According to Keyes (2002), hedonic well-being can be related to mental health. It includes components of subjective well-being and good functioning and depends on an individual’s perspective and appraisal of their livelihood and the quality of their existence (Keyes, 2002). Keyes (2002) continues by stating that emotional, social and psychological well-being are the three major components of subjective well-being. Emotional well-being is defined as the ability to develop pleasant emotions, moods, thoughts and sentiments and to adjust when faced with adversity and challenging conditions. Emotional well-being allows you to concentrate on the positive aspects of a situation while managing the unpleasant emotions and feelings that may arise (Keyes, 2002, 2014). Psychological well-being, on the other hand, refers to inter- and intrapersonal factors related to an individual’s functioning and evaluation (Keyes, 2014). Psychological well-being refers to how an individual relates to others and the self on an individual level and may include the following traits: self-acceptance, autonomy, personal development, healthy relationships, environmental mastery and a sense of purpose in life. Lastly, social well-being refers to social aspects such as consistency, upgrade, integration, acceptability and contribution (Keyes, 2002). Individuals with high levels of social well-being will embrace most aspects of society, regard themselves as contributing community members, and experience social well-being once they believe they are accepted by their environment (Keyes, 2002).

Factorial validity is defined as ‘the extent to which items are designed to measure a particular factor (i.e., latent construct) and actually do so’ (Byrne, 2010, pp. 97–98). Concerning factorial validity, studies in Argentina (Lupano Perugini et al., 2017), Canada (Lamborn et al., 2018), the Netherlands (Kennes et al., 2020), South Korea (Lim, 2014) and France (Karaś et al., 2014) have all found the MHC-SF to be a valid and reliable measure. The three-factor structure (emotional, social and psychological well-being) is supported by numerous research studies testing the factorial validity of the MHC-SF in the adult population (Karaś et al., 2014; Kennes et al., 2020; Luijten et al., 2019; Lupano Perugini et al., 2017). A study conducted by Keyes et al. (2008) in South Africa confirmed the three-factor structure of the MHC-SF among Setswana-speaking people in South Africa, demonstrating that the three-factor structure observed in United States (US) samples may be replicated in South Africa (Keyes et al., 2008).

This study will consider three types of invariance. Configural invariance refers to the degree to which the factor structure can be accurately replicated across groups (i.e., the factor structure fits the data to the same degree and has the same pattern across all sub-groups). Metric invariance indicates if each item contributes equally to the latent construct across different sub-groups (i.e., items have equal factor loadings across sub-groups). Scalar invariance requires the test scores to have the same meaning and interpretation across sub-groups (He & Van de Vijver, 2012; Van de Vijver & Tanzer, 2004).

Concerning the invariance of the MHC-SF, a study conducted in the United States and Iran demonstrated partial metric invariance between the two countries and full metric invariance between gender groups (Joshanloo, 2016). In a cross-cultural study, including 38 countries and 8066 university students, Żemojtel-Piotrowska et al. (2018) found that configural invariance could not be confirmed across cultural groups included in the study because of the model’s complexity. In a sample of 624 respondents from various South African organisations, Van Zyl and Olckers (2019) established good metric invariance across gender groups but could not establish invariance for age cohorts, language groups (Afrikaans, English and African groups) or marital status.

Item bias occurs when participants across different groups interpret an item differently based on item-level incongruities and not necessarily because of actual differences in the underlying construct. Item bias occurs because of several reasons, including the appropriateness of the item content based on group specifics, connotative meaning attached to the item, poor item translation, ambiguous items and different response styles (He & Van de Vijver, 2012; Van de Vijver & Tanzer, 2004). Concerning the item bias of the MHC-SF, there have been concerns with item content and wording in previous validation studies, particularly with the social subscale (Santini et al., 2020). Previous studies conducted among 38 countries, including South Africa, indicated that emotional content is less biased and more universal among cultures (Żemojtel-Piotrowska et al., 2018), while psychological and social items show more cultural variation.

The MHC-SF showed high internal consistency and discriminant validity in a sample of adolescents and adults from the United States, the Netherlands and South Africa (Keyes, 2009). In a sample of adult Setswana speakers, the following Cronbach’s alpha coefficients were reported: emotional well-being, α = 0.70; psychology well-being, α = 0.67; and social well-being, α = 0.59; however, the overall internal consistency was acceptable with α = 0.74 (Keyes et al., 2008).

Van Zyl and Olckers (2019) showed the scale has Cronbach’s alpha coefficients of 0.86 for emotional well-being, 0.88 for social well-being and 0.86 for psychological well-being. Among student samples, it was found that the internal consistency of the subscales was satisfactory, with Cronbach’s alpha coefficients ranging from 0.79 to 0.85 for emotional well-being, 0.63 to 0.80 for social well-being, and 0.81 to 0.86 for psychological well-being (Foster & Chow, 2019; Joshanloo et al., 2017; Lamers et al., 2011).

Although a range of psychometric properties could be considered when instruments are validated, this study focused on testing the factorial validity, structural invariance, metric invariance, scalar invariance, item bias and internal consistency of the MHC-SF.

