Validation of the satisfaction with life scale for Korean older adults using item response theory

Abstract

As Korea is rapidly becoming an aging society, people are increasingly interested in the life satisfaction of the older adults. Therefore, the need for a tool that can precisely measure the life satisfaction of the older adults in Korea is also increasing. In this study, SWLS, which has been widely used to measure life satisfaction, was applied to Korean older adults. This study analyzed the life satisfaction of the older adults using item response theory that can supplement the limitations of existing research methods. Data from 3543 older adults who responded to the 2021 Korean Happiness Survey. As a result of the analysis, it was found that the goodness of fit of item 5 exceeded the standard value, and item 4 functioned differentially between the young-old and old-old. Based on the results of this study, it presented an empirical basis for the application of SWLS to the older adults.

Keywords

Item response theory Korean older adults satisfaction with life validation

Introduction

It is predicted that Korea will enter a super-aged society and the older adults population will account for more than 20% in 2025 (Statistics Korea, 2022). The quantitative expansion of generation of the older adults is also sparking interest in the quality of their lives. In particular, the life satisfaction is attracting people’s attention as a key indicator of well-being subjectively perceived by the older adults and an important criterion for measuring the quality of their life (Wang et al., 2022). In other words, life satisfaction of the older adults is a concept that can evaluate the current life of the older adults overall, and can serve as a useful basis for establishing policy directions for future generation of the older adults. In particular, the life satisfaction of the older adults can be used as a mechanism that can predict tragic behavior and intervene in advance for generation of the older adults in Korea suffering the disgrace of the highest suicide rate among OECD countries (Pavot and Diener, 2008).

It was found in previous domestic studies that various studies exploring the factors that affect the life satisfaction of the older adults are being actively conducted (Kwon and Cho, 2000; Wang et al., 2022). Data were accumulated as life satisfaction began to be included in the category of gerontology, and studies examining longitudinal changes or studies verifying the influence of life satisfaction as a protective factor against depression in old age to prevent suicide rates among the older adults also continued (Chung and Lee, 2011; Shin, 2010).

However, compared to such active quantitative studies on the life satisfaction of the older adults, academic interest in tools that can precisely measure it has been relatively insufficient. Yang (1994) developed a scale composed of 33 items for the general public and verified its reliability and validity. Suh and Koo (2011) developed a short-form scale to measure the life satisfaction as a cognitive aspect of happiness. Studies that validated the scale of the life satisfaction targeting police officers, college students, and teenagers in addition to the general public continued (Lim, 2012). However, there is completely no study that has precisely measured the scale of the life satisfaction for the older adults in Korea up to date.

Among overseas studies, SWLS (Satisfaction with Life Scale) developed by Diener et al. (1985) is noteworthy. Since its development, validation studies have been continuously conducted. Therefore, it was found that it can be applied to various age groups because it secured internal validity and reliability (Pavot and Diener, 2008). Due to its simplicity and robustness, SWLS is widely used in various studies. SWLS, which considered the cultural traits of each country, has been already validated in foreign countries and they are applying it to research on the older adults (Durak et al., 2010; Sancho et al., 2014; Tomas et al., 2016). This suggests that the scores of the SWLS is truly a reliable and useful scale for measuring life satisfaction, but differences in cultural norms do exist (Pavot and Diener, 2008). In other words, it means that new validation work of SWLS needs to be continuously conducted in consideration of the older adults to be measured and their nationality. In Korea, where rapid aging is progressing and a collectivist culture that is different from the West is prevalent, it is necessary to examine the item level to measure the life satisfaction of the older adults (Brossoie et al., 2022).

Most of the study methods that have verified the validity of SWLS are commonly focusing on exploratory and confirmatory factor analysis only (Pavot and Diener, 1993). It mainly consists of exploratory factor analysis to examine the structure of sub-factors and confirmatory factor analysis to verify it. Factor analysis has been widely used in scale validation because it is a statistical analysis method easy to understand. However, this analysis method has limitations in terms of the validity of the measurement because it cannot precisely estimate the difficulty and discrimination of each item in the scale that changes according to the traits of the group (Hammond, 1995).

