Psychometric Properties and Measurement Invariance of the PERMA Profiler in an Ethiopian Higher Education Setting

Annotation. The primary goal of the present study was to test the Amharic version of the five-factor PERMA profiler: P (positive emotion), E (engagement), R (positive relationships), M (meaning in life), and A (accomplishment) aimed to assess University instructors’ positive functioning of their work. Exploratory factor analysis, single and multi-Group confirmatory factor analysis, measurement invariance, and path analysis were employed. The details of an examination of the PERMA profiler are discussed. This present study examined four competing models based on the best-fitted model (the correlated factor model): single-factor, bifactor, correlated factor, and higher-order factor and tested measurement invariance with the PERMA profiler across groups of university teachers in Ethiopia. One possible drawback of this study is that we only studied university and future researchers could examine secondary and primary school teachers.


Introduction
Well-being is of great interest to practitioners and the scientific community owing to its innumerable benefits to individuals and organizations (Li, 2018;Mayo et al., 2019). The meaning, formation, and measurement of well-being are central to understanding positive human flourishing and optimal functioning (Brdar, 2011).
Today, only a few well-being models dominate in organizational sciences (Mayo et al., 2019), health sciences (Aldrich, 2014), and education (Lambert et al., 2019). First, the two historically dominant models are the hedonic perspective (Diener, 2009b; life satisfaction, positive affect, negative affect) and the eudemonic model (Ryff & Keyes, 1995; Environmental Mastery, Personal Growth, Positive Relations With Others, Purpose in Life, Self-Acceptance; Autonomy); these two were originally the most influential. Later, Seligman's (2011) positive well-being model has defined well-being as the organization of five fundamental pillars: positive emotion, engagement in work and life, relationships with others, meaning in life, and accomplishment (PERMA; Singh & Raina, 2020). The positive psychology theory of Seligman's (2011) well-being model is a fresh approach that extends the focus beyond mitigating pathology to personal, societal, and organizational flourishing (Huppert, 2009). The positive well-being framework has been used for studying positive human qualities and flourishing life (Seligman's (2011); more comprehensive than earlier models, the model incorporated grand theories including the broaden-and-build theory of positive emotions (Fredrickson, 2004a), Franklin existential theory (Batthyany & Russo-Netzer, 2014), and self-determination theory (Ryan & Deci, 2017). Because of the lack of one comprehensive theoretical well-being model that used different assessments, Diener (2009c) called for examining well-being in different contexts such as work, with positive psychology appearing to predominate because of its potential benefits (Linley et al., 2006).
The broadening interest of practitioners and researchers in Seligman's (2011) positive well-being model has been determined to have many potential benefits for individuals, groups, and institutions (Gable & Haidt, 2005), especially for university teachers (Li, 2018) for developing scales to assess positive well-being (Butler & Kern, 2016). For instance, authors of multiple cross-cultural studies have assessed the psychometric properties of the PERMA profiler built on the positive well-being model. Butler and Kern (2016) and Wammerl et al. (2019) examined the construct validity of the PERMA profiler by comparing higher-order, single-factor, correlated factor, and bifactor models (see Wammerl et al., 2019). In addition, Pezirkianidis et al. (2019) ran first-order (correlated order) and higher-order models in the Greek cultural context. These studies on the PERMA profiler across various cultures lay the foundation and provide crucial psychometric information for current research. However, to the best of our knowledge, there are no studies validated with university teachers and using measurement invariance. Further, there is no research on the PERMA profiler's psychometric properties in the Amharic language or an African cultural context. Thus, for this research, we examined the Ethiopian Amharic version of Butler and Kern's (2016) PERMA profiler; following Schmitt and Kuljanin (2008), we examined the measurement invariances across gender, age, university type, and experience in teaching. Failure to establish measurement invariances hinders the sound interpretation of the data and the ability to demonstrate reliability and validity (Byrne & van de Vijver, 2010;Vandenberg & Lance, 2000).
(n > 200) (Strang, 2015). Table 1 presents the demographic information for all participants in both samples.

