Determinants of Subjective Well-Being and Invariance Measurement: Evidence from German and Ghanaian Data

This 
paper aims to test the invariance measures of subjective well-being and some of 
its determinants using Ghanaian and German data from the WVS (World Value 
Survey). From the WVS wave-6 data, the following dimensions are selected: 
religion, social capital, social trust, fear feeling or worry, political activities, personalities, security, economic 
conditions, and subjective well-being. To test the different types of 
invariance (configural invariance and metric invariance), MGCFA (Multi-group 
Confirmatory Factor Analysis) was used. The first result of our modeling was that all dimensions 
significantly determine subjective well-being in the local model with the 
German data. In contrast to the Ghanaian data, only the dimensions of political 
activity and the fear feeling or worries turn out not to be significant in 
explaining subjective well-being. Second, the configural invariance test 
revealed that social capital, religion, social trust, fear feelings or worries, 
and economic conditions are non-equivalent between the two countries. Security, 
political activities, and subjective well-being satisfy the partial invariance 
measurement. Only personality traits are fully invariant across the two 
countries. As a result, a comparison of the determinants of well-being across 
the two countries is only possible for personality traits (full invariance 
measurement) and security (partial invariance measurement).

map by Inglehart & Welzel (2005) where the countries are arranged in a matrix in which they are identified along two axes: traditional and secular values, on the one hand, and values of survival and self-expression, on the other. The authors thus identify nine different cultural regions. These are African-Islamic; Latin America; English Speaking; South Asia; Orthodox (Catholic); Catholic European; Baltic; Confucian, and Protestant Europe. The comparison in this paper focuses on two opposite cultural regions: the cultural area of European countries with Protestant traditions and that of African and Islamic countries. It is from these two groups that we have chosen the countries that pose the least constraints in terms of data availability in the selected variables. From an exploratory perspective, the comparison in this study will focus on Ghana and Germany, which after the elimination of missing data provide a sample whose difference is not so great.
Compared to the existing literature, to our knowledge, this paper is a contribution to the literature on several aspects. First, it seeks in an exploratory perspective to compare subjective well-being and its determinants between African and European cultures (Germany and Ghana). Second, this study uses the permutation method of the PLSPM-SEM (Partial least square path modeling-Structural Equation Modeling (SEM)) approach to test invariance, which would be a first in the empirical literature on subjective well-being.
The rest of the paper is structured as follows. In the second section, the theoretical background of equivalence measurement is presented. A third section explains the data sources, the methodology used, and the specification of the model. A fourth section is devoted to the presentation of the results. A fifth section concludes and discusses the results.

Source of Equivalence Bias
Before presenting the methods for detecting measurement equivalence, let us ask the question: what is the source of measurement non-invariance? According to Van de Vijver (1998), there are three types of biases that affect equivalence: construct bias, method bias, and item bias.
The first type of bias: the construct bias is the most crucial, it denotes that the theoretical concept has a different meaning across different groups (Davidov et al., 2014). The problem that is raised with such a bias comes back to that of the comparison of concepts as raised by Triandis (1972) in sociology by distinguishing: the emic concept, and universal, or etic concept. The emic concept has a meaning that is specific to a culture, unlike the universal or etic concept.
Method bias, the second type of bias, relates to the method used in sampling techniques, the treatment of non-response, and the procedures for administering questionnaires. Besides, this type of bias can lead to differences in scores between groups, which refer to a social desirability bias (Johnson &  Finally, item bias refers to anomalies observed in the translation of items (Harkness et al., 2010). It may also be due to the inclusion of a term that has a different interpretation from one society to another. Davidov et al. (2014) give an example of environmental protection, which may have different understandings among socio-cultural groups.

