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Measurement invariance of the Satisfaction With Life Scale (SWLS) by gender and age in Angola
Personality and Individual Differences 85 (2015) 182–186
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Measurement invariance of the Satisfaction With Life Scale (SWLS) by gender and age in Angola J.M. Tomás a,⇑, M. Gutiérrez b, P. Sancho c, I. Romero d a
Department of Methodology for the Behavioral Sciences, Faculty of Psychology, University of Valencia, Spain Department of Educational and Developmental Psychology, Faculty of Psychology, University of Valencia, Spain c Department of Education, Faculty of Social Sciences and Communication, Catholic University of Saint Anthony, Murcia, Spain d Departamento de Ciências da Educação, Instituto Superior de Ciências da Educação, Universidade Katyavala Bwila, Benguela, Angola b
a r t i c l e
i n f o
Article history: Received 3 December 2014 Received in revised form 2 May 2015 Accepted 4 May 2015
Keywords: Well-being Measurement equivalence Latent mean differences Confirmatory factor analyses
a b s t r a c t Subjective well-being is a research arena that has grown almost exponentially: over the last 20 years, the number of publications on subjective well-being has increased approximately 16-fold (Diener, 2009). The cognitive aspect of subjective well-being or life satisfaction is referred to a conscious cognitive judgment of life (Diener, Emmons, Larsen, & Griffin 1985), in which person’s quality of life is globally assessed (Shin & Johnson, 1978). The Satisfaction With Life Scale (SWLS, Diener et al., 1985) is the most widely used instrument for its measurement. A reliable, valid and invariant measurement is critical for meaningful comparisons. The aim of this study is to examine the configural, metric and scalar invariance across age in the Portuguese version of the SWLS with a sample of 5630 Angolans. A standard measurement invariance procedure has been applied both across gender and age. Results shown that scalar invariance of the SWLS held across gender and age. This strong invariance allowed for meaningful latent mean comparisons. There were latent mean differences due to gender and age, but while gender differences were modest, the age differences were larger. Results are discussed in their relation with existing literature. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Subjective well-being (SWB) research is a non-trivial task that touches on many areas of social and health sciences. Its interest has grown almost exponentially: over the last 20 years, the number of publications on well-being has increased approximately 16-fold (Diener, 2009), and articles on SWB have recently been published in journals such as Science (Oswald & Wu, 2010). Simply put, SWB aims to study and understand what makes people feel well in relation to their own values and standards (Diener, Oishi, & Lucas, 2003). Diener and Emmons (1984) distinguished two parts of SWB: an affective and a cognitive component (life satisfaction). Life satisfaction is referred to a conscious cognitive judgment of life (Diener, Emmons, Larsen, & Griffin, 1985), in which person’s quality of life is globally assessed according to his/her chosen criteria (Shin & Johnson, 1978). Life satisfaction has mostly been considered to be a state variable, something present and contextual (Hultell & Gustavson, 2008). However, other authors have found that life ⇑ Corresponding author at: Department of Methodology for the Behavioral Sciences, Faculty of Psychology, University of Valencia, Av. Blasco Ibañez, 21, Valencia 46010, Spain. E-mail address: [email protected] (J.M. Tomás). http://dx.doi.org/10.1016/j.paid.2015.05.008 0191-8869/Ó 2015 Elsevier Ltd. All rights reserved.