Target Measure
The PERMA profiler. The PERMA profiler measures positive emotion, engagement, relationships, meaning, and accomplishment and consists of 23 items; of these, 15 items measure profiler dimensions, and 8 are filler items (Butler & Kern, 2016), and we used the 15 PERMA items in this study. The items are rated on 10-point Likert scales (Pezirkianidis et al., 2019). The PERMA profiler has a good model fit, the best internal validity, cross-time consistency, and evidence for content, convergent, divergent, discriminant, and construct validity (Butler & Kern, 2016). worded and scored, 22 are negatively worded and scored, and 7 items delineate each subscale. All items are rated on scales that range between 1 = strongly disagree and 7 = strongly agree. The PWBS has shown excellent construct validity and reliability (Sasaki et al., 2020), with Cronbach's alphas ranging from 0.788 to 0.882; total scale reliability was α = 0.865.
Satisfaction with Life Scale (SWLS). The SWLS, developed by Diener et al. (1985), is the most widely used instrument for measuring global life satisfaction. It is a five-item unidimensional scale, and each item is rated on a range between 1 = strongly disagree, and 7 = strongly agree. The SWLS had excellent construct validity and reliability in different studies (α = 0.858).

Patient's Health Questionnaire of Depression and Anxiety (PHQ-4):
The PHQ-4 measures anxiety and depression over the last 2 weeks; it is the most well-validated, reliable, and comprehensive scale for anxiety and depression screening (Kroenke et al., 2009). Two of the scale's four items measure anxiety (e.g., "feeling nervous, anxious, or on edge"), while the other two items measure depression (e.g., "feeling down, depressed, or hopeless"; Kroenke et al., 2009). In this study, overall Cronbach's alpha for the PHQ-4 was 0.880 (anxiety: α = 0.836; depression: α = 0.800).

The Loneliness Scale (LS-3):
The LS-3 is described as a three-item scale with a 4-point Likert response format developed by Hughes et al. (2004). The scale uses unidimensional coding (1 = never, 4 = often). The scale's construct validity was good (Hughes et al., 2004), and in this study, the overall reliability was 0.911.
Socio-demographic information. The university teachers were asked about their gender, age, university, and experience in teaching.

Procedures
The most important issue in research is ethics, and this study was granted an ethical approval letter (Ref. No. 26/2019) from the institutional review board of Szeged University. All participants gave voluntary agreement before participating in this study. The research followed all procedures, rules, and regulations of the international research code of ethics.

Adaption, Translation, and Validation of the PERMA profiler
Well-being constructs and theories grounded in the PERMA profiler predominantly reflect Western, North American, and Asian realities, but cross-cultural validation and adaptation have vital roles for generalizability of an instrument across groups and are appropriate only after measurement equivalence has been confirmed (Davidov et al., 2018). Hence, the PERMA profiler was translated into the Ethiopian Amharic language by a bi-lingual expert at a university and by a professor of psychology to check content knowledge. These translators are bi-lingual experts with long years of teaching and research experience. Their work was followed by a back-translation procedure (from English to Amharic and from Amharic to English) to test the accuracy of the translated content. After the translation of the scales, the questionnaires were administered to the university teachers.

Data Analysis
We used IBM SPSS 25.0 and IBM Amos software version 26.0 for statistical analysis to test the study hypotheses.

Convergent, Divergent and Discriminant validity
Construct validity (positively associated with similar constructs) and divergent validity (negatively correlated to opposite constructs or non-correlated) was assessed by examining Pearson's correlations between PERMA Profiler well-being scores and other theoretically relevant outcomes, where suggested the standard cut-points of correlational coefficients suggested by Schober et al., (2018), where negligible ranged 0.00-0.10, weak correlation (0.10-0.39), moderate correlation (0.40-0.69), strong correlation (0.70-0.89) and very strong correlation (0.90-1.00), respectively. Convergent validity included self-reported psychological well-being and life satisfaction, whilst divergent validity measures anxiety, depression, and loneliness. In addition, convergent and discriminant validity were assessed using the Average Variance Extracted (AVE) and the Maximum Shared Variance (MSV). Constructs that have AVE values higher than 0.5 demonstrate good convergent validity. Moreover, factors whose AVE is higher than their MSV are characterized by a good discriminant validity (Hair et al., 2019).

