Centrality of Buddhist Religiosity Scale: Adaptation and Validation of the Centrality of Religiosity Scale in a Buddhist Sample in Vietnam

This paper describes an adaptation of the Centrality of Religiosity Scale to the Buddhist religious tradition (CBRS) and a validation in Vietnam. The sample included data from 421 Vietnamese Buddhists (300 females, 121 males), aged 17 to 71 years (M=35.03, SD=13.09). The results provided evidence for good psychometric properties of the short, intermediate, and long version: CBRS-5, CBRS-10, and CBRS-15 respectively. Specifically, exploratory and confirmatory factor analyses supported the measure’s original five-factor structure: intellect, ideology, public practice, private practice, and religious experience. Furthermore, the Centrality of Buddhist Religiosity has proven to be a stable psychological construct across the three versions of CBRS and was associated strongly with the Gordon Allport’s notion of the intrinsic religious orientation. The results also suggested that the Stefan Huber’s centrality of religiosity model can capture the Buddhist religiosity and that the CBRS can be used to measure the five theoretical defined core dimensions of religiosity in Buddhism.


Introduction
Although Buddhism was introduced to Vietnam a thousand years ago and thus its teachings and practices have been incorporated into the local culture, shaping the characteristics and personalities of the Vietnamese people, psychologists have not paid due attention to Buddhist elements when studying Vietnamese people. Such a gap in the literature can partly be ascribed to the lack of valid instruments designed for Vietnamese people that measures Buddhist religiosity, religious orientation, and spirituality. As a first step in designing psychometric instruments that measure Buddhist religiosity and spirituality specifically for the Vietnamese population, researchers may translate and adapt available psychological measurements which are available in other languages to Vietnamese. Three strategies lend themselves to this: (1) constructing scales to measure Buddhist concepts such as mindfulness, compassion, and acceptance, (2) modifying already established internationally used scales by integrating Buddhist concepts, or (3) translating already established internationally used scales into Vietnamese while preserving the original religious concepts used in the scales as much as possible. In this article, we follow the second strategy in relation to the Centrality of Religious Scale (CRS) and Intrinsic Religious Orientation (IRO).
The Centrality of Religiosity Scale was based on the sociological justification of religiosity and includes five core dimensions: intellect, ideology, experience, private practice, and public practice (Huber and Huber 2012). The CRS was adapted by many researchers and translated into other languages, e.g., Brazilian, Chinese, Georgian, Germany, Hindi, Korean, Philippines, Polish, and Russian and indicated comparable reliability indices as the original version. It has been used to measure the religiosity of religion followers from many cultures because " [t]he interreligious applicability of the CRS is supported by the fact that the social expectations addressed are present in all major religious cultures" (Huber et al. 2020, p. 1). Thus, the CRS five core dimensions were generally constructed such that they could be found in many different religious cultures. Indeed, past studies (Ackert et al. 2020a(Ackert et al. , 2020bdel Castillo et al. 2020;Demmrich 2020;Esperandio et al. 2019;Lee and Kuang 2020;Huber and Huber 2012;Huber and Krech 2009;Ju et al. 2018;Stanford and Jong 2019) also reported empirical evidence for these core dimensions in many different religions and cultures. Of particular relevance are the studies by Ju et al. (2018) and Stanford and Jong (2019). Ju et al. (2018) followed the third strategy and translated the CRS-15 into Chinese. They found reliabilities (Cronbach's alpha) between 0.60 and 0.84 for the five subscales measuring the five core dimensions-half of the subscales achieved reliabilities of 0.70 or higher. Unfortunately, the authors do not report reliability for the entire CRS. Stanford and Jong (2019) exemplify the second strategy. They operationalized two to four indicators for each of the five core dimensions, partly based on the items of the CRS, but mostly integrating Buddhist concepts such as Buddha, almsgiving, or feeling of antat (non-self). The result is a 30-item Burmese Buddhist Religiosity Scale (BBRS).
Furthermore, a review of the Buddhist teachings indicates that intellect, ideology, experience, private practice, and public practice are all important factors. Specifically, Buddhism compares the intellect as the lightning torch that reveals the path toward the elimination of sufferings for practitioners. Furthermore, the Buddhist teaching considers the intellect (e.g., wisdom) as the complete understanding of all things and the realization of all truths via the Eightfold Path. These practices included (a) right view, (b) right resolve, (c) right speech, (d) right conduct, (e) right livelihood, (f) right effort, (g) right mindfulness, and (h) right concentration (Dhammcakkappavattana sutta 1993). In contrast, Buddhism teaches that the opposite of wisdom is ignorance (incorrect views, distorted perceptions, and lack of understandings on the true nature of phenomena), which is the root of all sufferings. Buddhism suggests that to attain wisdom is the only means to eliminate ignorance and to achieve the ideology of ending sufferings and liberation from reincarnation (e.g., Samara). In Buddhist terminology, the liberation from ignorance means ending all sufferings and achieving the Nirvana of mind. As mentioned earlier, such goals can only be attained via the practice of Eightfold Path, which can be conducted in both private and public settings. The public practice includes participating in Sangha's (e.g., a Buddhist community) activities such as public chanting, scripture citing, praying, and performing charity and services. The private practice includes chanting, praying, and meditating. Both kinds of practices will bring the necessary experience for the spiritual progress of the practitioner towards liberation. Thus, Buddhism includes all five CRS core dimension, suggesting that there is a reasonable theoretical basis for adapting the CRS in the Buddhist population. To our knowledge, such a well-adapted CRS will be the first self-report questionnaire to assess psychological characteristics of Buddhist' religiosity and it has the potential to compare critical characteristics of religiosity among people from different religions.
To investigate to what extent these theoretical analyses and empirical results generalize, we adapted the Centrality of Religious Scale on a sample of Vietnamese Buddhists. The goal of the present study is to evaluate if the five CRS core dimensions can also be found within Vietnamese Buddhists. Specifically, we expect that when applied in a sample of Vietnamese Buddhists, the Centrality of Buddhist Religiosity Scale (that is, an adaptation of the original CRS version to the Buddhist tradition) has good psychometric properties in all three versions-CBRS-5, CBRS-10, and CBRS-15 according to conventional goodness of fit criteria of confirmatory factor analyses. Based on studies of the original CRS (Huber and Huber 2012), we expect that the Centrality of Buddhist Religiosity Scale (CBRS) will show a stable structure with one latent variable of the centrality of religiosity with the CBRS-5 Religions 2021, 12, 79 3 of 16 and a five-factorial core dimension structure with a second-level factor of the centrality of religiosity in the CBRS-10 and CBRS-15.
Since the construct of centrality-which is the importance or salience of religiosity in personality-has a lot in common with Allport's concept of the intrinsic religious orientation (Huber 2004(Huber , 2007Huber et al. 2011), we expect high correlations between the CBRS (CBRS-5, CBRS-10, and CBRS-15) and the Intrinsic subscale of the Intrinsic-Extrinsic Religious Orientation Scale by Gorsuch and McPherson (1989) adapted to the Buddhist tradition as Buddhist Intrinsic Religiosity Orientation Scale (BIRO).

