.10) for primary loadings and N(0, 0.01) for cross-loadings were supported. Exceptions occurred under overly restrictive priors: tightening cross-loadings to N(0, 0.005) resulted in a meaningful decrease in DIC (−7.33) and substantial prior-induced bias in cross-loadings (mean ARPB for λ ≈ 160% and σ ≈ 4900%), indicating an excessive prior influence (Table 5). Similarly, the most restrictive primary-loading prior, N(0.50, 0.05), yielded >10% item-level bias for six items on F1–F4 (11–30%), whereas the broader N(0.50, 0.20) prior produced only one >10% instance (PS6) with low absolute loadings. The results from N(0.5, 0.15) are omitted from Table 5 owing to redundancy, as all average ARPB values for λ and σ were low at 2.2% and 1.1%, respectively.

Overall, the selected baseline priors for loadings and cross-loadings were supported by sensitivity analyses and prior literature (Liang & Cao, 2023; Smid et al., 2020).

4.8. Bifactor BSEM with Correlated Residual Priors

To evaluate the bifactor model in Figure 2G, we specified baseline priors N(0.50, 0.10) for primary loadings and N(0, 0.01) for cross-loadings and applied small-variance priors to correlated residuals (d = 315), depicted as d³¹⁵ N^0.5,0.1 N^0,0.01 in Table 4. Such priors accommodate minor misspecifications while highlighting substantive residual misspecifications (Asparouhov et al., 2015). Using an inverse Wishart prior, θ ~ IW(Dd,d), we restricted the prior variance (d = 285, 300, 315, 330) until the posterior predictive p-value (PPp) fell below 0.05, approximating a significant chi-square value in the ML ESEM. We selected d = 315 because it yielded a near-threshold, non-significant PPp = 0.06, consistent with an ML ESEM solution in which minor residual misspecifications were resolved. The implied prior variances ranged from 0.0002 (95% CI ± 0.03) to 0.0034 (95% CI ± 0.11) (Figure 6), with a prior mean of 0. Doubling iterations (40,000 to 80,000) did not affect the convergence (PSR < 1.05) or estimates.

The chosen model (d³¹⁵ N^0.5,0.1 N^0,0.01) demonstrated an excellent fit (PPp = 0.06, RMSEA = 0.03, CFI = 0.98, TLI = 0.96) (Table 4). Notable correlated residuals were replicated in the ML ESEM model, including r = 0.25 between R8 and R11, r = 0.23 between AC9 and AC12, and r = 0.20 between OR6 and OR7. These residuals reflect substantive, generalisable method effects rather than spurious findings (Asparouhov et al., 2015) (Figure 7). In addition, redundancies (r = 0.19) between R6 (I can adapt to change) and R13 (I am open to change) can be eliminated in future research. Incidentally, the latter two items showed near-zero loadings for Factor 1 (see Appendix B).

The results of the sequence of the models used in the sensitivity analysis are presented in Table 4 under the headings d²⁸⁵ N^0.5,0.10N^0,0.01, d³¹⁵ N^0.5,0.10N^0,0.01, and d³³⁰ N^0.5,0.10N^0,0.01.

4.9. Sensitivity Analysis Findings for the Model with Correlated Residuals

For correlated-residual priors, varying the IW restriction around d = 315 (e.g., d = 285 vs. d = 330) produced minimal bias, with ARPB < 6% for factor loadings and standard deviations (

Table 6. Prior impact on primary loadings and standard deviations with tightly constrained priors for correlated residuals.

Priors Compared		d315 N0.5,0.10N0,0.01		d315 N0.5,0.10N0,0.01		d315 N0.5,0.10N0,0.01
		d285 N0.5,0.10N0,0.01		d330 N0.5,0.10N0,0.01		N0.5,0.10N0,0.01
Factors		ARPB		ARPB		ARPB
		% λ	% σ	% λ	% σ	% λ	% σ
Gf	M	0.2	1.0	0.2	0.1	1.8	4.5
	Max	0.6	3.3	0.57	1.9	4.4	12.5
F1	M	0.9	0.3	0.7	0.1	4.2	7.9
	Max	3.5	1.2	5.9	0.7	11.0	16.1
F2	M	0.3	0.0	0.1	0.0	1.4	3.1
	Max	1.1	0.2	0.5	0.1	2.4	5.1
F3	M	0.8	0.3	0.3	0.0	1.9	2.1
	Max	1.9	0.9	0.8	0.6	2.8	3.2
F4	M	0.6	0.4	5.1	0.5	5.5	9.7
	Max	1.5	0.7	0.2	0.1	31.5	20.9
Mean	M	0.5	0.8	0.3	0.0	2.9	5.8