IRT (Item Response Theory) can be considered as a method that can supplement the shortcomings of this traditional method. Because this theory analyzes the unique traits of individual items (Hambleton et al., 1991), it can precisely estimate the goodness of fit and difficulty of the items regardless of the person ability and traits (Embretson and Reise, 2013). The Rasch model, which is a type of 1-parameter model in item response theory, converts the person ability and item difficulty into logit scores, making relative comparison available (Wright, 1977). It is also effective in verifying the number of appropriate response categories by analyzing ordinal scales such as the Likert scale widely used in the field of social sciences (Andrich, 1978).

Therefore, in this study, we will review the items of the SWLS of Diener et al. (1985), which is the most widely used in domestic and foreign studies, by applying item response theory. The traits of individual items will be confirmed through strict standard values, and the appropriateness of the number of response categories will be determined in this study. In addition, we will examine whether each item functions differentially for the corresponding group through DIF (Differential Item Functioning), considering the differences between the young-old, who are newly entering the older adults group recently, and the existing older adults as well as the traits of the older adults between gender.

Method

Design

In this study, data from Korean people who responded to the 2021 Korean Happiness Survey conducted by the National Assembly Futures Institute were analyzed. The Korean Happiness Survey was conducted to find the level of happiness and the size of inequality of Koreans, predict various social phenomena, identify diverse factors that determine the happiness level and inequality of Koreans, and use the results of the survey to develop policy alternatives that can increase the level of happiness of the Korean people (NAFI, 2021). The survey was conducted in the form of a home-visiting interview between August and October 2021, and responses were received from a total of 17,357 people. In this study, among the responses of the older adults aged 65 years or older at the time of the survey, those from the older adults that responded to all five questions on the life satisfaction scale were selected as samples, and the data from a total of 3543 older adults people were analyzed. This study used secondary data that did not contain personally identifiable information, and obtained approval for review exemption (IRB No. P01-202303-01-007).

Participants

Among a total of 3543 respondents, 1616 (45.6%) were males and 1927 (54.4%) were females, and their average age was 72.96 (SD = 6.542). The number of respondents with a spouse was 2427 (68.5%), and the number of those without a spouse was 1116 (31.5%). The number of respondents who graduated from elementary schools or lower was 1351 (38.1%), and the number of respondents who graduated from middle schools and high schools or higher was 825 (23.3%) and 1367 (38.6%), respectively. The number of respondents with chronic illness was 1939 (54.7%) and the number of those without was 1604 (45.3%). 1472 (41.5%) respondents had religions, while 2071 (58.5%) respondents had no religion.

Measure

Diener et al. (1985) developed the SWLS as a tool for individuals to judge their overall life satisfaction independently. In that study, the first 48 items were collected and 10 items with high factor loadings were selected through factor analysis. Then overlapping between items and their reliability were verified, and finally a scale of five items was developed. For response category, a 7-point Likert scale ranging from 1 point “strongly disagree” to 7 point “strongly agree” was used. All of these items are positive items, and a higher total score indicates greater satisfaction with one’s life. The total score ranges from 5 to 35 points. 5 to 9 points indicate “very dissatisfied,” 10–14 points “dissatisfied,” 15–19 points a “little dissatisfied, 20 points “intermediate,” 21–25 points “a little satisfied,” and 26–30 points “satisfied,” and 31–35 points indicate “very satisfied” (Pavot and Diener, 1993).

Analysis

To verify the validity of SWLS, the Rating Scale Model (RSM) in item response theory was applied in this study. RSM is a type of Rasch model, 1-parameter model, and it is also a polytomous model that can convert an ordinal scale such as a Likert scale into an interval scale. It is a model suitable for the Likert scale, in which the psychological gap does not change significantly depending on the item (Fox and Jones, 1998). Additionally, this model has the advantage of allowing relative comparison by converting the person ability and item difficulty into log odd unit. Through this model, the goodness of fit, the difficulty, and the number of response categories can be determined. The data was analyzed using Winsteps 4.8.

This program provides statistics such as fit index, difficulty measure, and point-measure correlation coefficient. The goodness of fit of each item was analyzed by comparing it with the standard value of each index. In addition, item and person intercept were comparatively analyzed through the wright map. The appropriateness of the number of response categories of this measurement tool, which consists of a 7-point Likert scale, was identified using the thresholds between response categories calculated through category probability curve analysis. Considering that there may be differences in life satisfaction depending on the traits of older adults group, such as gender and age, this study reviewed whether there were items that function differentially in the reference group and focal group using the t-statistics calculated through differential item functioning analysis.