Sample
Research participants were selected based on the following criteria: (a) participants are Buddhists, including nuns, monks and lay practitioners; the lay practitioner group included both official followers (those who had taken refuge in the Three Jewels 1 ) and unofficial followers (those who had not taken refuge in the Three Jewels) who have knowledge of and faith in Buddhists teaching; (b) participants have practiced the Buddhist teachings; (c) participants have participated in Sangha activities; (d) participants have listened to or participated in the lecture of the Buddhist monks; (e) participants attended Buddhist ceremonies at the pagoda.

Centrality of Religiosity Scale (CRS)
In this study, the Centrality of Religiosity Scale by Huber and Huber (2012) was applied. The long Abrahamitic version of this scale consists of 15 Likert-items scored from 1 to 5 after the collection of the data and transformations suggested by the authors of the scale (see Table 1 for more details on the items). Although all items were scored from 1 to 5, there are three interpretations of the metric. Specifically, for items Int.1, Exp.1, Int.2, Exp.2, Int.3, and Exp.3, the metric ranges from 1 (never) to 5 (very often). For items Ide.1, Ide.2, and Ide.3, the metric assigns 1 to "not at all" and 5 to "very much so". For items Serv.1, Priv.1, Serv.2, Priv.2, Serv.3, and Priv.3, the metric ranges from 1 (never) to 5 (at least once a day). Notice that each dimension was measured using three items and the higher the mean, the stronger the dimension manifests. Furthermore, to adapt the CRS to Buddhist sample, we restructured some items such that they contained Buddhist teachings that would be familiar to participants in the study. This new version is denoted as the Centrality of Buddhist Religiosity Scale (CBRS-15). Based on the long-form, one can derive an intermediate (CRS-10) and a short version (CRS-5) of the CRS, and the same is done for the BIRO. The short version contains the items with the suffix ".1" and the intermediate This scale was developed by Gorsuch and McPherson (1989) to measure religious orientation. The I/E-R includes two subscales: intrinsic religious orientation and extrinsic religious orientation. As mentioned in the earlier paragraph, the CRS allows for group measurements of highly religious persons. In this group, it can be expected that an intrinsic religious orientation is dominant (Huber 2007;Huber et al. 2011). Based on this point and previous findings we used Intrinsic subscale of I/E-R to examine correlations between three versions of CBRS and intrinsic religious orientation. Intrinsic Religious Orientation subscale of the I/E-R consists of eight Likert-items, ranging from 1 (completely disagree) to 5 (totally agree). To adapt this scale to a Buddhist sample, we also made necessary content-wise changes in some items. We call this version, the Buddhist Intrinsic Religious Orientation (BIRO-8). Table 2 presents the original and adapted versions side to side. Although I believe in Buddhism, many other things are more important in life.
Note. Table 2 includes items of both IRO-8 and BIRO-8. IRO-intrinsic religious orientation scale. BIRO-Buddhist IRO. In the present study, the reliability of BIRO-8 measured by Cronbach's alpha was equal to α = 0.68.