ARPB = absolute relative % bias; λ = factor loading; σ = factor loading standard deviation; M = average ARPB over all parameters estimated; Max = maximum ARPB over all parameters estimated; ARPB ≤ 10% = minimal bias.

). However, relative to the fully constrained model, fit indices differed markedly (ΔCFI/ΔTLI = 0.09; ΔDIC = 513) and showed isolated item-level bias outliers (i.e., λ = 31.5%; σ = 20.9%).

These results indicate that applying tight constraints on all correlated residuals in a complex model yields only a minor decrease in parameter estimation accuracy relative to the fully constrained model; however, this trade-off substantially improves overall model fit. The factor loadings were essentially the same across the models, suggesting that the fit differences reflect accumulated minor misspecifications or white noise. This confirms that conventional fit indices may be less informative for complex models and small samples and that flexible Bayesian specifications may be required to capture substantive theory (Asparouhov et al., 2015; B. Muthén & Asparouhov, 2012).

4.10. Bayesian Bifactor Model Analysis

Table 3 and Table 4 report the bifactor BSEM model aligned with the bifactor ESEM structure, showing a clear, simple structure with minor cross-loadings. The model fit was strong (PPp = 0.06, RMSEA = 0.03, CFI = 0.98, TLI = 0.96) after accounting for minor misspecification in the correlated residuals. The model showed a strong general factor (Gf; ω = 0.98, PUC = 0.70, ECV = 0.65, ωH = 0.87) and moderate-to-high loadings (M_λ = 0.56), supporting essential unidimensionality (Reise et al., 2013). An ARPB of 0.13 suggested marginal factor-score bias, consistent with a good fit in the 1-factor BSEM model (PPp = 0.23, RMSEA = 0.03, CFI = 0.98, TLI = 0.97). Relative to Sample 1, Gf’s ECV was lower (ΔECVss = −0.10), indicating a less defined factor.

Specific factors were evaluated using item loadings and bifactor strength indices (Table 3), applying Dueber and Toland (2023) criteria (SS_λ ≥ 1.0; VAR ≥ 1.10) and treating loadings λ < 0.20 as non-substantive. All factors met these thresholds, indicating sufficient strength beyond Gf.

More specifically, F2 (entrepreneurial career innovativeness) and F3 (entrepreneurial career motivation) showed moderate-to-high loadings (M_λ = 0.57 and 0.59), high reliability (ωS = 0.95 and 0.89), sufficient strength (SS_λ = 3.03 and 1.80), and added value (VAR = 1.61 and 1.71). In contrast, F1 (entrepreneurial career mindset) and F4 (entrepreneurial career implementation) had weaker average loadings (M_λ = 0.31 and 0.33) but retained high reliability (ωS = 0.94 and 0.95), sufficient strength (=2.61 and 2.34), and added value (VAR = 1.26 and 1.23), respectively.

Overall, 10% of items had loadings below 0.20, below the 25% benchmark from bifactor meta-analyses (Petras & Meiser, 2024). Most were from F1 (R13, OA9, and OR5) and F4 (OR6, PS5, PS6, and VDA9) (see Appendix B). Notably, R13, OR6, PS5, and PS6 also ranked among the top six correlated residuals (Figure 7), suggesting item redundancy. Only items R13, OA9, and OR6 replicated items with low loadings (λ < 0.20) in the bifactor ESEM model and could be considered for review. Cross-loadings were minimal (−0.13 to 0.22), supporting a simple structure.

