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Measurement equivalence of the Kessler 6 Psychological Distress Scale for Chinese and Korean immigrants: Comparison between younger and older adults

Abstract Objectives The Kessler 6 (K6) Psychological Distress Scale is a well‐known instrument to screen for psychological distress of general populations. It is critical to perform the equivalence test of the K6 for Asian immigrant subgroups. Methods The 2012 California Health Interview Survey data were used (N = 1,210; Chinese = 640, Koreans = 570). Among 1,210, 734 were younger (18–64 years) and 476 were older (65+) adults. It was examined whether parameters in the measurement model is equivalent across the two groups, using multiple‐group analysis. The equivalence tests for Chinese and Koreans were separately performed based on different age groups (younger [18–64] vs. older [65+]). Results The younger group had good model fit (X 2 = 41.27 [df = 16, p = .001], X 2/df = 2.58, Comparative Fit Index [CFI] = 0.99, Goodness of Fit Index [GFI] = 0.98, root mean square error or approximation [RMSEA] = 0.05, standardized root mean residual [SRMR] = 0.03), and the older group also showed good model fit (X 2 = 41.70 [df = 16, p < .001], X 2/df = 2.61, CFI = 0.98, GFI = 0.97, RMSEA = 0.06, SRMR = 0.04). The model for older group indicated measurement noninvariance between Chinese and Korean immigrants (ΔX 2 = 17.86, Δdf = 5, p = .003, CFI = 0.972, ΔCFI = 0.009). The items “hopeless,” “restless,” and “depress,” were significantly nonequivalent between the two groups. Conclusions Clinicians/researchers should be aware of the potential risk for misclassification when they screen psychological distress of Chinese or Korean older immigrants. Professionals should pay attention to cross‐cultural comparability when interpreting results from the K6.

Asian immigrants are more exposed to risks of psychological distress compared to nonimmigrant populations because resettling in an alien society could cause stressful experiences in the processes of gaining employment, maintaining family cohesion, and recreating a social network (Drapeau, Marchand, & Beaulieu-Prévost, 2012). In order to address psychological distress issues of Asian immigrants, accurate screening using representative scales should be preceded.
The Kessler 6 (K6) Psychological Distress Scale (Kessler et al., 2002) is a well-known instrument that was developed to screen general populations for psychological distress through national surveys, such as the National Health Interview Survey and the National Household Survey on Drug Abuse (Kim, DeCoster, Bryant, & Ford, 2015).
According to Kessler et al. (2002), the K6 offers an "alternative to lengthy diagnostic interviews for measuring severity of symptoms and overall levels of distress." Prior studies have demonstrated that the K6 is strongly related to other gold-standard measures, such as the Diagnostic and Statistical Manual of Mental Disorders (DSM), that evaluate diverse psychological distresses (e.g., mood and anxiety disorders) (Furukawa, Kessler, Slade, & Andrews, 2003;Kessler et al., 2010;Slade, Grove, & Burgess, 2011;Sunderland, Hobbs, Anderson, & Andrews, 2012). As the population in the United States has become culturally diverse (e.g., the growth in immigrant and refugee resettlement; Stolk, Kaplan, & Szwarc, 2014), examining usability of the K6 for culturally diverse groups is very important. The term "culturally diverse" could be used as a collective term for ethnic, racial, migrant, and linguistic groups (The United Nations Educational, Scientific and Cultural Organization, 2009). The K6 scale was initially developed in English; later, researchers translated the K6 to evaluate the psychological distress of diverse target populations, including Arabic, Chinese, Italian, Japanese, and Spanish populations. However, many scholars have raised concerns about the cross-cultural comparability of the K6 (Andersen et al., 2011;Kim, Bryant, & Parmelee, 2012).
Although several studies (Andersen et al., 2011;Kim, 2010;Kim et al., 2015;Mitchell & Beals, 2011) have evaluated the performance of the K6 in screening for psychological distress in diverse racial or ethnic groups, few studies included disaggregated Asian subgroups as target populations; rather, many prior studies treated Asian subgroups as just one "Asian" group. Besides, the findings from the prior studies including aggregated Asian groups have been inconclusive. Kim (2010) and Mitchell and Beals (2011) performed validity evaluations for culturally diverse populations and reported that the K6 was an appropriate screening measure for capturing a level of psychological distress in certain racial and ethnic groups (Asian or American Indian; Kim, 2010;Mitchell & Beals, 2011). In contrast, Andersen et al.'s (2011) psychometric property examination (i.e., measurement equivalence test) concluded that the K6 was less equivalent in screening for the psychological distress of diverse racial and ethnic groups (White, African American, Asian, and Indian). Kim et al., (2015) found evidence for the measurement nonequivalence of the K6 across diverse racial and ethnic groups (18 years and older, White, African American, Hispanic/ Latino, Asian, American Indian): measurements of the functioning of items asking about "nervous," "hopeless," "restless," and "depressed" feelings varied across the different racial and ethnic groups.
Regarding the K6's measurement nonequivalence, Crockett, Randall, Shen, Russell, and Driscoll (2005) argued that the functioning of psychological distress measures could be influenced by cultural predictors (country of origin background, community circumstances, or family environment), which vary by racial and ethnic subgroup (Crockett et al., 2005). With that measurement nonequivalence of the K6, the US Department of Health and Human Services (2001) additionally proposed that the functioning of the psychological distress measures could be sensitive to different age ranges. When examining psychological distress among different age groups, some prior studies have indicated that aging is associated with decreases in the prevalence of mood disorders based on evaluation using the DSM, and this aspect has been replicated from K6 evaluations (Kessler et al., 2010;Trollor, Anderson, Sachdev, Brodaty, & Andrews, 2007). Kim and Choi (2010) also found that the unadjusted 12-month prevalence rate of psychological distress such as depression among older (60 years or older) Asian Americans was significantly lower than for younger people. However, other study has suggested different finding: Kim et al. (2012) compared Asian Americans' psychological distress across different age ranges using the K6 scale, and the findings showed that adults 75 or older indicated significantly more distress than adults aged 65-74.