Procedure
The two scales CRS-15 and I/E-R were translated to Vietnamese, then were backtranslated to English by a person who is proficient in English and has background knowledge of Buddhism. Then we discussed and completed the English version of the research. The data collection was done twice, in which in the first, we surveyed 30 Buddhists including monks, nuns and lay practitioners to get feedback on these measurement tools. Based on the feedback received, we have changed some vocabulary and content to be more in line with the Buddhist teaching (see Table 1 for an overview of the items). The official data collection was done in person and online. While most of the participants directly responded to the questionnaire at the temple after their ceremonies, 26 responded to the online questionnaire via a link sent to their email address.

Statistical Analyses
The obtained data were entered into IBM SPSS 23 software after coding. We checked the reliability of 15 items in the CBRS to select three versions: (i) the Centrality of Buddhist Religious Scale with 5 items-CBRS-5 (Cronbach's α = 0.85); (ii) the Centrality of Buddhist Religious Scale with 10 items-CBRS-10 (Cronbach's α = 0.92); and (iii) the Centrality of Buddhist Religious Scale with 15 items-CBRS-15 (Cronbach's α = 0.94). With a similar approach, we selected 6 items with high reliability and called the scale Buddhist Intrinsic Religious Orientation -BIRO-6 (Cronbach's α = 0.64). The items were selected after the confirmatory factor analysis check, resulting in a scale consisting of 6 out of 8 items: BIRO1, BIRO3, BIRO4, BIRO5, BIRO6 and BIRO7 (see Table 2 for the wording of the items).
Statistic descriptions such as mean (M) and standard deviation (SD) of CBRS-5, CBRS-10 and BIRO-6 were used. To determine the relationship between variables, Pearson's bivariate correlation coefficient was applied. To examine the properties of the CBRS Religions 2021, 12, 79 6 of 16 exploratory (EFA) and confirmation factor analysis (CFA) were used. The factor analyses are described in detail in the following paragraphs.

Exploratory Factor Analysis
Exploratory factor analysis was applied to examine the latent structure of the data and as a preliminary step to confirmatory factor analysis. The items of the CBRS-5, CBRS-10, and CBRS-15 should have at least a general factor structure that means one common factor with around 50% of explained variance in the indicators. Kaiser-Meyer-Olkin criterion for sample adequacy for factor analysis and Bartlett's test were applied to check the appropriateness of the data. The following model parameters are applied in the analysis: maximum likelihood estimator (ML) and varimax rotation which applies only if the number of identified factors is greater than 1. Factors with an eigenvalue bigger than 1 were considered relevant for models in the CFA. According to the proposed theoretical structure, one factor solution would represent the construct of "centrality of religiosity" additionally for the intermediate and the long forms factors should show up representing the five core dimensions of religiosity i.e., ideology, intellect, experience, private, and public practice.
Exploratory factor analysis of the BIRO should show an adequate sample characteristic for factor analysis according to the criteria established in the previous paragraph and a one factor structure representing the Intrinsic Religious Orientation of the Buddhist respondents.