The characteristics of the participants can be seen in Table 1.

The sample consisted of 1285 first-year university students studying at three different campuses at a South African university. In total, 672 (72.4%) were between the ages of 17 and 20 years, and 449 (35%) were between 21 and 22 years. Of these participants, 511 (39.8%) were Afrikaans, followed by 339 (26.4%) Setswana-speaking individuals, while 114 (8.9%) spoke Sesotho. Regarding gender, there were 410 (31.9%) male participants and 886 (67.4%) female participants. Most participants were black students (53.9%), followed by white students. The three campuses each has a unique and diverse culture. The first campus is considered peri-urban (i.e., an urban area adjacent to rural communities) and ideal for academic programmes focusing on rural development in indigenous knowledge. The second campus is the biggest and oldest of the three campuses and is situated in a town that is considered a suburban region. The third campus is the smallest and situated near a metropolitan city in an urban region. This campus hosts students from different cultures and language groups. Most of the sample was enrolled at campus 2 (55.5%), while campuses 1 and 3 make up for the other 45.5% of participants.

The MHC-SF comprises 14 items representing various aspects of well-being (Keyes, 2002). Each element represents a subjective sense of well-being rated according to the frequency over the last month on a Likert-type scale ranging from 1 (never) to 6 (every day). The instrument compromises three subscales: emotional well-being is measured by the first three items (e.g., ‘How frequently did you felt joyful’). Five items assess social well-being (i.e., ‘How frequently did you have a sense of belonging to a community?’). Six items measure psychological well-being (e.g., ‘How frequently did you feel at ease with the responsibilities of daily life?’).

A secure link was placed on the course module portals for courses first-year students from various disciplines across campuses were enrolled for. Throughout the study’s duration, students were encouraged to contribute voluntarily. Trained field workers presented brief awareness sessions in the corresponding classrooms. Pertinent information about the study’s goal and objectives was provided during these sessions. Completion took around 15 min – 20 min.

Both measurement invariance testing and Differential Item Functioning (DIF) analysis were implemented to ensure the scales were accurate and unbiased across different groups. Differential Item Functioning analysis enables specific items in scales to be identified that might be interpreted differently by different groups, measurement invariance testing ensured that the overall construct measured remained consistent across these groups. Together, these methods provided a comprehensive approach.

The statistical modelling program Mplus 8.6 (Muthén & Muthén, 2021) was used to examine the psychometric properties of the scale. Factorial validity was determined using confirmatory factor analysis (CFA) (Brown, 2015). Maximum likelihood estimation was used, with the covariance matrix as input (Muthén & Muthén, 2021). Based on the findings of previous validation studies reported in the literature, a three-dimensional structure was tested (emotional, social and psychological well-being), compared with an additional one-factor model. The following fit indices were used to evaluate the fit of the metric models: the χ² statistic, the comparative fit index (CFI), the Tucker-Lewis index (TLI), the root mean square error of approximation (RMSEA) and the standardised root mean square residual (SRMR).

A suitable fit is a CFI and TLI value of 0.90 or higher, a RMSEA and a SRMR value of less than 0.08 (Byrne, 2001; Hu & Bentler, 1999; Ed. Hoyle, 1995; Van De Schoot et al., 2012). The Akaike information criterion (AIC) and sample-adjusted Bayesian information criterion (BIC) were used to compare the fit of competing models – lower values indicate better fit. It should be noted that these cut-off points should only be regarded as guidelines, as there is little agreement on the values for good fit (Lance et al., 2016).

Measurement invariance was also investigated based on language, campus and gender groups. Multigroup analysis was used that included three models:

Comparative fit index and RMSEA were used as cut-off points when testing for metric invariance. In addition, changes in CFI were used (Shi et al., 2019). A difference in the CFI of less than 0.01 between two nested models indicates that the model’s fit does not deteriorate significantly (Choi et al., 2011; Rudnev et al., 2018). If the more constrained model is rejected, loadings of items are freed to establish partial metric invariance (Cheung & Rensvold, 2002; Preti et al., 2013). At least two factor loadings and intercepts must remain specified to be equal across groups for partial measurement invariance to hold (see Van de Schoot et al., 2013).

Differential item functioning was used to test for the presence of item bias for (1) the four official language groups of the participating university (Afrikaans, Setswana, Sesotho and English); (2) for three different campuses of the university; (3) and gender sub-groups. The lordif package (Choi et al., 2011) in RStudio (https://www.rstudio.com/) was used to test the presence of uniform and non-uniform item bias. Uniform bias occurs when groups are compared and systematic differences are detected in the underlying construct, while non-uniform bias occurs when there is a likelihood that answers on an item will differ or fluctuate across sub-groups (Teresi & Fleishman, 2007).