| Purpose of this study
Although some studies have conducted measurement equivalence tests across different racial or ethnic groups using the K6, few studies have focused on Asian immigrant subgroups (Andersen et al., 2011;Banh et al., 2012;Kim et al., 2015). Notably, few studies have examined whether the K6 is measurement invariant across Asian immigrant subgroups (Stolk et al., 2014). In the absence of clear information about the measurement equivalence of the K6 across Asian immigrant subgroups, the current study examined whether parameters in the measurement model (K6) are equivalent across the two Asian immigrant groups (Chinese and Korean) using structural equation modeling (SEM; Kim, 2010;Kim et al., 2012).
In addition, few studies were sensitive to age effects when per-

| Measures
The K6 scale consists of six items to assess psychological distress (Kessler et al., 2002). Respondents were asked to respond to the following question: "During the past 30 days, approximately how often did you feel nervous (Item 1), hopeless (Item 2), restless or fidgety (Item 3), so depressed that nothing could cheer you up (Item 4), that everything was an effort (Item 5), and worthless (Item 6)?" (Kessler et al., 2002). The Cronbach's alpha score for young-middleaged groups was .85, and the score for older adults was .88.

| Target sample
The top five countries of birth with over 1 million immigrants living in the United States are China, India, Philippines, Vietnam, and Korea (Gryn & Gambino, 2012). Of the top five Asian immigrant groups in the United States, Chinese and Korean immigrants are coherently considered as East Asian populations. Given that these two groups form the largest portion of immigrants in the United States and have regional similarity (i.e., country of origin), this study included Chinese and Korean immigrants. The current study tried to reduce ethnic heterogeneity in order to conserve statistical power, yet still include groups where measurement noninvariance could be anticipated.