Confirmatory Factor Analysis
Confirmatory Factor Analysis is applied to test the theoretical structure of the CBRS which is derived from the original proposed structure of Huber (2003). That is, the short version CBRS-5 should have a one factor solution with five reflective indicators which represent the five core dimensions of religiosity (i.e., ideology, intellect, experience, private, and public practice). The intermediate versions CBRS-10 should have a two-level latent structure. That means that in the first level five latent variables each representing one of the core dimensions of religiosity have every two reflective indicators (5 core dimensions × 2 items). The second level consists of one latent variable reflecting on the five first-level factors. This variable represents the psychological construct of the centrality of religiosity. With the CBRS-15 the factorial structure stays the same with one change which is that the first level factors have every three indicators (5 core dimensions × 3 items). See the result section for a graphical representation of the CFA-models. The model identification is achieved by setting one of the indicators loading to be equal 1, similarly, in secondlevel factor models one of the factor loadings of the first factors is set to be equal to 1. Each measurement model of the CBRS is checked for correlated residuals of indicators. Correlated indicator residuals are not considered as pejorative to the model but more in a way as a point of discussion.
The items of the BIRO were supplied to a CFA as well. A one factorial structure with 8 reflective indicators was modelled. Structural equation modelling (SEM) was used to correlate the latent factors of the centrality of religiosity and Buddhist intrinsic religious orientation. Latent correlations of the CBRS-5, CBRS-10, and CBRS-15 with the BIRO are reported in the result section.
Global goodness of fit criteria to assess the models were taken from the recommendation of Hu and Bentler (1999) which are: a Root Mean Standard Error of Approximation of RMSEA ≤ 0.06, 90% CI ≤ 0.06, pclose > 0.05, a Standardized Root Mean Square Residual of SRMR ≤ 0.08, a Comparative Fit Index of CFI ≥ 0.95, and a Tucker-Lewis Index of TLI ≥ 0.95. Offered indices inspect different facets of the model (i.e., absolute fit, fit adjusted for model parsimony, fit relative to a null model). That means that these indices allow a more conservative evaluation of the global model fit. Modification indices (MI) bigger than 3.84 (i.e., expected parameter changes of χ 2 > 3.84) are considered as a point of model discussion. This goes back to the fact that MI bigger than 3.84 are considered as comparison of two models with a difference of 1 degree of freedom and a critical p-value of p < 0.05. Therefore, significant model change can be achieved by following the MI and theoretical considerations. It is known that the size of MI depends on the sample size. Thus, only the biggest MI related to correlated indicator residuals are considered for iterative model adaptation. Local fit is evaluated according to a recommendation of Brown (2015) with a minimum factor loading of λ = 0.30 representing salient loading. All analyses were run with IBM AMOS software package for SEM version 26.

Scales' Descriptive Statistics and Psychometric Properties
From the data analysis on 421 Buddhists respondents of the final dataset, the mean of the CBRS-5, CBRS-10, and CBRS-15 were M = 3.71 (SD = 0.90), M = 3.76 (SD = 0.83), and M = 3.73 (SD = 0.82) respectively. The descriptive statistics of the core dimensions of each version are presented in Table 3. The highest mean value in CBRS-5 has the item of ideology (M = 4.31, SD = 0.88), the lowest mean value has the item of experience (M = 3.39, SD = 1.04). For the CBRS-10 and -15, there is a common pattern. The highest mean has the subscale of public practice and the lowest mean value is linked with the experience subscale (see Table 3 for concrete figures). For all three scales, the standard deviation does not fall under SD min = 0.79 and does not go higher than SD max = 1.32, thus one can say it fluctuates around a standard deviation of SD = 1.00. The mean value of the BIRO-6 scale is M = 3.54 with a SD = 0.67. The possible range of all presented means is from min = 1.00 to max = 5.00.
Pearson bivariate correlation analyses showed that five items of the CBRS-5 were positively correlated with one another, ranging from moderate to strong (correlations between r = 0.44 and r = 0.60, all p < 0.01). Each item correlated strongly with the composite score of the CBRS-5 (correlations between r = 0.75 and r = 0.83, all p < 0.01). Similarly, subscales of the CBRS-10 were all positively correlated with one another, ranging from moderate to strong (r from r = 0.49 to r = 0.70, all p < 0.01). The subscales were strongly correlated to the composite score of the CBRS-10 (correlations between r = 0.77 and r = 0.88, all p < 0.01). Finally, all five subscales of the CBRS-15 were strongly correlated with one another (correlation coefficients range between r = 0.53 and r = 0.76, all p < 0.01) and all subscales were strongly correlated with the total scale's score (correlations between r = 0.78 and r = 0.91, all p < 0.01). Table 1 in Appendix A reports the complete results of the correlation analyses.
Three versions' composite scores CBRS-5, CBRS-10 and CBRS-15 were strongly correlated with the composite score of BIRO-6 with the coefficients r were r = 0.68 (p < 0.01), r = 0.69 (p < 0.01), and r = 0.70 (p < 0.01) respectively. The results of the SEM show even higher values for the correlation of the factors, more on this in the paragraphs on SEM following in this result section.

Exploratory Factor Analyses
Results of the exploratory factor analyses show that the sample has sufficient statistical quality to be analyzed in a dimension reductionist way. With a KMO > 0.85 and statistically  Table 4 for more details on EFA. Results of the EFA serve as a preliminary check before the CFA. Generally, the results support the general factor solution of all but the CBRS-15 version. Still, in the CFA the planned factorial structures with second-level factor for the CBRS-10 and -15 are tested.