Strength indices were higher than those in Sample 1 for F1 and F2 (ΔSS_λ = +1.05 and +0.72), with smaller differences for F3 and F4 (ΔSS_λ = +0.11 and +0.51). Items with low specific factor loadings (λ < 0.20) typically had high Gf loadings (λ > 0.60), reinforcing the general factor. F1 and F4 contributed more to Gf, whereas F2 and F3 retained greater specific factor distinctiveness

We conclude that the decrease in Gf loadings and the increase in F1 and F2 loadings may reflect a minor bias from using slightly informative priors for primary item loadings across general and specific factors. Despite the differences introduced by the modelling paradigms, the factor structure remained largely consistent with that of Sample 1. Notably, F1 showed stronger loadings on the resilience items (R7, R10, and R14), thereby enhancing construct validity (see Appendix B for the complete factor structure and the File S4 for detailed BSEM structures).

4.11. Observations Summary for the Two Samples

The TCC values in Table 3 show congruent structures for the general factor (0.99) and sub-factors F1 (0.95), F2 (0.99), F3 (1.00), and F4 (0.98) (TCC ≥ 0.95). F1’s lower congruence likely reflects resilience being less represented in Sample 1 and may relate to differences in correlated-residual restrictions in ML ESEM versus BSEM. Applying the same primary loading prior to Gf and specific factors may have introduced bias into F1, contributing to minor incongruence. The 1-factor model showed low bias for weighted scores in Sample 1 (ARPB = 0.05) and marginal bias in Sample 2 (ARPB = 0.13). The ML ESEM and BSEM bifactor models converged on similar conclusions, supporting the bifactor structure across samples and indicating essential unidimensionality, with specific factors adding value beyond the general factor.

5. Discussion

To reduce ambivalence in the EC framework debate, we proposed a theoretically grounded hierarchical EC framework within the ECCI and a methodological basis for refining, testing and applying attribute-based EC measures across diverse contexts. The methodological-substantive synergistic approach used in this study yielded meaningful results. The findings support our hypothesis and suggest that the ECCI is structured hierarchically, consisting of an essential unidimensional (broad) factor and four distinct (narrow) group factors. This complex structure was conceptually replicated across the two study samples with imprecise item responses using different statistical paradigms. Moreover, the model’s stability under varying Bayesian prior assumptions supports refined prior settings for future studies, especially in small-sample contexts (Smid et al., 2020). A more detailed discussion of the substantive and methodological insights is provided below.

5.1. Substantive Insights and Contributions

It is almost universally acknowledged that measures of human traits such as intelligence, competencies, personality, interests, and values are commonly conceptualised in a hierarchical structure consisting of general (broad) and specific (narrow) components (Rodriguez et al., 2016a; Swami et al., 2023). More specifically, empirical support for EC measurement models of general and specific dimensions is needed to inform educational interventions (AERA et al., 2014). Our findings build on the contemporary literature that supports the EC’s hierarchical model (Cárdenas-Gutiérrez et al., 2021; Wirda et al., 2023; Zhensheng & Liu, 2019). Specifically, we propose ECs as an essentially unidimensional construct alongside distinct, specific multidimensional ones (Rodriguez et al., 2016a). We provided new insights, supported by statistical evidence, into the relationship between specific and general factors within a hierarchical bifactor structure, thereby enhancing measurement interpretation. In addition, we responded to calls to develop and validate entrepreneurial competency frameworks within specific regional and contextual settings (Tehseen et al., 2020) by investigating an English version of the hierarchical ECCI measurement model using a heterogeneous English-literate South African sample, in which specific factors captured the distinctiveness of the four ECCs. Our study shows that specific and narrow constructs add statistically significant value beyond the broad, general ECCI construct. Although latent-variable models of the ECCI are useful for research purposes, valid manifest scores are essential for educational intervention and personal development. The bifactor model used in this study facilitated a more refined interpretation and a more effective application of factor scores.

The factor-scoring approach used for the bifactor ECCI model can yield different insights and should be selected based on the specific goals of the assessment or research (DeMars, 2013). Specific factor scores represent the residual variance beyond the general factor and reflect the unique items that define the factor. This approach offers a more detailed profile of respondents’ strengths and weaknesses. For example, a profile with a high score on the general factor of the ECCI and a high score on entrepreneurial career innovativeness may be essential for business start-ups. Alternatively, a profile with a moderate score on the general factor but a high score on entrepreneurial career motivation may indicate a fundamental value (i.e., social responsibility) that inspires action through the development of general EC and additional specific ECs.

