The study’s target demographic group was first-year university students enrolled at a South African university. A sample of 1088 participants was used, of which 72.4% were between the ages of 17 and 20 years and 16.7% were between 21 and 22 years. South Africa has 11 official languages distributed in different parts of the country. The languages most frequently used by students of the participating university were included in the analyses: Afrikaans (260, 23.9%), Setswana (199, 18.3), Sesotho (152, 14.0%) and English (94, 8.6%). The university has three campuses: Campus 1 is a campus located in a peri-urban area (131, 12%), Campus 2 is located in a medium-sized urban city (478, 43%), and Campus 3 is a smaller campus located in a large industrial city. In total, 689 (63.3%) females and 319 (29.3%) males participated in the study. Most participants were black students (62.3%), followed by white students (22.2%).

The Flourishing Scale (Diener et al. 2010) is a concise eight-item measure of respondents’ self-perceived performance in critical life domains such as relationships, self-esteem, intention, and optimism. A 7-point Likert scale was used, ranging from 1 (strongly disagree) to 7 (strongly agree). An example item is: ‘I lead a purposeful and meaningful life’. A high score indicates that the individual possesses psychological resources and strengths. The scale showed good psychometric qualities. The Cronbach’s alpha coefficient is reported as 0.82 (Diener et al. 2010).

The participating university accepted and authorised the project, and the study was granted ethics clearance. A secure direct link to the questionnaire was put on the university’s online portal. Throughout the study’s duration, students were informed about the research and encouraged to participate voluntarily. This was accomplished through field workers who presented brief awareness sessions in classrooms. Before completing the questionnaire, participants were required to sign an informed consent form. Furthermore, participants were assured that their reported responses would be anonymous, that the data gathered in the study would adhere to the project’s confidentiality criteria, and that the findings would be carefully stored in a secure database that would be password protected.

MPlus 8.6 (Muthén & Muthén 2021) was used to conduct the statistical analyses. Confirmatory factor analysis was used to test the factorial validity of the Flourishing Scale. Maximum likelihood estimation was used, with the covariance matrix as input. The following fit indices were considered to assess the fit of the measurement model: 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). Proper fit is considered at a value of 0.90 and above for the CFI and TLI (Byrne 2001; Hoyle 1995). For the RMSEA, a value of 0.05 or less indicates a good fit, whereas values between 0.05 and 0.08 are considered an acceptable model fit (Browne & Cudeck 1993; Chen et al. 2008).

Differential item functioning was used to test for the presence of item bias for language (four of the languages most frequently used by students at the participating university: Afrikaans, Setswana, Sesotho and English), campus (the three campuses described here) and also included males and females. Two forms of bias were tested: uniform and non-uniform bias. Uniform bias refers to the systematic difference in ability levels of the underlying construct between compared groups (Swaminathan & Rogers 1990; Teresi & Fleishman 2007). Non-uniform bias is the difference in the likelihood of related answers across different groups fluctuating across all ability levels (Swaminathan & Rogers 1990; Teresi & Fleishman 2007). The lordif package (Choi, Gibbons & Crane 2011) in RStudio Team (2020) was used. The following formulas were used and compared with test for uniform and non-uniform bias, using ordinal logistic regression to generate three likelihood-ratio χ² statistics (Choi et al. 2011): Model 0:logit P(ui≥k)=αk[Eqn 1] Model 1:logit P(ui≥k)=αk+β1*ability[Eqn 2] Model 2:logit P(ui≥k)=αk+β1*ability+β2*group[Eqn 3] Model 3:logit P(ui≥k)=αk+β1*ability+β2*group+β2*ability*group[Eqn 4]

Biased items are flagged when statistically significant differences are detected, that is when the log-likelihood values of models are compared and p < 0.01; for uniform bias when comparing Models 1 and 2 (χ122;degree of freedom [df]=1), for non-uniform bias when comparing Models 2 and 3 (χ232;df=1); for a total DIF effect, comparing Models 1 and 3 (χ132;df=2) (Choi et al. 2011). The pseudo-Mcfadden R² statistic is used to quantify the impact or practically significant effect of DIF, classifying the magnitude of DIF as negligible (< 0.13), moderate (between 0.13 and 0.26), or large (> 0.26) (Zumbo 1999). In addition, the impact of uniform DIF can be determined using the β₁ coefficient when Models 1 and 2 are compared (Crane, Van Belle & Larson 2004). Different thresholds, ranging from a 10% difference between Models 1 and 2, indicate a practically meaningful effect (Crane et al. 2004; Maldonado & Greenland 1993).