Confirmatory Factor Analyses
A general observation from factor analyses is that correlated indicator residuals are present in all but the BIRO model. Whereby the original BIRO Scale with 8 indicators had two indicators eliminated because of weak factor loadings λ BIRO−8 = 0.18 and λ BIRO−2 = −0.25 resulting in a scale with six items. Thus, a modified BIRO model with six items is reported in this section. The CBRS were all left with the original items without any modification. The second level factor models for the intermediate and the long versions were kept after some modifications on the uncorrelated indicator residuals. Therefore, considering the global fit, all final models met the established statistical quality criteria except for the upper bond of the confidence interval of the RMSEA. Nevertheless, a non-significant p-value of the closeness of fit function of the RMSEA (Browne and Cudeck 1993) in all models show that the point estimate of the RMSEA can be accepted as to be less than 0.06. Expecting a non-significant chi-square value with a sample size of over 400 respondents would be a very strict model test in terms of an absolute model fit, therefore no cut-off criteria were formulated corresponding to this value. Still, two models out of four (CBRS-5 and BIRO-6) display a non-significant chi-square model test which is also reflected in high values of other goodness of fit criteria based on chi-square values. See Table 5 for an overview and comparison of all CFA-models. All but the model of BIRO-6 received correlated indicators residuals. This circumstance reflects that there is some systematic covariation in the indicators which is not covered by the factor of the centrality of religiosity or the respective underlying core dimension of religiosity. Therefore, discussions of each of the local model fits follow in the consequent paragraphs considering the factor loadings and the correlated indicator residuals.

Local Fit of CBRS-5
Figure 1 represents show in a graphical way the model of CBRS-5 and its results. Straight arrows are factor loadings and curved arrows show covariances. If two elements are not connected it means that this parameter is restricted to be zero in the statistical model. What the figure shows is that factor loadings reflecting on the indicators of the core dimensions vary between λ exp1 = 0.65 and λ serv1 = 0.89, the minimum having the factor loading of religious experience and the maximum shows the indicator of public practice. All factor loadings have a positive sign. Consequently, explained variance follow the same pattern with a minimum of 42% in the indicator of religious experience and a maximum of 79% in the indicator of public practice. Factor loadings of λ > 0.70 are desirable because this would result in an explained variance of more than 50% in the indicator. This condition is met by all but the factor loading of religious experience. The residuals of the indicators of the core dimension of ideology and intellect receive a correlation of δ ide1−int1 = 0.40, which is a medium-size value. The confirmatory analysis shows satisfactory results. Thus, the local fit of the CBRS-5 shows no points of weakness. All indicators can be kept in the model. dom; p-probability value; SRMR-standardized root mean square residual; CFI-comparative fit index; TLI-Tucker-Lewis index; RMSEA-root mean square error of approximation; CI-confidence interval; pclose-probability value of the Close-Fit-function proposed by Browne and Cudeck (1993

Local Fit of CBRS-5
Figure 1 represents show in a graphical way the model of CBRS-5 and its results. Straight arrows are factor loadings and curved arrows show covariances. If two elements are not connected it means that this parameter is restricted to be zero in the statistical model. What the figure shows is that factor loadings reflecting on the indicators of the core dimensions vary between = 0.65 and = 0.89, the minimum having the factor loading of religious experience and the maximum shows the indicator of public practice. All factor loadings have a positive sign. Consequently, explained variance follow the same pattern with a minimum of 42% in the indicator of religious experience and a maximum of 79% in the indicator of public practice. Factor loadings of > 0.70 are desirable because this would result in an explained variance of more than 50% in the indicator. This condition is met by all but the factor loading of religious experience. The residuals of the indicators of the core dimension of ideology and intellect receive a correlation of = 0.40, which is a medium-size value. The confirmatory analysis shows satisfactory results. Thus, the local fit of the CBRS-5 shows no points of weakness. All indicators can be kept in the model.  Table 1. The factor of "centrality" represents the psychological concept of the centrality of religiosity.

Local Fit of CBRS-10
The confirmatory factor analysis of the CBRS-10 shows that the first level factors which represent the five core dimensions of religiosity i.e., ideology, intellect, religious experience, private and public practice with either of them having two reflective indicators have all substantive factor loadings with a range of = 0.75 to = = 0.85. Thus, explained variance in the indicators vary between 56% (priv2) and 72% (int1) and 73% (exp1) following the pattern of the factor loadings. The second level factor of the  Table 1. The factor of "centrality" represents the psychological concept of the centrality of religiosity.

