Background
The aging population increases rapidly across the world. Mental-health problems such as depression and anxiety are prevalent in this population. They have both short-term and long-term consequences for individuals, families, and the whole society [
1]. According to Report on National Mental Health Development in China (2017–2018), in the past several years, prevalence estimate of depression disorder is ranged from 15 to 39.86%, and the prevalence rate of anxiety disorder is ranged from 11.51 to 22.02% among Chinese older population [
2]. Another survey with a large nationally representative sample (the China Health and Retirement Longitudinal Study (CHARLS)) also indicated that about 33.09% of Chinese older adults suffered depression disorders [
3]. In consideration of the largest population and fastest aging in China [
4], timely and effective screening of psychological distress is vital to help those at risk for early intervention.
The 6-item version of the Kessler Psychological Distress Scale (K6), a very brief instrument, has been developed to screen for non-specific psychological distress [
5]. It was initially designed for fast and accurate detection of severe mental illness among the general population. Later, it is also used in some clinical situations [
6]. It demonstrates strong psychometric properties in many populations, such as emerging adolescents [
7], adults [
8], and the elderly [
9]. It even outperforms the K10, a long-form with ten items, in screening for DSM-IV mood or anxiety disorder [
10]. Due to its excellent performance and high efficiency, it is widely employed in several major global and national surveys, such as the WHO World Mental Health (WMH) Survey, the US National Health Interview Survey [
6], the Australian National Survey of Mental Health and Well-Being [
10], the Canadian National Population Health Survey [
11], the South African Stress and Health study [
12]. It is also included in the China Family Panel Studies (Institute of Social Science Survey, Peking University, 2015), a longitudinal survey of Chinese communities, families, and individuals.
However, still some debates exist about the dimensionality of the K6, which is critical in interpreting scores on the scale. The K6 was initially developed as a measure for a unidimensional construct [
5]. The one-factor solution (with all items loading on a single factor) is also supported in most of the current studies [
6,
8,
11,
13‐
20]. Nevertheless, this model had a poor fit with the data from a large sample of adolescents in Australia, and a modified single-factor model was proposed instead [
21], allowing residual correlations among some items. Moreover, two-factor models were also reported in several studies [
6,
7,
22,
23]. Kessler et al. found a two-factor solution in the Indian sample, with an item (“Everything was an effort”) loading on the second factor [
6]. Lee et al. examined the dimensionality of the K6 among 3014 Hong Kong residents [
22]. They found a two-factor model best fit the data, with three items (“Nervous”, “Restless or fidgety”, and “Everything was an effort”) loading on the anxiety factor, another three items (“Hopeless”, “Depressed”, and “Worthless”) loading on the depression factor. Bessaha compared several models of the K6 among a large sample of emerging adults in the US and revealed that a two-factor model and a second-order two-factor model fit the data better than a one-factor model [
7]. In their two-factor model, two items (“Nervous” and “Restless or fidgety”) loaded on the anxiety factor, while the other four items loaded on the depression factor. Moreover, the anxiety factor and the depression factor loaded on psychological distress in the second-order two-factor model. Easton et al. reported a better fit of Bassaha’s two-factor model than the unidimensional model to the responses from Palestinian social workers [
23].
Traditionally, exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) are used in examining the factor structure of the K6 [
11,
21]. Mokken scale analysis (MSA) has demonstrated its unique value in addressing the problem of dimensionality [
24‐
26]. It belongs to the family of nonparametric item response theories. It assumes that all items in a scale are hierarchically ordered along the continuum of a latent construct. It is more flexible than IRT models like the Rasch model and logistic models regarding statistical assumptions and sample size. It is not restrictive with the assumption about the sigmoid-shaped curves of item characteristics [
27]. It requires a relatively small sample size to obtain a stable estimation [
28]. It is also superior to traditional factorial analysis in evaluating dimensionality and models simultaneously [
25]. Traditional factor analysis assumes a linear relation between items and latent construct under Classic Test Theory, and often suffers distortion from item-score distribution. In addition, factor analysis relies mainly on inter-item correlations. It assumes responses on high correlation item-pairs indicate similarities in the latent trait, which might be misleading due to some confusions, such as the similarity of wording [
29].