Methods for Testing Measurement Invariance
To correct these biases, it is possible to act a priori in the formulation of questionnaires by taking into account the translation question or to conduct cognitive interviews (Fitzgerald et al., 2011;Willis, 2004). However, according to several authors, no measure, a priori, can guarantee the comparability of a concept between two or more groups (Byrne et al., 2009;Chen, 2008;Davidov et al., 2011). It is therefore important to estimate the measure of invariance.
In this sense, there are several techniques for estimating the measure equivalence. Davidov et al., (2014) list the following techniques: Exploratory factor analysis (Meredith, 1964); MGCFA (Multi-Group Confirmatory Factorial Analysis) (Jöreskog, 1971); multidimensional scaling (Braun & Scott, 1998); Item Response Theory (IRT) (Raju et al., 2002); Latent Class Analysis (LCA) (Kankaraš et al., 2010).  (Byrne, 2010;Doll et al., 2004;Malhotra & Sharma, 2008). This approach uses the differences between the group models chi-square ( 2 χ ) to test invariance. Furthermore, as Chin et al. (2016) note, this approach has the disadvantage of M. Ba Open Journal of Social Sciences imposing a series of constraints on all parameters (factors, variance, and structural coefficients) to test invariance. This multitude of compulsion can lead to concealing non-invariance at much lower levels of analysis (Chin et al., 2016: p. 271). Also, this approach is very constraining in terms of the nature of the data and sample size.
With this in mind, alternative approaches are increasingly being used to test invariance in MGCFAs. Among these techniques is the PLS permutation approach proposed by Chin et al. (2016). This approach is part of the other technique for estimating SEM: PLS-PM or the variance-based approach. It is a less constraining technique in terms of data type and sample size. Unlike the CBSEM-based MGCFA, this approach allows testing the invariance at several levels of the analysis with the permutation test. This method is a non-parametric resampling procedure developed by Chin & Dibbern (2010). It is based on a repetitive random permutation procedure that ultimately seeks to test whether the difference between the structural coefficients is large enough to reject the null hypothesis that postulates an identity between the two groups. In this paper, we will use the latter technique to test invariance in subjective well-being configuration and its determinants.

Literature Review
Equivalence is then a necessary precondition for the comparison of measures between groups that differ by culture, gender, or other socio-economic factors.
Several studies have empirically tested the equivalence of different measures.
Most have concluded that the concepts are not comparable across countries. For example, With the WVS data, Ariely & Davidov (2011) found that the scales commonly used to measure attitudes across democratic societies do not have the same meaning across countries. Piurko et al. (2011) showed with the SSE data that questions on policy orientations (right and left) have a different meaning between Eastern and Western European countries. They find that a common question may refer to different ideological orientations depending on whether the respondent is from a liberal (Sweden), traditional (Greece), or post-communist (Czech Republic) country. Boeve-de Pauw et al., (2014) found by observing a non-invariance that the different attitudes of Belgian children towards the ecological issue would be linked to the gender difference which would lead to a lack of comparability between the two sexes. Also, Alemán & Woods (2016) tested the invariance using WVS data over the period 1981 to 2014 and found that most of the values defined in this database are not comparable between countries, except for a few European postmaterialist countries. The conclusions of these two authors will also be reinforced by Sokolov, (2018) who observed non-equivalence in the Inglehart & Welzel (2005) emancipatory value index measurement model.
With the MGCFA technique, he found that this index is not invariant across the ten different cultural zones defined by Inglehart & Welzel (2005) and concluded for partial scalar invariance across school levels. They subsequently found, by comparing the latent mean difference, that elementary students' satisfaction was higher than middle and high students.

Source of Data
This article uses WVS data for two countries for exploratory purposes: Germany and Ghana. The WVS is a database that has been documented since 1980 and collects perception data on several dimensions of life (cultural values, attitudes and beliefs towards gender, family, and religion; attitudes and experience of poverty; education, health, and security; social tolerance and trust; attitudes towards multilateral institutions; cultural differences and similarities between regions, and societies). Today this database covers more than 60 countries with 6 rounds. The seventh (WVS-7) is in progress and should be published during 2020 and will lead to a coverage of 80 countries. WVS-6 surveys covered all residents (not just citizens) in a country at the age of 18 years older and older. A full probability sample of the population aged 18 and over was used as the sampling process in this survey. In some cases, the application of a nationally representative random sample based on a stratified, multi-stage territorial selection has been allowed. Other sample design models were also possible depending on the concrete conditions of the country. The main objective was to achieve the samples in each country are representative and reflect the distribution observed in the country's population according to gender, age groups, urban/rural population, etc. Thus, the minimum acceptable sample size, in the vast majority of countries, in national data sets is 1200. However, where the country has a population of less than 2 million, a sample size of 1000 is considered acceptable; but this sample size should be at least 1500 when the country's population is large.
The sample for Ghana and Germany is 1501 and 1529 respectively. At this level, the sample size is representative of the population of each of these two countries. Table 1 summarizes some information on the socio-demographic description of the two populations.