Local Fit of CBRS-10
The confirmatory factor analysis of the CBRS-10 shows that the first level factors which represent the five core dimensions of religiosity i.e., ideology, intellect, religious experience, private and public practice with either of them having two reflective indicators have all substantive factor loadings with a range of λ priv2 = 0.75 to λ in1 = λ exp1 = 0.85. Thus, explained variance in the indicators vary between 56% (priv2) and 72% (int1) and 73% (exp1) following the pattern of the factor loadings. The second level factor of the centrality of religiosity reflects on the five first-level factors with factor loadings with high factor loadings where the minimum is λ exp = 0.79 and the maximum is λ publ = 0.98. All factor loadings have a positive sign. See Figure 2 for a graphical representation of the model results. The model receives four correlations of the indicator residuals. Similarly, as in the result of the CBRS-5, the residuals of the first indicators of the core dimensions of ideology and intellect have a medium size correlation of δ ide1−int1 = 0.38. A similar size correlation appears between the residuals of the first indicators of the private and public practice core dimensions with a δ priv1−serv1 = 0.40. A second link is between the residuals of the second indicators of the private and public practice core dimensions with a size of δ priv2−serv2 = 0.26. The last of the introduce residual correlations is set between the second indicator's residual of the intellect core dimensions and the first's experience core dimension residual with a size of δ int2−exp2 = 0.23. All indicators can be kept in the model the first and second level factors represent the latent structure of the ten indicators in an acceptable way. centrality of religiosity reflects on the five first-level factors with factor loadings with high factor loadings where the minimum is = 0.79 and the maximum is = 0.98. All factor loadings have a positive sign. See Figure 2 for a graphical representation of the model results. The model receives four correlations of the indicator residuals. Similarly, as in the result of the CBRS-5, the residuals of the first indicators of the core dimensions of ideology and intellect have a medium size correlation of = 0.38. A similar size correlation appears between the residuals of the first indicators of the private and public practice core dimensions with a = 0.40. A second link is between the residuals of the second indicators of the private and public practice core dimensions with a size of = 0.26. The last of the introduce residual correlations is set between the second indicator's residual of the intellect core dimensions and the first's experience core dimension residual with a size of = 0.23. All indicators can be kept in the model the first and second level factors represent the latent structure of the ten indicators in an acceptable way.  Table 1. The second level factor of "centrality" represents the psychological concept of the centrality of religiosity. The first level factors represent each the concept of a core dimension of religiosity.

Local Fit of CBRS-15
The confirmatory factor analysis of the CBRS-15 encompasses 15 items and allows modelling of the distinct core dimensions of religiosity with every three items which is a good condition in terms of model test and comparison with the intermediate and short   Table 1. The second level factor of "centrality" represents the psychological concept of the centrality of religiosity. The first level factors represent each the concept of a core dimension of religiosity.

Local Fit of CBRS-15
The confirmatory factor analysis of the CBRS-15 encompasses 15 items and allows modelling of the distinct core dimensions of religiosity with every three items which is a good condition in terms of model test and comparison with the intermediate and short versions.
The factor loadings of the first level factors have all substantial factor loadings in a range of λ priv2 = 0.73, λ priv1 = 0.85. The explained variance of the indicators moves between 53% and 72%. Considering the factor loadings of the second level factor of the centrality of religiosity the model displays high values in a range of is λ exp = 0.75 and λ publ = 0.99. Like in the models of CBRS-5 and -10, all factor loadings have a positive sign. Figure 3 demonstrates the results of the CFA in a graph. The pairs of correlated indicator residuals counting seven in this CBRS-15 model are well-recognizable. One of the correlations have a negative sign and a moderate size δ ide1−ide3 = −0.33, the remaining six are in ascending order: δ int2−exp1 = 0.22, δ priv2−serv2 = 0.23, δ int2−int3 = 0.36 δ priv1−serv1 = δ priv3−serv1 = 0.37, and δ ide1−int1 = 0.40. The total picture shows that there is a share of covariance in almost all residuals of all factors representing the core dimensions of religiosity. The link is especially strong between the residuals of both the factors of the practical core dimensions. All indicators can be kept in the model and the latent structure with two levels of factors captures the covariance in the indicators in an acceptable way. Figure 3 demonstrates the results of the CFA in a graph. The pairs of correlated indicator residuals counting seven in this CBRS-15 model are well-recognizable. One of the correlations have a negative sign and a moderate size = −0.33, the remaining six are in ascending order: = 0.22, = 0.23, = 0.36 = = 0.37, and = 0.40. The total picture shows that there is a share of covariance in almost all residuals of all factors representing the core dimensions of religiosity. The link is especially strong between the residuals of both the factors of the practical core dimensions. All indicators can be kept in the model and the latent structure with two levels of factors captures the covariance in the indicators in an acceptable way.  Table 1. The second level factor of "centrality" represents the psychological concept of the centrality of religiosity. The first level factors represent each the concept of a core dimension of religiosity.

Local Fit of BIRO-6
The local fit of the BIRO-6 statistical modelling shows no points of weakness. An interesting observation is the negative sign of the factor loading of the indicator BIRO6 with a = −0.54 it is also the smallest among others which go up to = 0.84. The range of explained variance varies between 29% and 70%. The measurement model receives no pairs of correlated indicator residuals. The indicators BIRO2 and BIRO8 had to be eliminated after the first iteration of the modelling because of very weak factor loadings and non-significance. Therefore, the final scale has six items graphically represented in Figure 4.  Table 1. The second level factor of "centrality" represents the psychological concept of the centrality of religiosity. The first level factors represent each the concept of a core dimension of religiosity.