However, summing the item variances shared between the specific and general factors for each factor in the bifactor model yields a score similar to that of the correlated four-factor model (DeMars, 2013). These weighted sum scores often align better with users’ intuitive understanding of a factor score, as they provide a holistic perspective. However, users must consider the underlying variance of general factors to avoid misinterpreting specific factors as distinct constructs when using weighted-sum scores (Rodriguez et al., 2016a). For instance, a profile with a high score for an entrepreneurial career mindset is likely to be predominantly influenced by shared variance with the overall factor. In this case, only a small portion of the variance (ECVss = 15%) could be attributed to the specific items related to the entrepreneurial career mindset factor. It is important to consider these proportions when interpreting scores. In addition, this study supports the use of a single ECCI score from either the general factor of the bifactor model or the unidimensional one-factor model, with minor to marginal bias (Rodriguez et al., 2016a). Users seeking an easily calculable single ECCI score can utilise the unidimensional factor model even if multidimensionality exists (Rodriguez et al., 2016a).

Moreover, evidence of the incremental value of the specific factors of the ECCI relative to the general factor is necessary to anticipate incremental validity with external variables. The bifactor ECCI model allows a secondary analysis of how general and specific factors relate to relevant external variables while simultaneously controlling for multicollinearity issues (Brunner et al., 2012; Sánchez-Oliva et al., 2017).

This study holds significant practical value, as the development of the ECCI self-report tool enables existing or potential entrepreneurs to identify areas for improvement and training opportunities. The ECCI hierarchical measurement model is valuable for entrepreneurship education specialists and academics because it supports curricula that target both general and specific entrepreneurial competencies (ECs) (Ferreras-Garcia et al., 2021; Menke, 2018; Zhu et al., 2022). It emphasises the development of observable skills and behaviours that both stem from and influence deeper personal drivers, such as traits, motives, and values, thereby promoting sustainable entrepreneurial success (Boyatzis, 2006; Boyatzis et al., 2017). Employers can use the ECCI to assess employee profiles and identify ECs for development, enabling curricula tailored to both generic and specific competencies. For instance, deeply rooted generic competencies, such as an entrepreneurial career mindset, may benefit from mentoring, while specific competencies, such as entrepreneurial career motivation (i.e., social responsibility), may require structured workshops. In addition, policymakers could employ the ECCI to evaluate current entrepreneurship education policies and provide clear guidance on which ECs should be prioritised.

5.2. Practical Insights and Contributions

We illustrate how business consultants may use the four-factor scoring model (DeMars, 2013) together with bifactor scores to refine score interpretation and support the development of clients’ entrepreneurial competencies. The four-factor model captures general and unique variance presented in the bifactor model, and developmental interventions should therefore address both sources of variance. The general factor reflects overall entrepreneurial career competency, whereas the unique component identifies more specific developmental priorities and informs targeted intervention strategies. A post-intervention ECCI profile can serve as a tool to monitor progress. Nel and Botha (2025) classify entrepreneurial career competence raw scores as high (≥70%), moderate (40–69%), and low (≤39%). The development strategy adopts a holistic approach, emphasising leveraging strengths through less-structured, more challenging autonomous learning opportunities, while simultaneously addressing weaknesses through structured programmes with increased oversight.

A high entrepreneurial career motivation score (e.g., 75%) may indicate a distinct strength, particularly when supported by the client’s bifactor specific factor score (e.g, 90%) as the factor retains substantial unique variance (ECVss = 0.56). This score suggests a value–driven orientation towards social responsibility and societal value creation; this can be reinforced through experiential learning, such as participation in collaborative project work. Conversely, a high entrepreneurial career mindset score (e.g., 80%) should be interpreted cautiously, with careful reference to the client’s bifactor-specific factor score (e.g., 75%), because it reflects only limited unique variance (ECVss = 0.15) and largely represents the general factor. The entrepreneurial career mindset competency can be cultivated through on-the-job coaching, mentoring, and reflective feedback to enhance resilience, autonomy, action orientation, a growth mindset, and self-efficacy. A low entrepreneurial career innovativeness score (ECVss = 0.35) contains a significant unique component alongside the general element, which can be improved through structured innovation workshops, opportunity recognition exercises, and controlled, calculated risk-taking activities. A moderate entrepreneurial career implementation score (ECVss = 0.18) primarily reflects the general competency domain, with a minor element of uniqueness, and can be strengthened through structured management programmes that foster problem-solving and value creation via supervised project-based work assignments.