Definition of Variables
In this paper, nine dimensions are selected and measured with items from the WVS. These dimensions are considered as latent variables in the model that will be specified in 3.3. From the literature, we have chosen the following dimensions: religion, social capital, social trust, political activities, security, feelings of fear or worry, personality traits, and economic status. Thus, each variable is defined by at least three indicators (see Table 2). In Appendix, a more complete table is given with the measurement scales for each indicator (see Table A1 in Appendix).  Social trust is a dimension whose items relate to trust in neighbours, family members and people one knows. Social trust is a dimension whose items relate to trust in neighbours, family members, and people one knows. The effect of social trust on well-being can be both positive and negative. In this study, it's assumed that this dimension has a positive and strong effect on subjective well-being (Churchill & Mishra, 2017).
The personality dimension refers to the personality traits that are characteristics of our motivational system and that determine what we do in the absence of strong influence. Personality is measured in this study by 4 personality traits de- The sense of safety is given by indicators related to the crime experienced by the individual in the past or by one of his or her family members, but also by the frequency of a perception of being unsafe. It is clear that a sense of insecurity harms the quality of life and subjective well-being (Stiglitz et al., 2009). In this sense, security is assumed to have a direct effect on subjective well-being in this paper.
Economic conditions define an individual's financial situation. It is measured by the individual's perception of his or her financial situation, the scale of income, and the social class to which he or she feels he or she belongs. Economic conditions, particularly income, have a positive effect on subjective well-being (Diener, 1984;Easterlin, 2001;Stevenson & Wolfers, 2013). In this paper, too, economic conditions are assumed to have a direct effect on subjective well-being.
Subjective well-being is constructed based on these components: life satisfaction and the feeling of happiness (Veenhoven, 2010). This is the dependent variable of our model and all variables have been shown in the literature to be determinants of subjective well-being (Diener et al., 2003;Helliwell, 2005Helliwell, , 2008Helliwell & Putnam, 2004;Stanzani, 2015).

Model Specification
This paper adopts a PLS-PM model of MES. These models are composed of two parts: an outer model and an inner model. In the latter, we will test the relationship between the latent variables that are represented in this paper by subjective well-being and its determinants.
The inner model will highlight the effects of the eight selected dimensions on subjective well-being. It can be formally written as follows: with ξ swb , the endogenous latent variable, i.e. subjective well-being, ξ i , i exogenous or model-independent latent variables, i.e. the eight (8) determinants selected. 0 β represents the intercept of the model. β i is a structural path associated with the relationship between the endogenous latent variable and the exogenous latent variables. μ represents the error term or disturbance. Each latent variable is associated with a block of manifest variables. The set of relationships between latent variables and manifest variables forms the external model or measurement model. In our model, the manifest variables are assumed to reflect the latent variables. The external model is written as follows: where h x is a manifest variables vector for the latent variables ξ , π h is a loading associated with the manifest variables h x , and h ε is a measurement error term for manifest variables.
The error terms, in (1) and (2) The results of the model will be analyzed according to the quality of the global model, the outer model, and the inner model.
The global model is analyzed in terms of goodness of fit. For this, it is recommended that absolute GoF be greater than 0.35 (Wetzels et al., 2009). It is also possible to observe also the relative GoF, which according to (Vinzi & Russolillo, 2010) must be greater than 0.90. The relative GoF can also be observed in addition to the absolute GoF.
The inner model validity is more concerned with the observation of structural paths that measure the effect of latent constructs on each other. Also, it is recommended to analyze the predictive quality of the model. Redundancy is the statistic that makes it possible to assess this quality. It determines the ability of the independent latent variables to predict the endogenous latent variable.
The outer model results are analyzed in the PLS-PM approach in terms of internal consistency, reliability indicators, and convergent and divergent validity.
The internal consistency reflects the requirement for the homogeneity of the constructions. To this end, the ρ Dillon Goldstein must be greater than 0.7. (Chin, 1998) The threshold of 0.6 is also allowed by Bagozzi et al. (1998). The indicator's reliability requires that they be well explained by their latent variable.
For this, they must have a communality that is equal to or greater than 0.5 or a loading equal to or greater than 07 (Chin, 1998). Furthermore, Barclay et al., (1995) considered that the threshold of 0.5 for loading may be acceptable for indicators reliability. Convergent validity refers to the ability of indicators to converge in the measurement of their latent variable compared to indicators measuring different constructs. The criterion of validity is based on Average Variance Extracted (AVE) which must be greater than or equal to 0.5 according to Fornell & Larcker (1981). Finally, the last criterion is external validity, which measures the fact that a manifest variable reflects only its latent variable. For this criterion, the AVE of each latent variable should be greater than the latent variable highest squared correlation with any other latent variable (Fornell & Larcker, 1981).