satisfaction may also reflect habitual judgment strategies that are closer to a trait. For example, Lucas (2007) provided evidence that around 34–38% of the variance in life satisfaction is trait variance. The stability of scores across the life span can be considered evidence of this trait-alike behavior of life satisfaction. A widely used measure of life satisfaction is the Satisfaction With Life Scale (SWLS, Diener et al., 1985). It aims at measuring a single trait of life satisfaction that could be used across the life-span. The scale has been validated across countries and areas of research. The bulk of validation studies have used the English version of the scale, among others: Diener et al., 1985; Lucas, Diener, & Suh, 1996; Pavot, Diener, Colvin, & Sandvick, 1991; or Shevlin & Bunting, 1994. Nevertheless, the scale has also been translated and validated in numerous countries and languages: French (Blais, Vallerand, Pelletier, & Briere, 1989); Spanish (Atienza, Pons, Balaguer, & García-Merita, 2000); Dutch (Arrindell, Heesink, & Feij, 1999); Chinese (Sachs, 2004); Hebrew (Anaby, Jarus, & Zumbo, 2010); Portuguese (Gouveia, Milfont, da Fonseca, & Coelho, 2009; Sancho, Galiana, Gutiérrez, Francisco, & Tomás, 2014); or German (Glaesmer, Grande, Braehler, & Roth, 2011). Most of this research has found a solid one-factor structure. Measurement invariance of the SWLS has also deserved careful and extensive attention. Tucker, Ozer, Lyubomirsky, and Boehm
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(2006) tested measurement invariance in Russia and North America. Gouveia et al. (2009) tested invariance in five Brazilian subpopulations, founding configural invariance. However, metric or scalar invariance were not tested. Sex differences have always been of great interest, and therefore it is not a surprise that gender invariance of the SWLS has been extensively studied (as a clue for its importance, a search of sex measurement invariance in the web of science from 2005 to now retrieved 526 entries). Shevlin, Brunsden, and Miles (1998) tested measurement invariance across sexes in a sample of British undergraduates and found evidence for strict invariance without latent mean differences. Atienza, Balaguer, and García-Merita (2003) surveyed Spanish high-school students and tested for sex invariance: they found a lack of metric invariance for two items, but failed to test for scalar equivalence. Wu and Yao (2006) also studied gender invariance of Taiwanese undergraduates. Their results showed factor loadings and uniquenesses equivalence, but failed to test for equal intercepts and therefore strict invariance was lacked. 2966 Swedish students for becoming teachers were also surveyed and SWLS gender and age invariance tested (Hultell & Gustavson, 2008). Gender scalar invariance was achieved. This same result held for a large and representative sample of Norwegian (Clench-Aas, Nes, Dalgard, & Aarø, 2011). Indeed, gender strict invariance was tenable across sexes. Finally, Moksnes, Løhre, Byrn, and Haugan (2014) also tested measurement equivalence in Norwegian adolescents, and found support only for metric invariance. An extremely interesting issue in the field of subjective wellbeing is how life satisfaction changes during the life-span (Blanchflower & Oswald, 2008; Easterlin, 2006), and several authors have also considered age potential differences and factorial invariance. For example, Wu, Tsai, and Chen (2009) examined longitudinal measurement invariance of students and found evidence for scalar equivalence over a period of several months. Atienza et al. (2000) studied the scale in two Spanish samples of elderly and students, but only tested for configural and metric equivalence. Clench-Aas et al. (2011) explored the dimensionality and measurement equivalence of the SWLS, across age, in a representative sample of Norwegians. They found partial measurement invariance. The German version of the scale was tested for age measurement equivalence across the life-span by Glaesmer et al. (2011). They found evidence for both gender and age equivalence, but they only tested for configural and metric invariance, not for scalar one, which would allow for meaningful mean comparisons. The findings on the age and life satisfaction relationship have been rather inconsistent (Pinquart & Sorensen, 2000), with some studies reporting a weak positive linear relation (e.g., Hansson, Hillerås, & Forsell, 2005), others a weak negative one (e.g., Chen, 2001), and still others a curvilinear relationship, either with subjective well-being highest among those in middle age (e.g., Easterlin, 2006) or U-shaped in relation to age (Blanchflower & Oswald, 2004, 2008). Finally, some studies have found no relationship at all (e.g., Diener & Suh, 1998). Therefore, previous research has found somehow conflicting results, with samples been mainly young people and university students from developed countries. Additionally, several of these studies have not tested the full range of equivalence restrictions. Thus, this field needs further scrutiny (Realo & Dobewell, 2011). The aim of this study is to examine the whole range of invariance restrictions in the Portuguese version of the SWLS in Angola. 2. Method 2.1. Participants and procedure The participants in this study come from three independent cross-sectional surveys made in Angola within 2013–2014: school