Results

Descriptive statistics and exploratory factor analysis

The descriptive statistics and exploratory factor analysis results of SWLS through classical test theory are shown in Table 1. The mean of item 1 was 4.32 (SD = 1.167), item 2 was 4.24 (SD = 1.213), item 3 was 4.57 (SD = 1.151), item 4 was 4.54 (SD = 1.126), item 5 was 4.13 (SD = 1.251). The reliability of the overall scale was found to be 0.910. As a result of EFA analysis, the KMO value was 0.888 and the Bartlett’s chi-square value was 11,481.337 (p < 0.001), confirming that it was a useful structure for factor analysis. The accumulated total variance was found to be 73.73%, and the component matrix was found to be 0.812–0.877.

Table 1.

Results of descriptive statistics and exploratory factor analysis.

Item	M	SD	Component	Cumulative %
1	4.32	1.167	0.877	73.73
2	4.24	1.213	0.877
3	4.57	1.151	0.866
4	4.54	1.126	0.860
5	4.13	1.251	0.812
Cronbach’s α	0.910

Measurement invariance in confirmatory factor analysis

Table 2 presents the results of measurement invariance verification through confirmatory factor analysis. Groups such as men and women, under and over 70 years of age, presence of spouse, presence of chronic illness and South Korea and United States, were distinguished, and measurement invariance was verified through configural, metric, scalar, and residual models (Widaman and Reise, 1997). For country comparisons, data from 56 American older adults collected through open data sources were analyzed. As a result of the analysis, the goodness-of-fit indices were good in all models (CFI > 0.9, SRMR < 0.03), confirming that measurement invariance of SWLS was maintained for each group.

Table 2.

Results of measurement invariance in confirmatory factor analysis.

Group	Invariance model	Model fit				Model comparison
Group	Invariance model	χ²	df	CFI	SRMR	Δχ²	ΔSRMR
Gender	Configural	164.752	10	0.986	0.016
	Metric	168.799	14	0.986	0.016	4.047	0.000
	Scalar	189.123	19	0.985	0.016	20.324	0.000
	Residual	190.183	20	0.985	0.017	1.060	0.001
Age	Configural	174.287	10	0.986	0.013
	Metric	179.716	14	0.985	0.014	5.429	0.001
	Scalar	225.999	19	0.982	0.014	51.711	0.000
	Residual	226.015	20	0.982	0.014	51.728	0.000
Spouse	Configural	163.168	10	0.986	0.018
	Metric	171.287	14	0.986	0.018	8.119	0.000
	Scalar	258.505	19	0.979	0.018	87.218	0.000
	Residual	268.237	20	0.978	0.022	9.732	0.004
Chronic illness	Configural	166.969	10	0.986	0.017
	Metric	171.075	14	0.986	0.018	4.106	0.001
	Scalar	292.356	19	0.976	0.018	121.281	0.000
	Residual	297.481	20	0.975	0.018	5.125	0.000
Country	Configural	166.312	10	0.987	0.017
	Metric	167.858	14	0.987	0.017	1.547	0.000
	Scalar	223.136	19	0.983	0.017	56.824	0.000
	Residual	259.732	20	0.980	0.017	93.420	0.000

Gender: Male/Female, Age: Under/Over 70, Spouse: Yes/No, Chronic Illness: Yes/No, Country: Korea/US.

Country: Open data source from OSF (Open Science Framework) https://osf.io/kzq7w/.

Unidimensionality and local independence

The basic assumptions of the Rasch model are unidimensionality and local independence. Unidimensionality means that one scale should be explained with only one latent trait. Local independence means that there is no relationship between item responses after taking latent trait into account. In general, when unidimensionality is satisfied, local independence is also considered to be satisfied (Hambleton and Swaminathan, 2013). These assumptions can be analyzed using standardized residuals through principal component analysis. In general, when the explained variance is 40% or more and the eigenvalues of the first contrast and the second contrast of the unexplained variance are less than 2.0, it can be judged that the assumption is satisfied (Linacre, 2020). The results of the analysis showed that raw variance explained by measures was 73.2% and unexplained variance in first contrast and second contrast was 1.44 and 1.42, respectively. Therefore, we can see that the assumptions of unidimensionality and local independence of SWLS measured for Korean older adults are satisfied.

