Current Psychology https://doi.org/10.1007/s12144-017-9742-1
Factorial/Discriminant Validity and Longitudinal Measurement Invariance of MHC-SF in Korean Young Adults Mohsen Joshanloo 1
# Springer Science+Business Media, LLC, part of Springer Nature 2017
Abstract This article investigated the factorial and discriminant validity of the Mental Health Continuum-Short Form (MHCSF) as well as its longitudinal measurement invariance in Korean samples. The samples consisted of mostly young adults. Confirmatory factor analysis and exploratory structural equation modeling were used for data analysis. The results generally supported the 3-dimensional factor structure of the scale, with some cross-loadings. Factor correlations were found to be modest, and the 3 dimensions of the scale showed differential patterns of association with external variables. Full measurement invariance was supported across four time points in a period of about 14 months. These results support the validity and longitudinal invariance of the 3 dimensions of the MHC-SF in Korea. Keywords MHC-SF . Discriminant validity . Factorial validity . ESEM . Longitudinal measurement invariance
Introduction The Mental Health Continuum-Short Form (MHC-SF; Keyes 2002) is a widely used scale to measure the emotional, social, and psychological aspects of mental well-being. Previous factor analytic research on the MHC-SF across cultures has shown that the three well-being dimensions are related yet distinct, supporting the factorial validity of the scale (Keyes et al. 2008; Lamers et al. 2011; Petrillo et al. 2015). Previous research has also documented acceptable reliability for the dimensions of the scale across various cultural groups (e.g., Perugini et al. 2017). The popularity of the scale has been growing given these promising results, and the scale is now one of the widely used measures of mental well-being. Confirmatory Factor Analysis (CFA) has been the main approach in examining the factor structure of the MHC-SF. In CFA, all of the secondary factor loadings are fixed at zero. Yet, more recent research indicates that some of the items of the MHC-SF tend to load on more than a single factor (Joshanloo 2016a, b; Joshanloo and Jovanović 2017). Therefore, there is growing concern that simple-structure CFA may not be the best available analytic approach to examine the factor structure of the scale. Constraining non-zero
* Mohsen Joshanloo
[email protected] 1 Department of Psychology, Keimyung University, 1095 Dalgubeol Boulevard, Dalseo-Gu, Daegu 42601, South Korea
secondary loadings has potential adverse consequences, including inaccuracy of the estimates, worse fit, and inflated factor correlations (Joshanloo 2017a; Joshanloo and Lamers 2016). Exploratory Structural Equation Modeling (ESEM), a more recent analytic approach, seems to be a better alternative to simple-structure CFA in capturing the factor structure of multidimensional constructs (such as mental well-being) when there are cross-loadings (Asparouhov and Muthen 2009; Marsh et al. 2014). Whereas the secondary loadings are constrained at zero in CFA, they are all freely estimated in ESEM. That is, all items are allowed to load on all factors in ESEM. ESEM yields less biased estimates and better fit in the presence of nontrivial cross-loadings (Marsh et al. 2011). In some previous studies in Iran, the USA, Serbia, the Netherlands, and Italy, ESEM has been used in tandem with CFA to study the factor structure of the MHC-SF (Joshanloo 2016a; Joshanloo 2017a; Joshanloo et al. 2017; Joshanloo and Jovanović 2017; Joshanloo and Lamers 2016). In all of these studies, ESEM has resulted in a better fit than CFA. In addition, ESEM has unraveled some nontrivial cross-loadings in the measurement model of the MHC-SF. Collectively, these results raise concern over a mere reliance on CFA when studying the factor structure of the scale. Therefore, in the present article (Study 1 and Study 2), both CFA and ESEM were used for a more comprehensive evaluation of the Korean version of the MHC-SF. The fit indices of the corresponding CFA and ESEM models can be compared to see which one provides a better fit. In the presence of nontrivial cross-loadings, ESEM virtually always provides a better fit. Furthermore, ESEM is