Local Fit of BIRO-6
The local fit of the BIRO-6 statistical modelling shows no points of weakness. An interesting observation is the negative sign of the factor loading of the indicator BIRO6 with a λ BIRO6 = −0.54 it is also the smallest among others which go up to λ BIRO5 = 0.84. The range of explained variance varies between 29% and 70%. The measurement model receives no pairs of correlated indicator residuals. The indicators BIRO2 and BIRO8 had to be eliminated after the first iteration of the modelling because of very weak factor loadings and non-significance. Therefore, the final scale has six items graphically represented in Figure 4. Religions 2021, 12, x FOR PEER REVIEW 12 of 16 Figure 4. Results of the confirmatory factor analysis with the Buddhist Intrinsic Religious Orientation Scale with 6 items. For an explanation of the item abbreviations please consider Table 2.

Structural Equation Modeling of CBRS and BIRO
The latent correlations from the structural equation models of the BIRO-6 with the CBRS-15 deliver the following results

Discussion of the Psychometric Properties of the Buddhist Versions
The remarkable difference between the core dimension patterns of CBRS-5 compared to its longer counterparts-where the core dimension of ideology is much higher than the CBRS-5 and the public practice dimension is much lower-is, in our opinion, linked with the fact that there is a difference in the social investment with these dimensions. While the investment to openly believe in Buddha and Bodhisattvas is much lower, the commitment to regularly visit public religious activities is higher. Once the threshold is passed, the answers are more likely to turn, which happens with the intermediate and long version where the public practice core dimension has a higher value than the ideology. That means, once committed to a religious community, the believer shows higher values in public practice. The corresponding questions in CBRS-10 and CBRS-15 address exactly these aspects of public practice while the items linked with the core dimensions of ideology address neither importance nor salience of ideology but facets of it. . The models were trimmed by applying correlations to the residuals of the manifest variables until they had the correct size according to the established recommendations. This procedure allows control over the systematic covariance in the obtained data structure.

Discussion of the Psychometric Properties of the Buddhist Versions
The remarkable difference between the core dimension patterns of CBRS-5 compared to its longer counterparts-where the core dimension of ideology is much higher than the CBRS-5 and the public practice dimension is much lower-is, in our opinion, linked with the fact that there is a difference in the social investment with these dimensions. While the investment to openly believe in Buddha and Bodhisattvas is much lower, the commitment to regularly visit public religious activities is higher. Once the threshold is passed, the answers are more likely to turn, which happens with the intermediate and long version where the public practice core dimension has a higher value than the ideology. That means, once committed to a religious community, the believer shows higher values in public practice. The corresponding questions in CBRS-10 and CBRS-15 address exactly these aspects of public practice while the items linked with the core dimensions of ideology address neither importance nor salience of ideology but facets of it.
Our results suggest that the structural invariance of the CBRS in comparison to the original CRS and its good global fit in the new environment are corroborated by the data and analyses based on it. Nevertheless, none of the versions of the new CBR Scale could perform well in the measurement model without pair-correlated indicator residuals. The systematic covariance of some residuals in all the CBRS models shows that the CBRS captures the biggest single portion of the variance in the data but not all of it. This conclusion is also supported by the findings of the EFA where the proportions of explained variance vary between 56% and 61% for the CBRS. However, the examined CRS versions adapted to Buddhist traditions show decent model performance. Regarding the third hypothesis about the correlation of the CBRS and the BIRO, we can see a strong correlation of both latent factors which is in line with our expectations. The cross-validation with the BIRO, which, on its side, performs well with six out of eight original items, the factor of the centrality of religiosity demonstrates a high value of association with the concept of intrinsic religious orientation. This is a further argument to the suitability of the CBRS to assess Buddhist religiosity. The advantage of the CBRS is that it makes possible to grasp all domains of the religiosity which are said to be based on social expectations and are universally present in human religiousness (e.g., Huber and Huber 2012). Therefore, the general model of the centrality of religiosity, which is an evolution of the multidimensional model of Glock (1954), finds corroboration in the data from the present study in a Buddhist sample from Vietnam.