Item fit

If the value of Mean Square residual (MnSq) of the goodness-of-fit index is higher than 1, it is considered that the item does not well explain the concept to be measured, and if the value is lower than 1, it is considered that the item is highly likely to overlap with other items in the scale (Hong and Cho, 2006). In general, when the MnSq of the goodness-of-fit index has a value between 0.7 and 1.3, it is considered that the criterion is satisfied (Smith et al., 1995). When the MnSq value is lower than 0.7, it is classified as overfit, and the item is considered to have no discriminative power from other items and have a high possibility of overlapping with other items. When the MnSq value is higher than 1.3, it is classified as misfit, and it is considered that the item does not well explain the construct of the scale. In addition, the point-measure correlation coefficient means the correlation between individual items and whole items. In general, when the value of the point-measure correlation coefficient is lower than 0.3, it can be considered that the item needs to be reviewed again (Wolfe and Smith Ev, 2007).

The analysis results of Table 3 show that the point-measure correlation coefficient of all items satisfies the standard value. However, the infit and outfit of item 5 was 1.31 and 1.32, respectively, exceeding the standard value of 1.3, so the item 5 can be considered as an overfit item. In other words, item 5 is considered a little inappropriate for explaining the life satisfaction of the older adults in Korea. However, it should be noted that there are studies that apply the satisfaction range of the goodness of fit more leniently to between 0.6 and 1.4 (Waugh and Chapman, 2005). Therefore, cross-judgment with other measurements is considered necessary rather than hastily deleting or correcting the item 5.

Table 3.

Item fit.

Item	Measure	S.E.	Infit		Outfit		p-Measure corr.
Item	Measure	S.E.	MnSq	ZSTD	MnSq	ZSTD	p-Measure corr.
1	0.10	0.03	0.85	−6.51	0.85	−6.04	0.87
2	0.33	0.03	0.96	−1.59	0.96	−1.48	0.87
3	−0.56	0.03	0.86	−5.87	0.85	−6.15	0.86
4	−0.48	0.03	0.93	−3.08	0.91	−3.56	0.85
5	0.62	0.03	1.31	9.90	1.32	9.90	0.82

Person ability and item difficulty can be visually analyzed through the wright map in Figure 1, which shows that the difficulty of the five items is distributed very close to the logit value 0. Person ability is also distributed generally evenly around 0, but there are quite a few respondents with ability exceeding 2. This indicates that it may be difficult to precisely measure the life satisfaction of respondents with high ability levels with these five items. In other words, it is necessary to find a way to adjust and distribute the difficulty of the items concentrated on the logit value 0.

Figure 1.

Wright map.

Category analysis

RSM assumes that the probability of selecting a high response category value increases when the respondent’s ability increases (Andrich, 1978). Therefore, the threshold between response categories should increase gradually. As shown in Figure 2, the probability of selecting the response categories 2 points, 4 points, and 6 points appears relatively narrow, but with the highest probability in each applicable section. Therefore, the number of response categories composed of 7-point Likert scale in the SWLS for the older adults in Korea is considered appropriate.

Figure 2.

Category probability curve.

Differential item functioning (DIF)

Through DIF, we analyzed whether there were any items that functioned differentially among the SWLS items. In this study, the analysis was focused on gender and age, which are known to have differences in life satisfaction in previous studies in Korea (Kim et al., 2016; Kwon and Cho, 2000). Among them, the age group was divided into the older adults under 70 and over 70, considering the baby boomer generation that is currently entering the generation of the older adult.

The analysis results of Table 4 show that there were no items that functioned differently according to the gender of the older adults. However, it was found that item 4 functioned differentially (t = 13.99, p < 0.001) according to the age groups classified based on 70 years of age. This indicates that even though they have the same latent trait score, the older adults over the age of 70 is more likely to respond with a higher response category value than the older adults in their 60s.

Table 4.

DIF across gender and age groups.