Factorial Analysis
The researchers used both exploratory and confirmatory factor analysis to test the construct validity of the PERMA profiler (Seligman, 2011). To examine exploratory factor analysis, robust maximum likelihood for factor extraction and varimax were used along with Kaiser normalization rotation. Regarding the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy, Kaiser (1974) recommended the following cut-points: excellent = 0.90 and above, very good = 0.80-0.89, acceptable (moderate) = 0.70-0.79, mediocre or average = 0.60-0.69, miserable or inadequate = 0.50-0.59, and unacceptable = 0.50. To further analyze the structure of the PERMA profiler, we performed confirmatory factor analyses(CFA) using Seligman's five blocks (Butler & Kern, 2016) and then compared four model alternatives as in earlier studies on well-being (e.g., Wammerl et al., 2019 in Germany): Model 1: We first examined the Butler and Kern (2016) original inter-correlated five-factor PERMA model. Model 2: A bifactor model helps examine a fit mismatch between a unidimensional and multidimensional model (Immekus & Imbrie, 2008). These models are plausible for higher-order models (Wammerl et al., 2019), and they are highly credible for extensive data; they accurately describe the given data structure in CFA (Brown et al., 2011;Immekus & Imbrie, 2008;Reise et al., 2007). Model 3: The single-factor model included a single variable for each of the five core pillars of the PERMA model to test a general well-being factor against the dimensional factor structures (Butler & Kern, 2016;Wammerl et al., 2019). Model 4: For the higher-order model, we then added a second-order well-being factor whose effect was fully mediated by the five PERMA factors (Wammerl et al., 2019). In addition, in explaining our CFA models, we disregarded the chi-square test (χ2) owing to the oversensitivity of sample size based on the suggestion of Barrett (2007) and Steiger (2007) and instead used the most globally reported goodness-of-fit indices: Tucker-Lewis index (TLI), comparative fit index (CFI), and root mean square error of approximation (RMSEA) and information criteria such as the Akaike information criterion (AIC); using the following cut points for RMSEA: poor fit = greater than 0.10, mediocre fit = 0.08 to 0.10, good fit = 0.05 to 0.08, close fit = 0.01 to 0.05, and exact fit = 0.00 (Hu & Bentler, 1999). For groups of 10 to 20, Hu and Bentler (1999) suggested RMSEA cut points of ≤ 0.08 for acceptable fit. For TLI and CFI, the recommended cut-points are the following: poor fit > 0.85, mediocre fit = 0.85-0.90, acceptable fit = 0.90-0.95, close fit = 0.95-0.99, and exact fit = 1.00 (Hu & Bentler, 1999). In addition to goodness-of-fit indices, the information criteria such as the AIC and BIC are the most appropriate for model comparison and useful for selecting a good model (Hooper, Coughlan, & Mullen, 2008). Small values of AIC and BIC indicate good fitting of the model, and statistics also need a sample size of 200 to make their use reliable (Hooper et al., 2008).

Measurement invariance (MI)
We tested the measurement invariance of the PERMA Profiler separately across gender (men, women), university types (research, applied, and general university), experience in teaching (below 5 years, between 6-10 years, and 11 years or above), and ages (ages 25-35, 36-45, 46 or above) using the best fitting model created by the CFA. More specifically, we have tested configural, metric, scalar, and residual measurement invariance to ensure that factor structure and loadings are equivalent across multiple groups. The present study's MI of configural, metric, scalar and residual invariances used single, and multi-group CFA following Millsap (2011) and Putnick and Bornstein (2016) and arrived at the following recommendation criteria: ΔTLI, 0 = perfect and ≤ 0.01 = acceptable, ΔRMSEA, 0.015 for metric, scalar, and residual invariance (Chen, 2007;Putnick & Bornstein, 2016). Table 2 shows the constructs' descriptive statistics (minimum, maximum, means and standard deviations), and the normality of distribution using kurtosis and skewness.