Results
MGCFA is based first on estimating the general model with data from the different groups. This results in local models that are in this paper the model with the Ghanaian and German data. The model in Figure 1 is then estimated for Ghana and Germany respectively. The comparison of the different parameters of the model gives an estimate of the measurement invariance between the two countries. Therefore, in this paper, the results of each local model are presented before analyzing the measurement invariance which is a comparison of the difference in the parameters of the two models. Besides, the descriptive results of the overall model are given in the appendix (see Table A2 in Appendix).

The Local Ghanaian Model
The global model for Ghana has an absolute GoF of 0.35. This is a fair value compared to the threshold defined by Wetzels et al. (2009), while the relative GoF is below the 0.9 thresholds defined by Vinzi & Russolillo (2010). Based on these two indicators, it can be concluded that the model adjusts moderately to the Ghanaian data (see Table 3).
Concerning the outer model, the internal consistency is verified for all latent variables that have Dillon Goldstein ρ between 0.689 and 0.9727. For the reliability of the indicators, only the indicators of the constructs of "subjective well-being" and "economic conditions" have loadings or communalities above the different thresholds. The convergent validity of the constructs is observed for the following dimensions: social trust, political activities, fear feeling, economic conditions, and subjective well-being (see Table 4).
Analysis of the inner model shows that all dimensions have a positive and significant effect on subjective well-being, except for political activities and the fear feeling. The most important determinant is related to economic conditions and social capital (see Table 5).

The Local German Model
The local model for Germany has an absolute and relative GoF that is above the different thresholds used to judge the fit quality of the model. Thus, the model appears to fit well with the German data.

The outer model fully satisfies the criterion of internal consistency with Dillon
Goldstein ρ all of which are above 0.7. Concerning the reliability of the indicators, the results meet the reliability criterion better than the outer local Ghanaian model. There are only a few indicators in the "personalities" block (perso2 and perso3) and the "security feeling" block (secu1) that have loadings below 0.6.
Convergent validity is observed for the following dimensions: religion; political activities; subjective well-being; economic conditions and fear feeling (see Table   4).    The inner model shows that all variables or dimensions have a positive and significant effect on subjective well-being. The most important variables in determining subjective well-being among Germans are economic conditions; social trust and social capital (see Table 5).

Invariance Measurement across Ghanaian and German Data
The configural invariance is described in Table 6. Five constructed: social capital, religion, social trust, fear feeling or worries, and economic conditions are non-equivalent across two cultures. Thus, these dimensions are not comparable between Germany and Ghana and it is not relevant to compare their effects on subjective well-being between the two countries.
The results in Table 7 show that several indicators are non-invariant between the two groups. First, all items in the "religion" dimension are full non-invariant.
worries of a terrorist attack (fear2) and worries of civil war (fear3) are two indicators of fear feeling dimension that are not equivalent between Germany and Ghana. The same is also true of political actions: "signing a petition" (actpo1) and making a "peaceful march" (actpo4) and the feeling of safety resulting from having a family member who has been the victim of a crime (secu2 and secu3).
The importance of friends (socap2), trust in people one knows (trust3), and the feeling of belonging to a social class (ecosit2) were found to be non-equivalent between the two societies after all permutations (n = 100, n = 500 and n = 1000).
Finally, well-being in the composition of the two indicators turns out to be non-equivalent only in terms of life satisfaction (swb1). The dimensions of political activity, security, and subjective well-being satisfy the criteria of configurative invariance. Given that some of their indicators do not meet the criterion of In the inner model, Table 8 shows that the effect of social trust, political activities, fear feelings, and economic conditions prove to be non-equivalent. All these dimensions, except "policy actions", were found to be non-respect configural invariance measurement. Thus, Social capital and religion do not satisfy the criterion of configural invariance. As a result, they are non-invariant in both countries and it is not relevant to compare their effects on subjective well-being even if they are significantly different. This leaves only those personality traits and feelings of fear or dread that have effects on well-being that can be compared across the two countries. The personality traits that are invariant determine significantly subjective well-being across the two countries, but the effect is larger among Germans than Ghanaians. On the other hand, the sense of security that satisfies partial invariance has a much stronger effect on subjective well-being among Germans than among Ghanaians.