Item	Male		Female		DIF contrast	t	p
Item	Measure	S.E.	Measure	S.E.	DIF contrast	t	p
1	0.08	0.04	0.10	0.04	−0.02	0.61	0.434
2	0.33	0.04	0.33	0.04	0.00	0.08	0.767
3	−0.60	0.04	−0.53	0.04	−0.07	1.43	0.231
4	−0.48	0.04	−0.48	0.04	0.00	0.01	0.916
5	0.66	0.04	0.58	0.04	0.08	1.52	0.217
Item	Under 70		Over 70		DIF contrast	t	p
Item	Measure	S.E.	Measure	S.E.	DIF contrast	t	p
1	0.06	0.04	0.13	0.03	−0.07	1.87	0.171
2	0.26	0.04	0.37	0.03	−0.11	2.21	0.137
3	−0.61	0.05	−0.53	0.04	−0.07	1.47	0.224
4	−0.35	0.05	−0.57	0.04	0.21	13.99***	0.000
5	0.64	0.04	0.62	0.03	0.02	0.06	0.793

***

p < 0.001.

Discussion

In this study, a validity analysis was performed to apply the SWLS developed by Diener et al. (1985) to the older adults in Korea. The traits of individual items were reviewed through item response theory by supplementing the limitations of previous studies focused on factor analysis. This study analyzed classical test theory and item response theory in parallel. Through item response theory, it was possible to receive information on the item fit, comparison of the person ability and item difficulty, and the number of response categories. In addition, in classical test theory, internal consistency is presented only as Cronbach’s α value (0.910), but in item response theory, it is presented as the person separation reliability (0.90) and the item separation reliability (1.00), providing various information. This supported the results of previous studies showing that item response theory is more advantageous in verifying the quality of scales than classical test theory (Akif, 2021; Oishi, 2006). As a result of the analysis, it was confirmed that there is no big problem in applying the SWLS to the older adults in Korea to measure their life satisfaction. It can be seen that the five item set and the 7-point response category of the SWLS are useful. Nevertheless, continuous discussion and research are needed for the following several points that were revealed in this study.

The first is the necessity for revising item 5 (“If I could live my life over, I would change almost nothing.”). In this study, it was found that both infit and outfit of item 5 were exceeding 1.3. The goodness of fit of the item 5 can be interpreted differently depending on whether the standard for goodness of fit is applied strictly or leniently. However, it is true that the goodness-of-fit index and difficulty of the item 5 are relatively higher than other four items.

In the same context, the problems in item 5 were also constantly pointed out in previous studies. In the study by Senécal et al. (2000), who performed an exploratory factor analysis, the factor loading of item 5 was found to be significantly lower than that of other items. In the study by Vázquez et al. (2013), who performed a confirmatory factor analysis, the standardized coefficient of the item 5 was found to be much lower than that of other items. In the study by Oishi (2006), who performed a DIF analysis between Chinese and American groups using item response theory as well as factor analysis, the problems in item 5 were also pointed out.

The reason why the problems in item 5 were frequently pointed out may be because the item 5 considers the past state, while the remaining four questions consider the present state (Pavot and Diener, 2008). Unlike other items that ask the respondents to answer only by recalling the present, item 5 asks the respondents to recall both the past and present life, so the cognitive process of the item 5 is different from other items (Lim et al., 2010). In Asian cultures where people are not familiar with counterfactual thinking, there is a possibility that the item 5 is considered difficult (Oishi, 2006). Some may be satisfied with their present life but still want to change the past for a better life, while others may want to change the past because they are not satisfied with their present life. In other words, there is a possibility of non-sampling error because the respondent’s interpretation of item 5 is inconsistent. This error can be further aggravated in the process of adapting SWLS in each country (Lim et al., 2010). Therefore, it is considered necessary to consider revising the item 5 in the follow-up study.

In addition, item 4 (“So far I have gotten the important things I want in life.”) also needs to be considered. In the DIF analysis, it was found that item 4 showed a statistically significant difference between the older adult group in their 60s and those in their 70s or older. In other words, it was found that the older adults in their 60s were more likely to choose a lower response category than the older adults in their 70s or older. This is in a similar context to the analysis result in previous studies that item 4 is sensitive to age (Hultell and Petter Gustavsson, 2008; Schnettler et al., 2017). Domestic studies also report that the intercept for item 4 of the SWLS is not consistent between the age groups (Koo, 2019).