Factor structure
Bartlett's test of sphericity was significant (χ 2 (105) = 3425.940, p < 0.001), indicating that it was appropriate to use the factor analytic model in this study. The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy was moderate for this study (0.776), with 81.317 % of the variance explained, indicating that the variables' relationships were moderate and acceptable. The eigenvalues for all 15 items exceeded 1.00. Note: a % of variance explained in each factor loading. The factor analysis extraction method was maximum likelihood with a varimax rotation. All the factor loadings are above .50 and acceptable.
We evaluated the reliability of the five-factor PERMA profiler sub-scales (positive emotion, engagement, positive relationships, meaning in life, and accomplishment). The reliability coefficients of the PERMA profiler were a) positive emotion: α = 0.96, CR = 0.96, b) engagement: α = 0.95, CR = 0.95, c) positive relationships: α = 0.95, CR = 0.95, meaning in life: α = 0.93, CR = 0.93, and accomplishment: α = 0.95, CR = 0.95. The results of this study indicated that the five core PERMA profilers are characterized by high levels of reliability or internal consistency. The other variables used for convergent (psychological well-being and life satisfaction) and divergent validity (anxiety, depression, and loneliness scales) demonstrated acceptable reliability (see Table 4).

Convergent, Divergent, and Discriminant Validity
The researchers evaluated the validity of the teacher well-being dimensions based on their respective scores in AVE and MSV (see Table 4). The results indicated that all the PERMA well-being subscales have convergent validity of (AVE > .05), which means that the corresponding items that compose each of the five factors correlate well with each other. The PERMA well-being subscales' discriminant validity was also tested since their AVE values were higher than their MSV. Hence, the result of this study indicated that the subconstructs of the PERMA well-being subscales AVE was greater than MSV: for positive emotion (AVE=0.90 > MSV=0.70), engagement (AVE=0.87 > MSV=0.58), positive relationships(AVE=0.87 > MSV=0.65), meaning in life(AVE=0.81 > MSV=0.69), and accomplishment (AVE=0.87 > MSV=0.70), which suggests that each factor's variance is better explained by the corresponding items that mainly load on each factor.
In addition, convergent and divergent validity of the PERMA profiler subscales were further assessed by testing its correlation with other positive and negative measures. To explore the convergent validity with positive constructs (psychological well-being and life satisfaction) and with negative constructs to explore divergent validity (anxiety, depression, and loneliness) were used (See Table 4). We found weak and positive correlations between instead of the PERMA well-being model with the PWBS and the SWLS: r = 0.190 (p < 0.01) and r = 0.134 (p < 0.01), respectively. We also found negligible to weak correlations between the PERMA well-being model subscales and the PWBS and SWLS subscales. The PWBS (Lee et al., 2017) is the most widely used tool for measuring the convergent validity of the PERMA well-being model. Regarding the divergent validity, we compared the PERMA profiler to depression, anxiety, and loneliness scales and found negative associations (r = −0. 264, −0.215, and −0.179, p= 0.01, and r = −0. 255, −0.248, and −0.228; p= 0.01, respectively).

Single and Multi-Group Confirmatory Factor Analysis (SGMGCFA)
We arrived at a five-factor PERMA well-being model with 15 items derived from Butler and Kern (2016). We examined the theoretically driven PERMA well-being model using the correlated, single-factor, bifactor, and higher-order factor models following the global goodness-of-fit indices. Figures 1a-d clearly shows the single-factor, correlated, higher-order, and bi-factor PERMA well-being models. As, the Appendix 5 shows the goodness-of-fit findings for all four models; the five-PERMA correlated factor (χ2 (90) Table indicates that the PERMA single-factor model showed poor fit with the data (χ 2 (104) = 4166.65, P < .001, TLI = .719, CFI = .759, RMSEA = .1161, CI: .155-.167). In addition, all models showed statistically significant differences in the variances and factor loadings (see Appendix 3).
The inter-scale correlations for the five-factor model ranged from 0.71 to 0.81 (see Appendix 2), indicating strong relationships (Schober et al., 2018), and the standardized factor loadings were high as well (see Appendix 2). The bi-factor model showed the lowest factor loadings, with loadings below 0.72 t 0.88 of the 15 items (see Appendix 3). In conclusion, the five-factor PERMA model showed the best fit with the data and instead fit with the original assumptions of the PERMA well-being theory (Butler & Kern, 2016;Wammerl et al., 2019).

Figure 1
The Four CFA Computing Models of the PERMA Profiler Note PERMA comparison models for this study: (a) single-factor model, (b) bifactor model, (c) higher-order factor model, and (d) five-factor correlated model.