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more efficient in uncovering the exiting cross-loadings in measurement models, given its less restrictive approach. Concerns have also been raised over the discriminant validity between the three dimensions of emotional, social, and psychological well-being (e.g., Kashdan et al. 2008). Solely relying on CFA, a small number of previous studies have yielded rather strong correlations between the three dimensions of the MHC-SF (e.g., Perugini et al. 2017). However, this may be a side effect of using CFA. When non-zero crossloadings are fixed at zero, they are forced to manifest themselves in factor correlations, resulting in overestimated factor correlations (Asparouhov and Muthen 2009; Marsh et al. 2014). By using both CFA and ESEM, the present study enables an investigation of how various factor analytic approaches can affect estimated latent correlations. In the presence of cross-loadings, ESEM produces more accurate factor correlations, on which to base discriminant validity judgments (Marsh et al. 2014). In addition, in a small number of previous studies, the three aspects of well-being have shown very similar patterns of relationship with external variables (for a review see, Kashdan et al. 2008). This may be considered as a threat to the discriminant validity of the three dimensions of well-being. However, in many of these studies, external variables have been used that are highly inter-correlated between themselves, and are conceptually related to all well-being dimensions (e.g., Disabato et al. 2016). Such selection of external variables can result in similar correlations with the well-being dimensions, and accordingly ambiguous evidence of discriminant validity. In the present article (Study 2), three external variables were chosen based on theoretical considerations to establish the discriminant validity of the dimensions. Given the theoretically-based selection of the external variables, they were expected to show more differential relationships with the three well-being dimensions. Although the measurement invariance of the MHC-SF has been investigated across gender and cultural groups (Joshanloo 2017a; Joshanloo et al. 2013), the longitudinal invariance of the measure has received virtually no attention. An exception is Lamers et al. (2012) who used item response theory analyses to examine differential item functioning over nine months. However, the longitudinal invariance of the measure has never been established under the ESEM framework. Study 3 used ESEM to examine the longitudinal measurement invariance of the three dimensions of the scale to determine whether the longitudinal changes are caused by an actual change in the variables or changes in the measurement model over time. Together, the three studies of the article sought to provide comprehensive (yet initial) evidence on the statistical properties of the ESEM in Korea. The statistical properties of the Korean version of the MHC-SF have been investigated in two previous studies. Lim et al. (2013) reported acceptable internal consistency and test-retest reliabilities (over 4 weeks) in a Korean sample.
Lim (2014) used CFA to investigate the factor structure of the scale. The three-factor model yielded mediocre model fit. In addition, the correlations between the factors were found to be high, ranging between .77 and .91. The present studies sought to expand these findings by using ESEM along with CFA, including theoretically-chosen external variables to establish the discriminant validity of the scale. The study also sought to investigate for the first time the longitudinal measurement invariance of the three dimensions of the scale in a Korean sample. The three-factor structure of mental well-being has been replicated in various cultures, including Korea (Lim et al. 2013; Lim 2014) and other East Asian cultures (Guo et al. 2015; Yin et al. 2013). Therefore, it was expected that the three-dimensional model of well-being would be consistent with the data in the present samples.
Statistical Analysis Across the studies, model fit was assessed using the robust maximum likelihood (MLR) estimation. Missing data were handled using full information maximum likelihood (FIML). An oblique geomin rotation (ε = .5) was used in ESEM (Joshanloo and Jovanović 2017). A minimum cutoff of .90 for Comparative Fit Index (CFI), a maximum cutoff of .08 for Root Mean Square Error of Approximation (RMSEA), and a maximum cutoff of .08 for Standardized Root Mean Square Residual (SRMR) were considered as indicative of acceptable fit (e.g., Brown 2015). Models with smaller values of Akaike information criterion (AIC) and Bayesian information criterion (BIC) are preferred. Loadings >0.3 were regarded as salient indicators of the factors (Joshanloo 2017a). In the invariance analyses, the models were compared using cutoffs of .01 for ΔCFI and .015 for ΔRMSEA (Chen 2007). All the research projects included other variables that were not relevant and thus were not used in the present studies.