Mokken scale analysis (MSA) evaluates the fit of two models of nonparametric item response theory to data: monotone homogeneity model (MHM) and double monotonicity model (DMM). MHM, the most general Mokken model, has assumptions of unidimensionality, local independence, and monotonicity. Unidimensionality implies that all items on the scale measure the same latent construct. Local independence implies that an individual’s response to one item is not influenced by their responses to the other items on the same scale. Monotonicity implies that an individual who has a higher trait level will always obtain a higher score on the items. DMM, a particular case of MHM, has an additional assumption of Invariant Item Ordering (IIO), which assumes nonintersection of item response functions [
30]. Mokken scale analysis provides an automated item selection procedure (AISP) to help assess the latent structure of a scale [
31,
32]. The total score of all items reveals different levels of the latent construct [
25]. The first aim of our study is to employ Mokken scale analysis to evaluate the dimensionality of the K6.
The K6 is often used in the comparison of psychological distress across ages, sex, education, job categories, and nations [
6,
11,
20,
33]. Most studies implicitly assume that the K6 measures psychological distress in the same way in different groups. However, the assumption is not always correct and should be justified before comparison [
34]. Regarding the findings on the K6, women are higher than men in the mean level and prevalence of psychological distress in both adolescent and adult populations [
21]. The differences may be the results of higher vulnerability and more exposure to stress events for women, or the consequences of the way they understand some items [
11]. Few studies have examined measurement invariance for the K6 across sex, with the exceptions of Drapeau et al. and Mewton et al. [
11,
21]. Drapeau et al. used multi-group confirmatory factor analyses testing sex invariance in different age groups with data from the Canadian National Population Health Survey. They found that though some items might vary over life-course in the sex invariance patterns, the K6 hold measurement invariance across sex in general. Mewton et al. also examined sex invariance in a sample of Australian adolescents under the framework of confirmatory factor analysis. They indicated that the data didn’t support the strong invariance model, and further examination of partial invariance models revealed that all items lacked invariance in the item thresholds. Item thresholds are related to response categories. They refer to the points along the latent trait at which transition from one response category to the next occurs, for example, from “None of the time to “A little of the time” [
21]. These studies are conducted among people of different ages in western cultures. We are not sure whether the findings could be replicated in eastern cultures, such as China.
Multi-group confirmatory factor analysis is commonly used in examining measurement invariance, but it might not be accurate in figuring out the source of non-invariance. A flexible and robust iterative hybrid logit regression/ item response theory (LR/IRT) framework is recommended to deal with such a problem [
35]. The logit regression approach makes comparisons among several models representing the prediction of latent trait and group membership on item performance. In addition, item response theory (IRT) models provide the estimation of latent trait scores. Simulation studies have proven the advantage of this framework in detecting DIF in comparison to other methods. Therefore, the second aim of our study is to employ differential item functioning (DIF) analysis to evaluate measurement invariance of the K6 across sex.
In all, the present study would investigate the dimensionality of the K6 and its measurement invariance across sex with data from China Family Panel Studies in the year 2010. The results would contribute to the understanding of the factor structure of the K6 in eastern cultures and shed some light on the sex difference in psychological distress.
Discussion
The present study employed a Mokken scale analysis on the K6 to evaluate its dimensionality and structure, and employed DIF analysis to examine whether the same structure existed across sex in a national representative sample of old Chinese people. The results confirmed the unidimensionality of the instrument and justified the sum score of all the six items as an indicator of psychological distress. Our study also supported the measurement invariance of the K6 between male and female populations.