The prominent general factor component of entrepreneurial career mindset and implementation can be regarded as core entrepreneurial competencies, indicative of the client’s overall potential for success in business venturing. Entrepreneurial career motivation and innovativeness competencies possess more unique elements beyond the general competency factor; when developed, they are expected to contribute more distinctly to entrepreneurial success.

5.3. Methodological Insights and Contributions

The bifactor statistical model, strength indices, and the criteria of Dueber and Toland (2023) provide a clearer understanding of the relative contributions of each factor within the hierarchical framework of the ECCI, thereby enhancing its effective use across various contexts (Reise et al., 2013). Moreover, using ESEM combined with the bifactor model accounted for many minor inaccuracies typical of human subjective responses to the ECCI questionnaire items (Swami et al., 2023). The challenge of achieving model fit with the lengthy and complex ECCI was effectively addressed using ESEM, which produced unbiased and non-inflated estimates likely to replicate across different contexts (Hong et al., 2024).

BSEM analyses provided a solid foundation for overcoming the challenge of testing the lengthy ECCI bifactor measurement model on a small sample without compromising the parameter estimation accuracy or being plagued by model identification issues or non-permissible solutions (Zitzmann et al., 2021). With BSEM, the challenge of testing the complex ECCI model in the presence of many minor misspecifications (white noise) caused by imprecise human responses allows for the practical study of the signal (ECCI theoretical model) over noise (Asparouhov et al., 2015). More specifically, the data support the theoretical model after accounting for the systematic errors acknowledged in classical test theory. To enhance the model fit of the ECCI, it is advisable to freely estimate the three substantively correlated residuals associated with method effects, as they have been consistently replicated across the two samples. The use of thoughtfully derived, slightly informative, and small-variance priors, supported by an extensive sensitivity analysis, enhanced the credibility and generalisability of the ECCI model (Smid et al., 2020; van Erp et al., 2018; Zitzmann et al., 2021).

Our study demonstrated the value of drawing on large-sample empirical evidence, test theory, and expert judgement to construct appropriate priors for factor loadings, cross-loadings, and correlated residuals, which produced stable and reliable parameter estimates. While there was a possibility of minor bias in the item loadings of the Gf general factor and the specific factors in the BSEM model, it was mitigated by obtaining sufficient parameter accuracy for the small sample using slightly informative priors, something that would not have been possible using, for example, the ML SEM estimator (Zitzmann et al., 2021). Although the items in F1 and F4 had low to moderate factor loadings, their large number (23 and 19 items, respectively) contributed to a sufficient factor strength. In contrast, models with fewer items (e.g., 5 to 10) and comparable loadings would most likely fail to achieve an adequate level of strength (Petras & Meiser, 2024).

5.4. Study Limitations

The samples in both Studies 1 and 2 did not proportionally represent the regional population demographics, highlighting the need for further studies involving more diverse groups in the region.

Despite efforts to address potential inaccuracies in self-reported data, challenges such as acquiescence bias, social desirability bias, careless responses, and limited self-awareness among participants may have affected data accuracy and reliability. Researchers should interpret factor scores as broad indicators with a margin of error, rather than as exact scores.

We examined the incremental value of the group factor over the general factor for internal structure but did not consider external criterion variables in this study. Criterion validity of the measure for relevant external variables should be part of the appropriate interpretation of the factor scores within the hierarchical structure of the ECCI (Moore & Lahey, 2021).

Although the circular bias in using the pilot study group as the second sample for the conceptual replication of the bifactor model has been substantially mitigated, the authors acknowledge that minor bias may still exist.