Study 1 This study examined the factor structure of the MHC-SF, using both CFA and ESEM.
Method Participants Data from two separate research projects were merged to make an aggregated sample of 562 Korean university students (65.1% females) for this study (Mage = 20.42, SDage = 2.48). Participation was compensated for by course credit or small gifts.
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Measure The MHC-SF (Keyes 2002) consists of 14 items to measure hedonic well-being (items 1–3), social wellbeing (items 4–8), and psychological well-being (items 9–14). Respondents indicate how often within the last month they experienced the 14 symptoms of well-being, on a scale from 1 (none of the time) to 6 (all of the time). The internal consistencies of the subscales are reported in Table 3.
Results As shown in Table 1, both the CFA and ESEM models provided acceptable fit. However, the ESEM model fitted considerably better than did the CFA model. The three ESEM factors clearly represent the three predicted well-being factors (Table 2). In ESEM, 13 out of 14 items had salient loadings (> 0.30) on their intended factor. Items 4 (Bthat you had something important to contribute to society^) had a salient loading on psychological rather than social well-being. The ESEM model revealed a large number of significant cross-loadings (Table 2), which explains the gain in model fit. The ESEM model also indicates more differentiated constructs (i.e., smaller factor correlations) because of not imposing zero constraints on the secondary loadings (Asparouhov and Muthen 2009; Brown 2015).
between the well-being factors and three external variables: openness to experience, meaning in life, and existential quest (defined as Bthe readiness to engage in the process of questioning one’s opinion regarding … existential issues^ (Pachterbeke et al. 2012, p. 2). Openness has been found to be significantly related to psychological well-being, and generally unrelated to emotional well-being (Anglim and Grant 2016). As shown in prior research, meaning in life is expected to be more strongly related to psychological well-being, than with the other two well-being dimensions (e.g., Huta 2015). Finally, considering that rationality, deep thinking, self-discovery, and intellectual flexibility are traditionally considered as integral components of a eudaimonistic (rather than hedonistic) lifestyle (Belliotti 2003), existential quest was expected to be more strongly related to psychological well-being than emotional well-being.
Method Participants The sample consisted of 338 Korean participants who responded to an online survey (62.4% females), which is part of a broader longitudinal project, the data of which are also used in Study 3. Only data produced in the first round of the project were used here (Mage = 26.19, SDage = 5.57).
Study 2
Measures
In addition to examining the factor structure of the MHC-SF in a separate Korean sample, this study examined the relationships