Ordinal logistic regression was used to generate three likelihood-ratio χ² statistics using the following formulas to compare models to determine uniform and/or non-uniform bias (Choi et al., 2011): Model 0 (Baseline):logit P (ui≥k)=αk[Eqn 1] Model 1 (Ability):logit P (ui≥k)=αk+β1*ability[Eqn 2] Model 2 (Ability and Group):logit P (ui≥k)=αk+β1*ability+β2*group[Eqn 3] Model 3 (Interaction):logit P (ui≥k)=αk+β1*ability+β2*group+β2*ability*group[Eqn 4]

Using DIF, biased items can be detected when the log-likelihood values of models are compared and statistically significant differences are detected (p < 0.01). Because the lordif package (Choi et al., 2011) in RStudio was used for the analyses in this study, only dimensions with more than three items could be tested. Therefore, the results of item bias were analysed for the emotional and psychological well-being items. Uniform bias is seen when comparing logistic Models 1 and 2 (χ122; df = 1). Non-uniform bias is detected when comparing logistic Models 2 and 3 (χ232; df = 1). Total bias is detected when comparing logistic Models 1 and 3 (χ132; df = 2) (Choi et al., 2011). In summary, comparing Model 1 (which only considers ability) with Model 2 (which adds group information), uniform bias was assessed – that is, whether a group’s responses are consistently different, regardless of their ability level. Then, by comparing Model 2 with Model 3 (which also considers the interaction between ability and group), non-uniform bias, where the difference in responses might change at different ability levels, was assessed. Finally, by comparing Model 1 directly with Model 3, total bias, combining both uniform and non-uniform biases, to see the overall impact of group membership on responses is assessed.

The pseudo-McFadden R² statistic was used to test the impact or practically significant effect of the DIF. The magnitude of DIF can be classified as negligible (< 0.13), moderate (between 0.13 and 0.26), and large (> 0.26) (Zumbo, 1999). In addition, the impact of uniform DIF can be determined using the difference in the β₁ coefficient from Models 1 and 2. The practical significance of uniform DIF was determined with 10% differences between Models 1 and 2, which indicates a practically meaningful effect (Crane et al., 2004). Lower 5% and even 1% thresholds are also used (Crane et al., 2007).

Cronbach’s alpha coefficient was used to determine the reliability of the scales, with α ≥ 0.70 indicating internal consistency (Nunnally & Bernstein, 1994). In addition, McDonald’s omega was calculated and reported for a more accurate estimation of internal consistency (Cortina et al., 2020). Reliability coefficients ≥ 0.70 indicate good internal consistency (Kline, 2015).

The study was approved by the Ethics Committee-Faculty of Economic and Management Sciences (EC-EMS) (ethics number: NWU-HS-2014-0165-A4). Participants signed an informed consent form before completing the questionnaire. Participants completed the questionnaires anonymously and were assured that their reported responses would adhere to the project’s confidentiality criteria and that the findings would be stored in a secure database that is password protected.

The hypothesised three-factor structure of the MHC-SF was a good fit for the data (χ² = 462.36 (p < 0.001); df = 74; CFI = 0.94; TLI = 0.93; RMSEA = 0.07; SRMR = 0.04; AIC = 48570.78; BIC = 48797.13) when compared to the one-factor model (χ² = 1262.86; df = 78; CFI = 0.82; TLI = 0.79; RMSEA = 0.12; SRMR = 0.08; AIC = 50478.66; BIC = 50684.89). Therefore, further analyses were based on the three-factor model. Table 2 indicates the results for the items’ standardised loadings for the MHC-SF latent variables. The factor loadings were all rule of thumb values of 0.50 and even 0.70 (Hair et al., 2015).

The correlation matrix for the latent variables is presented in Table 3.

The results in Table 2 show that emotional, social and psychological well-being are correlated. All relationships had a large effect size (r ≥ 0.50; Sullivan & Feinn, 2012).

Even though the invariance results are encouraging, bias was also tested across sub-groups of language, campus, and gender to test for uniform, non-uniform and total bias.

According to Nunnally and Bernstein (1994), Cronbach’s alpha reliability is acceptable when α ≥ 0.70. All factors had an acceptable coefficient: emotional well-being (α = 0.88), social well-being (α = 0.87) and psychological well-being (α = 0.89). In addition, McDonald’s omega (ω) was 0.88 for emotional well-being, 0.88 for social well-being and 0.89 for psychological well-being, indicating good internal consistency (Kline, 2015).

The study’s primary focus was on first-year university students. To further evaluate the findings of this study, future research could include students from different academic year groups (pre-graduate and post-graduate). Most participants were either Afrikaans or Setswana-speaking and mainly female, which restricts a holistic view of all language and gender groups. Future studies can present an equal representation of the population demographics to address this limitation. The study was conducted at a specific South African university and should be replicated at other universities with their unique characteristics, campuses and demographics. Some items of the MHC-SF were biased, which could hinder the comparability of findings across groups in other studies (He & Van de Vijver, 2012). Although these effects were negligible (p < 0.01; Choi et al., 2011), more research is needed to determine if the bias found in this sample is also problematic in other student samples. In addition, partial scalar invariance was established because the intercept of Item 12 in the Afrikaans language group had to be released. Future studies should examine whether this item is problematic in other language groups. Thus, more research is needed to validate invariance across different student sub-groups.