5.5. Recommendations and Future Research Avenues

We recommend that future studies develop a shorter ECCI bifactor ESEM model for English-literate entrepreneurs using an independent sample to test measurement invariance across genders, races, languages, and ethnic groups, ensuring score comparability. Diverse groups from the informal sector may influence the measure’s factor structure if items are culturally loaded or English proficiency is low (De Kock & Foxcroft, 2023). A shorter, cross-validated version that takes less time to complete would attract more responses from a broader population. Recruitment could leverage community channels (e.g., local community centres, schools, networks and support programmes) with support from multilingual fieldworkers, using materials such as ads, invitations, and consent forms. The measure can be completed digitally on various devices, supervised by trained fieldworkers, or in paper form where needed. Stratified sampling should ensure representation of all English-proficient ethnic groups in South Africa, based on self-reported English proficiency and English language subject marks from school. (Harmse & Evans, 2021).

A shorter ECCI version for a broader audience can be created by reducing items based on statistical evidence and content-based judgement within Sample 1 using bifactor ESEM. The aim is to keep items with the highest content validity, uniqueness, clarity, and conciseness, while maintaining the measurement model’s factor breadth and psychometric integrity. Items with highly correlated residuals (r ≥ 0.20) and low factor loadings (λ < 0.20) should be removed. Items that exhibit significant loadings on both the general factor (λ ≥ 0.40) and the specific factor (λ ≥ 0.20) can be considered for retention after content evaluation. Examples of items that may be retained include autonomy item A7 “I can do anything I put my mind to” in Entrepreneurial Career Mindset; value creation item VC6 “I act to serve others” in Entrepreneurial Career Motivation; or problem-solving item PS14 “I find unique solutions to problems” in Entrepreneurial Career Implementation.

The impact of removed items can be assessed using bifactor auxiliary indices, MI and EPC indicators, and model fit. It is advised to keep five to seven items for each specific factor, provided the factor is robust (SS_λ ≥ 1) and distinct (VAR ≥ 1.1). Differential item functioning (DIF) across race and gender can be examined with MIMIC analyses, and problematic items can be excluded (Morin et al., 2016). The shortened measure can then be validated in Sample 2 using bifactor BSEM, followed by replication in a new, independent English-proficient but more diverse sample.

As this study was conducted in a South African context, replicating it in the broader African region, as well as in Global South and Global North contexts, is recommended to allow for a comparison of findings. In addition, future research could assess the additional value of specific factors in predicting criterion variables to enhance the understanding of factor score interpretation within the hierarchical framework of the ECCI (Moore & Lahey, 2021).

Based on the empirical findings of this study, we recommend using BSEM analysis in future studies and implementing more concise priors for factor loadings that allow testing the model on smaller samples. Researchers can use prior variances between 0.10 and 0.20 for main factor loadings; however, we recommend priors with a mean factor loading of 0.60 for Gf, F2, and F3, and 0.35 for F1 and F4, which should lead to more precise estimates.

6. Conclusions

The identification, development, and measurement of EC are crucial to advancing entrepreneurship education and fostering entrepreneurial intention, capacity, and business success. This study advances EC frameworks by employing contemporary statistical techniques that have been underutilised in EC measurement. These methodological developments yielded deeper insights into the ECCI measure and contributed to EC theory, thereby achieving substantive–methodological synergy. More specifically, this study confirmed the hierarchical structure of the ECCI in a bifactor model with a general EC factor and four distinct specific factors, particularly after accounting for human response noise using an ESEM and BSEM. The conceptual replication of the ECCI across the two study samples provides strong empirical support for the model, which is likely to generalise to other contexts in future research. Moreover, the model stability was supported by a sensitivity analysis conducted using Bayesian models. A valuable spin-off of using Bayesian models is that prior settings are refined, enabling future studies with smaller sample sizes. In practice, the bifactor model allows distinct scoring approaches for general and specific factors, providing a nuanced understanding of the EC construct and facilitating score interpretation. Overall, the ECCI bifactor measurement facilitates the development of general and specific competency profiles that can be enhanced and refined through training. Moreover, it helps design curricula that focus on general and specific EC competencies, which is valuable for entrepreneurship education specialists and academics.