Openness The openness subscale of the mini-IPIP (Donnellan et al. 2006) was used (α = 0.71). The subscale has 4 items, but one extra item was also selected from the longer IPIP measure
Table 1
Fit indices 90% CI for RMSEA
Model Study 1 CFA ESEM Study 2 CFA ESEM ESEM with covariates Study 3 Configural Metric Scalar
χ2
df
CFI
SRMR
AIC
BIC
RMSEA
Low
High
ΔCFI
ΔRMSEA
318.7
74
0.924
0.047
22,483.3
22,678.3
0.077
0.068
0.085
–
–
207.1
52
0.952
0.029
22,368.8
22,659.0
0.073
0.063
0.083
–
–
261.8 159.9 231.0
74 52 85
0.915 0.951 0.944
0.056 0.033 0.033
13,621.7 13,511.9 16,154.5
13,793.8 13,768.1 16,479.5
0.087 0.078 0.071
0.075 0.065 0.060
0.098 0.092 0.082
– – –
– – –
2041.8 2091.0 2149.2
1246 1345 1378
0.899 0.905 0.902
0.047 0.050 0.051
27,636.9 27,565.4 27,554.8
28,948.8 28,557.4 28,440.1
0.058 0.054 0.055
0.054 0.050 0.050
0.063 0.059 0.059
– 0.006 −0.003
– −0.004 0.001
All χ2 values are significant at p < .001
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Standardized factor loading ESEM Emotional
CFA Social
Psychological
Study 1 Emotional 0.745*** 0.827*** 0.795***
0.050 0.134*** 0.097**
0.048 0.041 0.048
0.788*** 0.918*** 0.864***
Item 4 Item 5 Item 6 Item 7 Item 8 Psychological
0.236*** 0.208*** 0.079 0.043 −0.040
0.358*** 0.129** 0.917*** 0.448*** 0.591***
0.279*** 0.423*** −0.123*** 0.182** 0.090
0.721*** 0.618*** 0.675*** 0.561*** 0.533***
Item 9 Item 10
0.210*** 0.168***
0.122** 0.124**
0.533*** 0.565***
0.727*** 0.732***
Item 11 Item 12 Item 13 Item 14 Study 2 Emotional Item 1 Item 2 Item 3 Social Item 4 Item 5 Item 6 Item 7 Item 8 Psychological Item 9 Item 10
0.186** 0.121** 0.113* 0.179***
0.057 0.143** 0.172* 0.212**
0.619*** 0.629*** 0.564*** 0.556***
0.734*** 0.765*** 0.727*** 0.796***
0.896*** 0.843*** 0.796***
0.076* 0.030 0.093**
0.177** 0.228** 0.135** 0.007 0.050
0.181* 0.412*** 0.667*** 0.764*** 0.684***
0.537*** 0.205* 0.089 0.000 0.019
0.724*** 0.690*** 0.767*** 0.652*** 0.642***
0.210** 0.237***
0.285** 0.147*
0.346*** 0.435***
0.686*** 0.698***
0.122 0.062 0.146** 0.141**
0.378** 0.125* 0.093 0.057
0.333** 0.693*** 0.661*** 0.778***
0.686*** 0.781*** 0.776*** 0.846***
Item 1 Item 2 Item 3 Social
Item 11 Item 12 Item 13 Item 14
−0.009 0.133** 0.110**
0.911*** 0.934*** 0.903***
Loadings that are larger than .30 are shown in boldface *
p < .05; ** p < .01; *** p < .001
and added to the scale (i.e., BSpend time reflecting on things^). Items were rated on a 5-point scale from 1 = Very inaccurate to 5 = Very accurate. Meaning in Life The presence subscale of the Meaning in Life Questionnaire-Short Form (Steger and Samman 2012) was used to measure the presence of meaning in life (α = 0.90).
The measure has 3 items, rated on a 7-point scale from 1 = absolutely untrue to 7 = absolutely true. Existential Quest Pachterbeke et al.’s (2012) 9-item existential quest scale was used to measure this construct. However, Items 7 and 8 were removed, because initial analyses showed that removing them would substantially improve the alpha of the scale (from 0.64 to 0.76). The items were rated on a 7point scale from 1 = not at all true to 7 = completely true.