Measurement invariance was investigated for the same language, campus, and gender groups. This was carried out in a multigroup analysis framework including the: (1) configural invariance model (i.e. the baseline model for the more constrained models and the test if a similar underlying latent factor is evident in the different groups); (2) metric invariance model (assumes the invariance or similarity of the factor loading in the different groups); and (3) scalar invariance model (test if the factor loadings and item intercepts are invariant or similar in the different groups) (Preti et al. 2013). The CFI and RMSEA values were used. For CFI, the fit is considered adequate if values are > 0.90 and better if they are > 0.95. For RMSEA, the cut-off value is < 0.08, but better is < 0.05 (Van De Schoot, Lugtig & Hox 2012). In addition, changes in CFI were used as recommended by Shi et al. (2019). A ΔCFI value higher than 0.01 between two nested models indicates that the added group constraints have led to a poorer fit; in other words, the more constrained model is rejected. By freeing the loading of items, partial metric invariance can be achieved (Cheung & Rensvold 2002; Preti et al. 2013). Cronbach’s alpha coefficient was used to determine the reliability of the scales. A cut-off point of 0.70 is deemed satisfactory (Nunnally & Bernstein 1994).

The study was approved by the Ethics Committee, Faculty of Economic and Management Sciences (EC-EMS) (Ethics no.: NWU-HS-2014-0165-A4). Before completing the questionnaire, participants were required to sign an informed consent form. In addition, participants were assured that their reported responses would be anonymous, that the data gathered in the study would adhere to the project’s confidentiality criteria, and that the findings would be stored in a secure database that is password protected.

With regard to the factorial validity of the Flourishing Scale, a one-factor structure showed a good fit to the data (χ² = 180.11; df = 19; CFI = 0.94; TLI = 0.91; RMSEA = 0.079; SRMR = 0.04). The standardised loadings are shown in Table 1.

All items had high factor loadings (λ) (Shevlin et al. 1998), ranging from 0.65 (Item 8) to 0.80 (Item 1).

Uniform, non-uniform and total bias were tested (see Table 2).

Items 2, 3 and 7 showed statistically significantly uniform and total bias for the included language and campus groups, while no bias was detected between males and females. To determine if the magnitude of DIF for these three items were of practical significance, pseudo-McFadden R² values and the difference in the β1 coefficient were inspected. In addition, visual graphs are provided for each item to demonstrate the effect between language and campus groups (Figure 1, Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6). Each of these figures present four graphs providing additional diagnostic information, including the item characteristic curve for the different groups (in this case, language and campus groups; upper-left graph); the item response functions for the parameter estimates for each group (lower-left graph); the absolute difference between item characteristic curves for sub-groups (upper-right graph); and the absolute difference between the item characteristic curves of the sub-groups weighted by the score distribution (Choi et al. 2011).

For all three items in language and campus groups, the differences between language and campus groups were slightly different compared with each other; however, these differences were negligible, as can be seen in the density-weighted impact in each figure (bottom right plots). Also, the pseudo-McFadden R² statistic values were all smaller than 0.13 and the difference in β₁ coefficients smaller than 5%. As a result, DIF’s magnitude or practical impact on these three items can be classified as negligible.

The results of the configural, metric and scalar invariance testing across the language, campus, and gender groups included in this study are shown in Table 3.

With regard to language and campus, configural and metric invariance were established. The results of scalar invariance showed that ΔCFI for language was –0.024 and for campus –0.018 (higher than 0.01). Consequently, partial scalar invariance was established, releasing the intercept of items 4 and 7 in the Afrikaans and English language groups and items 3 and 7 in all three campus groups. Configural, metric and scalar invariance was confirmed for gender.

As a measure of internal consistency, Cronbach’s alpha coefficient was calculated to establish the internal consistency of the Flourishing Scale. With α = 0.91, the Flourishing Scale was found to be reliable (Nunnally & Bernstein 1994).

Even though the findings of this study are promising, several limitations must be mentioned. The study’s primary focus was on first-year university students in South Africa. Therefore, the study should be replicated for senior students, other universities, and other countries with multicultural populations. South Africa has 11 official languages, of which only 4 were included in this study. Other language groups should also be included in future studies. Three items seemed to be somewhat problematic (items 3, 4 and 7) regarding bias and invariance. Even though the practical effect was small and negligible, future studies should investigate how these items function in other samples.