Discussion of Confirmatory Factor Analyses
When looking into the details of the statistic models, the result of the CFA with the short version of the CBRS shows that the composite score of the CBRS-5 approximates the true mean of the centrality of religiosity. The correlated residuals tell us that there is a proportion of systematic covariance in the indicators of ideology and intellect which is not linked with the remaining three indicators of the centrality of religiosity of Buddhists. This observation might be of interest in further investigations of the new scale. If it reappears in a new sample, one can open a discussion about some particularity in the Buddhist religiosity.
In the confirmatory model of the CBRS-10, the residuals of the indicators of both practical dimensions show a particular closeness. Thus, besides the other two pairs of correlated residuals of intellect with ideology and experience, there is a systematic covariance which goes beyond of what can be explained only by the factors of the single-core dimensions of religiosity and centrality of religiosity itself. One can raise the question of whether private and public practices are closely linked together. This observation might be of interest in further studies with the intermediate and the long versions of the new scale.
In the exploratory factor analysis with the CBRS-15, three indicators formed a second factor. All three were indicators of the core dimension of religious experience. Not only in the CFA of the CBRS-15 but also with the intermediate and the short versions the experiential dimension receives the weakest factor loading relative to the other core dimensions. From the absolute value of the experiential factors, one cannot say that this dimension is not well measured. However, the relatively small size of its factorial loadings raises the question about the meaning of religious experience for Buddhists.
When speaking of the modification of the original eight-item scale of IRO with its adaptation to Buddhism, it becomes evident that two of the adapted items did not fit to the expected one factorial model of the BIRO. The two items were BIRO2 (i.e., "It doesn't much matter what I believe so long as I am good".) and BIRO8 (i.e., "Although I believe in Buddhism, many other things are more important in life".). In comparison with the remaining items of the scale, these two items have a negative formulation. The opposition which is expressed in the item formulation might have led to the inconsistent respondent pattern which consequently separates these two items from the others. The second subject of the adapted scale is that the item BIRO6 (i.e., "I am mindful in daily life situations.)" is negatively associated with the factor of intrinsic religious orientation. In other words, the higher a person scores on the intrinsic religious orientation, the more he or she disagrees to be either "mindful" or to be mindful in "daily life situations". The second option suggests that intrinsic religiosity is linked stronger with some situations outside of everyday life such as religious services and private prayers and meditations. However, the first option, which is "to disagree being mindful is more intrinsic oriented," implies that our participants had a special understanding of mindfulness that warrants further study. Another reason might involve our translation of the IRO. Specifically, in the original version of the IRO scale, item 6 states that "I am religious, I don't let it affect my daily life". We replaced this original sentence by the BIRO6 because we wanted an item that could capture the influence of Buddhist practice, assuming that the Buddhist with an intrinsic religious orientation should be able to integrate his/her religious practice (i.e., mindfulness) in his or her daily life. Therefore, we used the BIRO6 which means that Buddhists practice mindfulness in everyday life situations. Nonetheless, the psychometric properties of the BIRO6 mentioned above are important to be considered in order to improve it in the overall structure of the BIRO in future studies.
We consider several major limitations of the present study. First, some authors suggested that in Christianity-influenced Western societies, women appear more religious than men (Batson et al. 1993;Beit-Hallahmi and Argyle 1996;Collett and Lizardo 2009;Miller and Hoffmann 1995;Schnabel 2017;Walter and Davie 1998). In our study sample, more women than men participated, which indicates that the sample is not representative of the overall population and sampling biases may be a concern. However, as Loewenthal et al. (2002) suggested, gender differences in religiosity were also culture-specific. Since there have not been any studies in Vietnam that examines the influence of gender on religiosity, we suggest that future researchers investigate gender influence on religiosity in Vietnam Buddhists. Second, Vietnamese Buddhism consists of three main schools: (1) Zen Buddhism, (2) Pure Land Buddhism, and (3) Vajrayana Buddhism. Although these schools may share fundamental Buddhist teachings, they have different goals (religious ideology) and practices. For example, Zen Buddhism focuses on meditation, whereas Pure Land Buddhism emphasizes praying and chanting mantras. The Vajrayana Buddhists practice both meditation and Vajrayana mantra. Since approximately two-thirds of our participants practiced Pure Land Buddhism, future research is needed to assess participants from other schools.
In summary, the present results support preliminary evidence that the translated items of the CBRS show more comparable psychometric properties than the CRS. All tested versions (i.e.,  are suitable for research on Buddhist religiosity. While the short version is enough to assess the basic notion of religiosity via a multidimensional model, the intermediate and long versions make it possible to investigate the details with the subscales representing the five core dimensions of Buddhist religiosity. The centrality of Buddhist Religiosity appears as a stable factor in a one-level and a two-level factorial structure thus the approximation with a composite score of the CBRS-5, -10, and -15 seems to be an appropriate way to do research if SEM methods are not available. The centrality of Buddhist Religiosity seems to greatly represent what theoreticians associate with the so-called intrinsic religious orientation which is based on the notions developed by Allport (1950). This is in line with the model of religiosity proposed by Huber (2003).

Institutional Review Board Statement:
The study was approved by the Institutional Review Board (or Ethics Committee) of Vietnamese National University (protocol code 4587/QÐ-ÐHQGHN and 28 December 2018).
Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Acknowledgments:
We would like to express our gratitude to students for supporting in data collection. We also want to thank Stefan Huber from the University of Bern for his very important comments that greatly improved scientific quality of the paper.

Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.