| Preliminary data evaluation
Univariate frequencies, descriptive statistics, and histograms as well as bivariate scatterplots were examined for outliers, adequate variability, skewness (<2), and kurtosis (<21) (Curran, West, & Finch, 1996): there were no outlier and no missing values for the K6 items, and there was no severe violation in normality (the highest skewness score was 3.33 on the "feeling worthless" item among Chinese), following Curran et al.'s (1996)  However, the sensitivity analysis did not show a significant difference (i.e., sample with the potential outliers vs. sample without the potential outliers), so this study kept the two cases including potential outliers. All VIF values in ordinary linear square (OLS) regression models (e.g., six different OLS models) were under 2.5. Scatterplots between the standardized residuals and scores on the six items showed that residuals fell randomly within a band of ±2 SDs. Therefore, the assumption of independence of residuals was satisfied (Lomax & Hahs-Vaughn, 2013).
2.6 | Configural model and covariance-based multiple-group invariance test 2.6.1 | Model specification and identification A single-factor structure was selected for further analyses in the current study: all loadings of error were fixed as 1, and one-factor loading (i.e., everything is an effort) was fixed as 1. In accordance with prior studies and empirical suggestions (Arnaud et al., 2010;Brooks, Beard, & Steel, 2006), the current study gave a pair of correlations on the error variances of "nervous" and "restless." For identification, the single-factor rule (i.e., at least three indicators) and the T rule, "if n is the number of observed variables in the model, the number of observations equals n (n + 1) 2 when means are not analyzed," were applied (i.e., known information > unknown information indicates overidentification, known information = unknown information indicates just identification, and known information < unknown information indicates underidentification; Kline, 2016). The single-factor rule for model specification was satisfied since K6 includes more than three items. Based on the T rule for identification, the chosen model was overidentified (known = 21 > unknown = 13).  Table 2 shows "Goodness of fit statistics for test of multiple-group invariance targeting older adults." Specifically, the second model (measurement comparison Model B in Table 2), which constrained "nervous" factor loading as equal, reported that ΔX 2 was not significantly different across the two groups. The "nervous" item was invariant across the two groups. The third model (Model C in which constrained both "nervous" and "hopeless" factor loadings as equal, found that ΔX 2 was significantly different across the two groups; these results indicate that the "hopeless" item could be problematic. The fourth model (comparison Model D in Table 2) constrained "nervous" and "restless" factor loadings as equal and showed significant difference in ΔX 2 ; these items were noninvariant across the two groups. The item "restless" could thus be problematic. The fifth model (comparison Model E in Table 2) constrained factor loadings of "nervous" and "depressed" as equal and found that ΔX 2 was significantly different, which means the "depressed" item could be problematic. Finally, the sixth model (comparison Model F in Table 2) constraining "nervous" and "worthless" factor loadings as equal did not show significantly different ΔX 2 . In conclusion, the three items of "hopeless," "restless," and "depressed" were nonequivalent across the two groups (i.e., Chinese vs. Korean immigrants 65 years of age and older). Given factor loadings on Models C-E, the magnitude of factor loadings for the three items was different between older Chinese and Korean immigrants. Overall, the "hopeless" item was more reflected in the K6 of older Chinese adults, the "restless" item was more reflected in the K6 of older Korean adults, and the "depressed" item was far more reflected in the K6 of older Korean adults (the factor loadings were consistently 0.80 or higher on older Korean adults in Models C-E when the K6 is modeled to have a single-factor structure. In particular, the "hopeless," "restless," and "depressed" items varied between older Chinese and older Korean immigrants. Given findings indicated the fact that older adults could have more complicated experiences or more accumulated stress factors than younger adults. A prior study (Jang et al., 2018) found that each Asian subgroup (18 years and older Chinese, Korean, and Vietnamese) showed different endorsement of K6 items based on language format (English format vs. non-English format): "Non-English survey users consistently showed a higher degree of endorsement compared with their English survey user counterparts" (Jang et al., 2018, p. 211); this finding highlighted the importance of understanding differences in cross-linguistic contexts. In the current study, 53% of young-middle-aged Chinese and Korean immigrants reported that they are good at speaking English (i.e., can do so well or very well), while only 17.9% of older adults perceived that they are good at speaking English. Although the CHIS allowed respondents to select Asian language options (e.g., Mandarin and Cantonese dialects, Korean, Vietnamese, and Tagalog; CHIS, 2014), there are still concerns about whether the questions administered in different languages would address the same meanings equivalently for the two (Chinese and Korean) older groups (Cole, Kawachi, Maller, & Berkman, 2000). The two groups (older Chinese and Korean immigrants) could have different ways of thinking and delivering or articulating their emotional condition (hopeless, restless, and depressed). Moreover, the interpretation of given words and sentences could be influenced by different nuances and connotations stemming from linguistic differences (Kim et al., 2012;Kim et al., 2015).
Regarding the meaning of the depression item, there could be ethnocultural variations of depressive disorders or symptomatology in the measurement of depressive experiences (Kalibatseva & Leong, 2011). Scholars have argued that the existing measures for evaluating depressive symptoms have limited cultural validity, and this limitation reduces their clinical utility with foreign-born immigrants. The symptomatology of depression described by the K6 might not be culturally sensitive to depressive experience (i.e., might be endorsed differently) in different older immigrant subgroups (Kessler & Bromet, 2013;Marsella, Sartorius, & Jablensky, 1985). Notably, the current study found that "depressed" item was highly reflected in the K6 of older Korean immigrants as compared to their counterparts (older Chinese immigrants). This difference could be related to older Chinese adults' tendency to be more likely to present their psychological problems as physical complaints (Mak & Zane, 2004). In general, "somatization is defined as the presentation of one or more medically unexplained physical symptoms without reference to their possible psychodynamic origins" (Wu & Kelley, 2007, p. 14). Scholars (Parker, Cheah, & Roy, 2001;Parker, Gladstone, & Chee, 2001;Suen & Tusaie, 2004) (Drapeau et al., 2010). Depending on target groups' own experiences of different timing in immigrating to the United States, the meaning of "hopeless" and "restless" could be differently interpreted by older Chinese and Korean immigrants.
As the current study discussed at the beginning of the discussion section, the English proficiency effect should be more thoroughly considered. Concerning the potential effects of English proficiency among older adults, the current study performed additional data analyses.