Measurement Invariance Testing Results
We then examined the measurement invariance across gender, age, university type, and experience in teaching groups on the PERMA model (Appendix 6, Figure 2). The PERMA profiler was constructed independently across groups, and the model fit was examined before we tested MI.

Figure 2 Four Stages of Measurement Invariance of the PERMA Profiler
Note. Measurement invariance of the PERMA profiler's well-being across groups (gender, age, university type, and experience in teaching).
Age. The age of university teachers in between 25-35, 36-45, 46, and more, among the three age categories showed the best model fit to the data, (χ2 (80)  From the above findings of the RMSEA, the teachers 46 and above age showed not a good fit; however, the CFI and the TLI results are acceptable. We examined MI group differences between the five-factor PERMA model across age categories in the measurement invariance stages; the configural invariance test yielded sufficient fit to the data at the correlated order factor, χ 2 (240) = 560.342, P < .001, CFI = .979, TLI = .973, RMSEA = .039 for the PERMA well-being model. As displayed in Table 6, the metric invariance test scores across age were invariant: Δχ 2 (20) = 28.22, ΔCFI = .000, ΔTLI = -.001, ΔRMSEA = .001. In the third step of MI, the more restrictive model constrained the item intercepts, and we then calculated the SMI factor loadings: Δχ 2 (28) = 176.11, ΔCFI = .010, ΔTLI = −.008, ΔRMSEA = −.006, which indicated that the item intercept and the factorial loadings are the same for the three age categories on the PERMA well-being model. The residual invariance (constrained item intercept, factor loadings, and strict measurement invariance) fitness indices to check the model across the age groups of five PERMA well-being models showed excellent fit to the data: Δχ 2 (2) = 115.53, ΔCFI = .008, ΔTLI = .008, ΔRMSEA = −.005.
University type. The PERMA five-factor correlated model showed an excellent fit to the data regarding university type (research, applied, or general) at a single factor level (χ2 (80)  The PERMA five-factor correlated model also fits with the data regarding university type at all four MI stages.
Experience in teaching. University teachers' years of teaching experience (fewer than 5 years, 6-10 years, and 11 years or more) showed an excellent fit to the data (see Appendix 6), as did MI on the configural, metric, scalar, and residual tests. The strict model (residual) was achieved, and all item loadings, intercepts, and residual variances were equivalent or equal across the three levels of experience in teaching.