The K6 was developed as a unidimensional measure for psychological distress at the beginning [
5]. Later studies reported different factor solutions, one-factor models, and two-factor models, with exploratory factor analysis and confirmatory factor analysis in diverse samples [
13,
14,
22,
41]. The incongruent findings may result from differences in populations (e.g., emerging adults and mid-age general population) and statistical methods (e.g., principal axis factor analysis, principal component analysis). Considering the J-shape distribution of item scores in the K6, we employed a new approach, Mokken scale analysis, to address the problem in older people. The approach is more flexible, relying less on item score distributions and sample size [
42]. Mokken scale analysis is recommended as a more appropriate method for dimensionality assessment with discrete data [
43]. In addition, previous studies mainly focused on the general population, or some specific population, such as adolescents, emerging adults, but few have taped the aging population. Our findings supported the unidimensional solution, which is consistent with the original design of the K6 and most previous studies investigating the factor structure of the K6. It contributes to the understanding of the sum score of all six items of the K6 as the indicator of psychological distress among aging populations.
Measurement invariance is the premise for group comparison [
34]. Previous studies indicate that females always have more severe symptoms than males, but only a few studies have examined measurement invariance of the K6 across sex [
21]. Drapeau et al. [
11] and Mewton et al. [
21] examined measurement invariance under the framework of confirmatory factor analysis. We explored measurement invariance under the LR/IRT framework and found two items were marked as with uniform DIF in terms of Chi-square. For Item 4 (“Hopeless”), Drapeau et al. found that women had higher first three thresholds, but lower last thresholds than men. For Item 5 (“Everything was an effort”), they only found sex invariance only in the younger age group and only at cycle 7 of the study. In the India sample, this item was separated as a second factor [
6]. Mewton et al. [
21] revealed that all six items had higher endorsement rates for females than males. Since the likelihood ratio test is largely influenced by sample size, DIF magnitude is also recommended to consider in detecting items with DIF. In terms of McFadden’s pseudo R
2, the impact of the two items is negligible. Therefore, we agree with Drapeau et al. that the items in the K6 measure distress in males and females at the same degree [
11]. The sex difference in the K6 scores is a reflection of the true difference in psychological distress rather than bias in reporting of the K6 items. In general, the psychological distress for females is more severe than that for males.
We also employed exploratory factor analysis and confirmatory factor analysis to explore the dimensionality of the K6. The two-factor model is the only acceptable model in comparison to other models in terms of fit indices. Our solution is somewhat distinctive from findings in other studies, partly due to the different treatment of the data and the analytical methods. Most of the previous studies treated the data as continuous, used principal axis factor analysis for exploratory factor analysis, and maximum likelihood estimator in the CFA. We conducted the analysis based on polychoric correlation with WLSMV estimator, which is more recommended due to the ordinary nature and the non-normal distribution of the data [
44]. However, it might be hard to explain the solution itself: Why “Depressed” loads on the same factor with “Anxiety” and “Nervous” rather than “Hopeless” or “Worthless”? Why “Everything was an effort” loads on the same factor with “Hopeless” and “Worthless” rather than “Anxiety” or “nervous”. Factor analysis greatly depends on inter-item correlations, which may result in forming a scale in terms of insignificant factors (e.g., the similarity of wording) rather substantial relationship in the construct [
29]. According to traditional indexes to determine factor numbers in EFA (eigenvalues greater than one, scree plot, and parallel analysis), the one-factor solution seemed to be more reasonable. Even in Lee et al. ‘s study, EFA results also suggested a one-factor solution: only one eigenvalue was greater than 1, and explained 56.4% of the total variance [
22]. In fact, the one-factor solution is supported in most studies.
Some limitations should be acknowledged about the study. The present study among the few studies focused on examining the psychometric properties of the K6 among a relatively large and national representative sample of the Chinese older people. We only focused on the general aged population here. People in different age groups endorse the items in a somewhat different way [
11,
21]. Therefore, the conclusion might not apply to other age groups. In addition, the epidemiological character of psychological distress may not be the same in different cultures [
12]. We should be careful before generalization of the findings to populations in other cultures. Moreover, we only investigated the factor structure and sex invariance of the K6 here. Further studies can extend to other issues, such as screening efficiency in comparison with clinical diagnostic measurements.
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