| LIMITATIONS AND SUGGESTIONS ON FUTURE RESEARCH
The current study has several limitations. The generalizability of this study could be limited by the use of CHIS data collected only from California. Thus, future investigations should examine the equivalence of the K6 across diverse target groups using nationally representative data. Furthermore, other important factors such as gender, socioeconomic status, and acculturation that can possibly contribute to observed differences were not controlled. In particular, acculturation may be directly or indirectly related to the portion of one's lifetime spent in the United States as well as to language proficiency, and these factors might affect differential responses to items to measure psychological distress.
Measurement nonequivalence in the K6 between older Chinese and Korean immigrants may imply true population-based differences in addition to methodological artifacts. Given the findings from the current study, we may raise concern about the use of the K6 as a screening assessment for older Asian immigrant subgroups: as the K6 has been frequently used for diverse populations, researchers should pay attention to cross-cultural comparability when interpreting results from the K6, especially when the K6 measure is utilized to provide prevalence of psychological distress among racially, ethnically, or linguistically diverse older populations.
Furthermore, clinicians or researchers need to be aware of the potential risk for misclassification when they try to screen for psychological distress in diverse older Asian subgroups. But again, dropping off specific items or modifying/adjusting total-score calculation strategies should be carefully performed. The decisionmaking toward ethnic relevant and culturally sensitive approaches should be based on replicated and valid empirical findings from future research. F I G U R E A 2 Model C (in Table 2). Note: Factor loadings for nervous and hopeless constrained equal APPENDIX A. Table 2). Note: Factor loadings for nervous and restless constrained equal F I G U R E A 4 Model E (in Table 2). Note: Factor loadings for nervous and depress constrained equal