Discussion and Implications
For a century, practitioners and researchers in various disciplines have primarily examined well-being by focusing on its pathological aspects (Spilt et al., 2011) and assessed it using multiple scales (Gallagher & Lopez, 2019). However, the scientific study of positive psychology and well-being has recently undergone dramatic expansion because of its positive outcomes for individuals, organizations, and societies (Seligman & Csikszentmihalyi, 2000). For this study, following Butler and Kern (2016) and Wammerl et al. (2019), we conducted further psychometric validation of the five-factor PERMA profiler and tested the MI across gender, age, university type, and experience in teaching to assess positive psychological state and healthy functioning among university teachers in an Ethiopian setting. Specifically, we tested group differences across university type, experience in teaching, age, and gender using the best-fitted model (the correlated factor) compared with four competing models (single-factor, bifactor, correlated, and higher-order).
The PERMA profiler has the best factor loadings, excellent reliability, and construct validity of all the well-being scales tested in this study. In contrast to other studies, in which researchers found weak psychometric properties of the engagement subscale (Butler & Kern, 2016;Pezirkianidis et al., 2019), we found in this study that all five pillars showed moderate to high inter-item correlations (see Appendix 2). The Amharic version of the profiler adequately measured the multidimensional aspects of well-being among university teachers in East African Ethiopian culture.
Regarding the convergent and divergent validity of the Ethiopian Amharic version of the PERMA profiler (Butler & Kern, 2016), the related measures include five measures that are not included on the other scales we used in this study (PWBS, Ryff & Keyes, 1995Environmental Mastery, Personal Growth, Positive Relations With Others, Purpose in Life, Self-Acceptance; PHQ-4, depression and anxiety, Kroenke et al., 2009;SWLS, Diener et al., 1985;and LS-3;Hughes et al., 2004). The PWBS and SWLS showed positive correlations with the PERMA profiler dimensions and negative correlations with depression, loneliness, and anxiety, consistent with earlier research (Butler & Kern, 2016;Pezirkianidis et al., 2019;Wammerl et al., 2019). The divergent validity in this current study showed negative correlations with depression, anxiety, and loneliness, and this finding also supports Pezirkianidis et al. (2019). We also explored another method to check convergent, divergent and discriminant validity and proved the PERMA profiler was valid. Overall, the Ethiopian, Amharic-language version of the PERMA profiler correlated well with the other well-being, life satisfaction, and psychological health status scales; the AVE is greater than 0.05, and AVE was less than MSV, which we used with a sample of Ethiopian university teachers.
A series of measurement invariance tests must be conducted for cross-cultural validation and firm conclusions (Millsap, 2011;Putnick & Bornstein, 2016;Vandenberg & Lance, 2000) tests of group mean differences, invariance of structural parameter estimates, and for this current study, we tested MI with a correlated factor model. We found similar factor loadings for all models, and we used the PERMA five-factor model for MI concerning gender, age, university type, and experience in teaching using single-and multi-factor CFA.
CFA with four competing models indicated a good fit of the PERMA profiler to the correlated factor (Seligman, 2011), bifactor, and higher-order (Wammerl et al., 2019) factor models. Additionally, the goodness-of-fit indices were compared with the findings from other validation studies ( Butler & Kern, 2016;Pezirkianidis et al., 2019;Wammerl et al., 2019). Based on the findings, the five-dimension model (positive emotion, engagement, relationships, meaning in life, and accomplishment) of the PERMA profiler was the most suitable for assessing the Ethiopian university teachers' well-being across subgroups: gender (male, female), age (25-35, 36-45, 46 and above), university type (research, applied, general), and experience in teaching (5 years or fewer, 6-10 years, 11 years or more).
This present study examined four competing models based on the best-fitted model (the correlated factor model): single-factor, bifactor, correlated factor, and higher-order factor and tested measurement invariance with the PERMA profiler across groups of university teachers in Ethiopia. One possible drawback of this study is that we only studied university teachers, and future researchers could examine secondary and primary school teachers.
Furthermore, a study in Africa showed that culture, economic system, religion, ethnicity, kinship system, marriage, gender, age, education, employment and institutional practices played a pivotal role in the well-being of employees (Bonthuys et al., 2011)SD=13.28. Therefore, future studies should take the opportunity to examine these basic and important demographic variables using multi-variate analysis by taking cross-cultural samples.
Finally, the present study should offer a practical intervention in the well-being of university teachers using positive psychology theory (Seligman, 2011), COR theory (Hobfoll, 2002), and a broaden-and-build approach (Fredrickson, 2004). In addition, the results have some implications for the effectiveness of university managers. For example, Li (2018) and (Zewude & Hercz, 2021) pointed out that university leaders or managers can enhance teachers' well-being by increasing their meaning in life and applying positive psychology.

Conclusion
Besides acknowledging that an Amharic version of the PERMA profiler in Ethiopian higher education settings is psychometrically sound, reliable, valid, and invariant using multi-modal CFA model comparisons. This study also offers the scientific community a sophisticated validated scale exclusively intended to assess university instructors' positive psychological states.
Furthermore, this research employed multi-modal model compressions (single factor, bifactor, correlated factor, higher-order factor), single group and multi-group CFA, and measurement invariance for university instructors of the PERMA profiler. Besides, it was conducted by the university instructors by taking large-scale data from the diverse Ethiopian higher education system. This study was also triangulated using various recommended sophisticated statistical methods to ensure the psychometric properties of the PERMA profiler.

Data Availability Statement
The data sets generated and analyzed during the current study are available from the corresponding author, who is willing to share with the journal.

Ethical Approval
All procedures performed in studies involving human participants followed the institution's ethical standards and the 1964 Declaration of Helsinki.

Informed Consent
Informed consent was obtained from all participants included in the study. Notes: * p < 0.001. MI = measurement invariance, RMSEA = root mean squared error of approximation, TLI = Tucker-Lewis index; CFI = comparative fit index; ΔRMSEA = change root mean squared error of approximation, ΔTKI = change Tucker-Lewis index; ΔCFI = change comparative fit index; PERMA = PERMA well-being model.