Conclusion
The use of MGCFA to test the invariance of constructs between Germany and Ghana showed that there are concepts for which comparison between the two countries is impossible. These are social capital, religion, social trust, feelings of fear or dread, and economic conditions. The non-invariance of these dimensions between the two countries can be attributed to sociological as well as linguistic differences (Ghana is an English-speaking country). The objective of this paper is not to search for the source of non-invariance but just to show that it exists.
However, it should be noted that apart from economic conditions, the other dimensions refer to values that appear in the WVS. In this sense, the non-invariance confirms to some extent the results of Davidov et al., (2011), andSokolov, (2018) on the non-equivalence of most of the values measured in the WVS between countries with different cultural backgrounds such as those in Africa and Europe. The non-invariance of religion is one of the most striking between the two countries. This implies that religiosity, religious commitment, and faith issues are understood differently and that there is a different understanding of the opposition of a secularized society (Germany) to a traditional one (Ghana). The non-invariance of social capital and social trust between the two countries is more related, respectively, to the importance of friends in life and trust in neighbours. It may turn out that the notions of neighbours and friends are not the same in the two countries because of their cultural oppositions (Inglehart & Welzel, 2005). The invariance of feelings of fear is linked to the fear of a terrorist attack and the fear of civil war. The geopolitical situation of the two countries is one reason for this difference. Germany, like many European countries, has been the victim of a terrorist attack in recent years, which is not the case in Ghana, even though it is a neighbour of Nigeria, which is under this type of threat.
There could be a difference in the knowledge or experience of a danger such as a terrorist attack. The non-equivalence of economic conditions is related to the significant difference in the perception of belonging to a social class. This result suggests the importance of checking the invariance of economic situations before making a comparison of its effects on well-being between European and African countries.
Political activities, security, and subjective well-being have partial measure invariance, as they satisfy the configurative invariance but not the metric invariance. There are no studies in the literature that have tested the invariance of security and political activities. However, the welfare results are consistent with those of Bieda et al., (2017);Oishi, (2006), and Zanon et al., (2014) for the partial invariance observed in SWLS. Furthermore, the results on subjective well-being in this paper show that the item "life satisfaction" is non-invariant between Germany and Ghana. This result is different from those of Bieda et al., (2017);Jang et al., (2017); Jovanović & Brdar, (2018) for whom the partial invariance of SWLS is more related to items 4 and 5 and not to item 3 (the one used in this paper). In Germany, the invariance of well-being is related to the item that is  (Bieda et al., 2017). Unlike this author, the results of this paper suggest an invariance of the perception of happiness between the two countries.
The personality traits associated with Scharwtz's values is the one dimension that is full invariant across the two countries. This result may to some extent confirm the idea that the five dimensions that form the personality traits defined by Schwartz are common to all cultures and societies (McCrae & Terracciano, 2005). Moreover, this invariance can also be observed at the level of effects on subjective well-being, with a fairly small difference in favour of Germans. Besides, the sense of security for which there is partial measurement invariance has an effect on subjective well-being that is greater for Germans.
This study had an exploratory objective, and a future paper should focus on the analysis of invariance between a large number of African and European, Asian, or American countries to examine what is comparable in the measurement and determination of subjective well-being. Also, it would be more important in the future to compare tests of invariance using covariance-based SEMs (LISREL) and variance-based SEMs (PLSPM). The fact of not having integrated scale invariance is one of the limitations of this research and to remedy this, the LISREL method should be used with data that meet the criteria of normal distribution and heterogeneity among others.

Conflicts of Interest
The author declares no conflicts of interest regarding the publication of this pa-