Results The results related to the factor structure of the scale were similar to those of Study 1 in showing that the ESEM model provided a better fit to the data structure (Table 1), and yielded less elevated factor correlations (Table 3) than did the CFA model. However, there were a few differences in the pattern of cross-loadings (Table 2). In Study 2, instead of Items 4, Item 5 (Bthat you belonged to a community like a social group, or your neighborhood^) had a salient loading on psychological well-being, and Item 11 (Bthat you had warm and trusting relationships with others^) had a salient loading on social well-being. In order to further investigate the discriminant validity of the three well-being factors, the three external variables (i.e., openness to experience, meaning in life, and existential quest) were added as manifest variables to the ESEM model. The external variables were specified to covary with each other and with the three ESEM factors. The results revealed that, as expected, openness was only significantly related to psychological well-being, and meaning and quest had their highest relationships with psychological well-being. Hence, the three well-being factors showed partially unique patterns of relationship with the external variables, indicating acceptable discriminant validity. Table 3
Alphas and latent factor correlations α
Emotional
Psychological
Social
0.89 0.76 0.88
– 0.488 0.421
0.739 – 0.433
0.747 0.863 –
0.94 0.82 0.88
– 0.497 0.406
0.734 – 0.468
0.697 0.843 –
Study 1 Emotional Psychological Social Study 2 Emotional Psychological Social
CFA and ESEM correlations are presented above and below the diagonal, respectively All correlation estimates are significant at p < .001
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Study 3 Longitudinal measurement invariance is needed to ensure that the same variables are assessed across time. It seems that the longitudinal measurement invariance of the MHC-SF has been investigated only in a single past study using item response theory analysis (Lamers et al. 2012). The present study examined the longitudinal measurement invariance of the MHC-SF in a period of about 14 months. Considering that ESEM proved to be more appropriate than CFA in the first two studies, it was used in the invariance analyses.
Method Participants and Measure Data related to the MHC-SF from a 4-wave longitudinal study were used. Only 187 participants (64.7% females) who participated in all four waves of the study were included in the present study (Mage = 26.72, SDage = 5.76). The first wave of data collection ended on Sep 18, 2015, and other waves were completed with intervals of about four months, with the last one ending on Nov 22, 2016. The study was advertised via email and social media. Participation was compensated for by electronic gift coupons (ranging from about 2.7 to 4.5 US dollars for each wave).
Results Configural, metric, and scalar invariance models were tested across the four time-points, with autocorrelated errors to account for indicator-specific effects. The fit indices are presented in Table 1. Given the large number of free parameters, the fit of the configural model was considered acceptable. The ΔCFI and ΔRMSEA values were also supportive of metric and scalar invariance. These results are consistent with the findings of Lamers et al. (2012) in a Dutch sample indicating that the MHC-SF showed no differential item functioning across four time-points during nine months.
General Discussion Consistent with prior research across cultures (e.g., Joshanloo 2016a), the a priori three-dimensional model of the MHC-SF was replicated in the present ESEM analyses. ESEM also provided a better fit with the data than did CFA. Overall, these results support the structural validity of the scale in these samples, and confirm the superiority of ESEM over CFA for evaluating the factor structure of the MHC-SF. The present study is the first to use ESEM in addition to CFA to investigate the factor structure
of the MHC-SF in an East Asian country. Despite the remarkable differences between Korea and western countries in terms of language, culture, and socio-political indicators (Hofstede et al. 2010; UNDP 2012), the results are largely in line with the previous research conducted in western cultures (e.g., Joshanloo 2017a). The results are also consistent with previous research comparing CFA and ESEM in other regions of the world. Overall, the present findings support the cross-cultural validity of the MHC-SF, and confirm that ESEM shows promise in the field of mental well-being. As in previous research (e.g., Joshanloo 2016a), the results showed a large number of non-zero cross-loadings in the measurement model of the MHC-SF. This necessitates the application of ESEM in future research with the scale to effectively take the cross-loadings into consideration. Constraining the secondary loadings at zero, as done in CFA (including bifactor analysis) can result in biased estimates. For example, previous research has shown that an undesirable consequence of using CFA is the overestimation of factor correlations (Marsh et al. 2014). After accumulating enough data across cultures, we may be able to move towards more confirmatory model testing relying largely on CFA. Yet, before we reach that point, researchers are encouraged to always include exploratory methods (such as ESEM) when investigating the factor structure of mental well-being. ESEM produced less inflated factor correlations (overall M = 0.45) than did CFA (overall M = 0.77). These results are consistent with previous research on the MHC-SF in other cultures (e.g., Joshanloo 2016a; Joshanloo and Jovanović 2017). Hence, the three constructs are found to be sufficiently discrete to be recognized as separate constructs, considering that the ESEM factor correlations were smaller than the conventional threshold of 0.80 (Brown 2015). These results are supportive of the discriminant validity of the three well-being dimensions. In addition, the three well-being factors had unique patterns of association with external variables Table 4