This reason for this can be found in the traits of the young older adults who are newly entering the generation of the older adults. Currently, the life expectancy of Koreans is 83.6 years, and it is gradually increasing (Statistics Korea, 2021). The period of senescence is also getting longer for the older adults as their rest of life is getting longer. The young old may be more interested in spending the remaining 20 years of their lives rather than evaluating their lives now. Therefore, the young-old have enough opportunities in the future to get the “important thing” in item 4.

In Korea, people born between 1955 and 1963 are defined as the Baby Boomer generation. They account for 14.6% of the Korean population, and since 2020, the proportion of older adults in Korea is increasing significantly as the baby boomers enter generation of the older adults (MOIS, 2023). The baby boomers show very different characteristics from the existing older generation. They are known to be economically wealthy, highly educated, and have a high desire for social participation and life (Chung and Lee, 2012). They have experienced a life different from the existing older generation, and the “important thing” in their life may not necessarily be an external thing that they can own. Considering the rapidly changing generation of older adults in Korea, it is considered that item 4 also needs to be revised.

Finally, the number of response categories also needs to be further discussed. As a result of this study, the 7-point Likert of SWLS was analyzed to be an appropriate scale. However, it was found that the response categories with 2, 4, and 6 points had relatively narrow interval with the highest probability. This may indicate that the value of the response category is less useful than the value of adjacent response category. These results are in the same context as the results of other studies, which report that the probability intervals of some response categories of SWLS overlap or change order (Akif, 2021). A study by Hanzlová (2022) also suggests reducing the number of response categories to 5 points, and reports that it is also necessary to verify 6 points which do not allow neutral responses.

For the past 30 years, many studies have suggested that SWLS response categories are useful for measuring life satisfaction. In general, it is known that the 7-point Likert scale enables more precise estimation than the 5-point Likert scale because it increases the sensitivity of each item (Finstad, 2010). A study by Allen and Seaman (2007) also reports that the 7-point Likert scale has the highest reliability. This indicates that providing as many choices as possible is more advantageous in discriminating respondents. Nevertheless, considering that Koreans are familiar with the 5-point Likert scale, it is considered necessary to apply the 5-point Likert scale in future studies.

In this study, additional analysis could not be conducted about the issues raised in the discussion above. In addition, due to the limitations of secondary data, we could not reflect various socio-demographic factors that could cause differences in the life satisfaction level of the elderly older adults. Another thing to consider when interpreting the results of this study is the timing of the survey. The survey for this study was conducted during the COVID-19 pandemic. Although life satisfaction overall decreased compared to before COVID-19, the difference in life satisfaction of older adults before and after COVID-19 was not statistically significant (Kivi et al., 2021; Yeo, 2022). Therefore, it can be seen that this survey to measure life satisfaction was not significantly contaminated. Nevertheless, in future studies, life satisfaction needs to be re-measured in an endemic state where the influence of the external environment is excluded.

Despite these limitations, it is considered timely that we tried to verify the validity of the SWLS scale for the older adults in Korea, where population aging is proceeding the most rapidly in the world. This study is significant because it examined the traits of each item one by one by applying the item response theory to precisely measure the life satisfaction of the older adults in Korea. In addition, we presented academic and empirical grounds for follow-up studies by revising the items and adjusting the number of response categories. It is hoped that continuous research on the changing generation of the older adults. in Korea will be conducted in the future based on the results of this study.

Footnotes

Data sharing statement

The current article is accompanied by the relevant raw data generated during and/or analyzed during the study, including files detailing the analyses and either the complete database or other relevant raw data. These files are available and accessible as Supplemental Material via the Sage Journals platform. Ethics approval, participant permissions, and all other relevant approvals were granted for this data sharing.

Declaration of conflicting interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by a research grant from 2023 Halla University.

Ethics approval

This research received ethics approval from the Korea National Institute for Bioethics Policy (IRB No. P01-202303-01-007).

Informed consent

All participants provided informed consent prior to their participation in this study.

ORCID iD

Kyeongwon Lee

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