Relationships with covariates Standardized estimate
Emotional Openness Meaning in life Quest Social Openness Meaning in life Quest Psychological Openness Meaning in life Quest *
p < .05; ** p < .01; *** p < .001
0.077 0.460*** 0.147* −0.051 0.296*** 0.169** 0.206** 0.708*** 0.257***
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(Table 4). Prior research has also shown that the well-being factors have differential external correlates (e.g., Huta 2015; Joshanloo et al. 2017). For example, Joshanloo (2017b) showed that the three well-being dimensions had different relationships with the Big Five traits in a large American sample. Thus, the present results join the previous research to support the discriminant validity of the three well-being dimensions. The ESEM results supported the three-dimensional structure of well-being, with only a few unexpected loadings (Items 4, 5, and 11) across the studies. Items 4 and 5 have been repeatedly found to have significant relations to the social and emotional well-being factors in various cultures (Joshanloo 2016a; Joshanloo and Jovanović 2017). The loading pattern of Item 11 in Korea is unprecedented, but it is understandable because Item 11 is associated with positive interpersonal relationships, which is conceptually related to social well-being. It is noteworthy that despite the existence of a large number of significant and three salient secondary loadings, all three factors were clearly dominated by their intended items, and the contribution of secondary loadings was relatively marginal (Table 2). The results related to salient cross-loadings have been concealed in previous CFA studies in Korean samples (Lim et al. 2013; Lim 2014). Therefore, the present findings illustrate how ESEM can be used in addition to CFA for a better representation of the factor structure of the MHC-SF in Korea, and other cultures. Full measurement invariance was supported for the three dimensions across the four time-points. These results suggest that changes in the levels of the well-being dimensions over 14 months reflect actual changes in these variables rather than changes in the meaning of the constructs over time. This is an especially important insight in the field of mental well-being, where the degrees of stability and change in the levels of wellbeing are currently debated (Sheldon and Lucas 2014). The issue of the malleability of well-being is believed to have important policy implications. Longitudinal measurement invariance should be established before future research can reliably examine change trajectories of the well-being dimensions and understand how and when well-being changes. Yet, longitudinal measurement invariance has not received much attention among well-being researchers. As can be established, this is the first study to examine the longitudinal measurement invariance of the MHC-SF under the ESEM framework. These promising results lend support to the applicability of the MHC-SF in research on stability and change of mental well-being. These results, however, will need to be replicated in additional studies for firmer conclusions to emerge. The limitations of the study include the relatively small convenience samples, consisting predominantly of university students. This affects the generalizability of the results. Future studies will need to use larger and more age-diverse samples.
Also, a fruitful direction for future research would be to include more external variables to establish the discriminant validity of the three well-being dimensions. Given that the present study included only Korean samples, a thorough cross-cultural comparison was not possible. An important next step to take is to include both Korean and non-Korean samples to enable an investigation of cross-cultural measurement invariance and latent mean differences. Despite these limitations, the results presented in the current studies provide preliminary support for the Korean version of the MHC-SF. The article illustrates how ESEM can be used along with CFA for a more comprehensive assessment of psychological measures. Taken together, the results suggest that the Korean version of the MHC-SF can be used as a short scale to reliably measure the dimensions of mental well-being in Korea. Acknowledgements This research was supported by the Keimyung University Research Grant of 2017. The author wishes to thank Yeong O. Park and Sang H. Park for their contributions to this research. Compliance with Ethical Standards Conflict of Interest The authors declare that they have no conflict of interest. Human Participants and Animal Studies All procedures performed in studies involving human participants were in accordance with the conventional ethical standards. Informed Consent Informed consent was obtained from all participants included in the article.
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