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and high-school students, young adults, and adults. For the purposes of this study the samples were aggregated into a single one with some socio-demographic variables and the items of the SWLS. The sample consisted of 5630 Angolans with ages ranging from 14 years up to 65 years old. 50.8% were men (N = 2860), while women were 49.2% (N = 2770). Six age groups were considered, each group consisting of 10 years with the exception of the two first groups to divide in those under age majority (less than 18 years old) and young adults. The groups and their sample sizes were then: 34.4% (N = 1937) were 14–17 years old; 30.08% (N = 1694) were 18–24 years old; 17.2% (N = 966) were in the range 25–34; 8.5% (N = 476) were 34–44; 6% (N = 338) were 45–54; and 3.9% (N = 219) were in the range 55–65 years old. 2.2. Measures The surveys included socio-demographic variables and other scales, but the one of interest is the SWLS, composed of five items ranging from 1 (=totally disagree) to 5 (=totally agree). Author’s Portuguese version of the SWLS was used (Diener, 2009). 2.3. Statistical analyses A standard measurement invariance routine using a set of Confirmatory Factor Analyses estimated in EQS 6 was applied, with ML estimation with robust corrections. Establishing measurement invariance involves running a set of increasingly constrained confirmatory factor analyses, and testing whether differences between these models are significant, either from a statistical or a practical point of view (van de Schoot, Lugtig, & Hox, 2012). First, a one-factor model was separately tested on each group. After the determination of good fit for each group, a configural model was tested simultaneously for the groups and established as the baseline model. This model tested configural equivalence, or same factor structure holding for all groups. Then, factor loading were constrained across groups (metric invariance). Metric invariance tests whether respondents across groups attribute the same meaning to the latent construct under study. Then, a model with constrained item intercepts tested for scalar invariance which implies that the meaning and the levels of the underlying items (intercepts) are equal across groups, and accordingly groups may be compared on their scores on the factor. Finally a test of strict invariance, equal errors, was also proposed, although it is a very stringent test that it is not really needed for mean comparisons (Millsap & Olivera-Aguilar, 2012). The plausibility of the models was assessed using several fit criteria: (a) chi-square statistic; (b) the comparative fit index (CFI) and (c) the root mean squared error of approximation (RMSEA). Hu and Bentler (1999) suggested that a CFI of at least .90, and a RMSEA less than .06 together, would indicate a good fit. Nevertheless, cut-off criteria established in Hu and Bentler (1999) should also be taken with caution as they depend on sample size (Fan & Sivo, 2005). With larger sample sizes (N > 250) RMSEA lower the .05 and CFI of more than .95 are probably needed to stablish good baseline models to start the invariance routine. Models in the invariance routine are nested, and may therefore be compared with two rationales, the statistical and the modeling one. The statistical employs v2 differences (Dv2) to compare constrained to unconstrained models, with non-significant values suggesting multigroup equivalence. This statistical approach has been criticized (Cheung & Rensvold, 2002), recommending the modeling approach that uses practical fit indices to determine the overall adequacy of a fitted model. From this point of view, if a parsimonious model (such as the ones that posit invariance) evinces adequate levels of practical fit, then the sets of equivalences are considered a reasonable approximation to the data. Usually, CFI
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differences (DCFI) are used to evaluate measurement invariance. CFI differences lower than .01 (Cheung & Rensvold, 2002) are usually employed as cut-off criteria. 3. Results Table 1 shows descriptive statistics for the overall sample and the correlation matrix for the total sample and also for female and male groups. The alpha for the scale in the overall sample was adequate (a = .73). 3.1. Gender invariance Previous to the multi-group analyses, the one-factor model was separately tested in men and women. The model adequately fitted in both samples: men (v2(5) = 21.66, p = .001, CFI = .99, RMSEA = .03) and women (v2(5) = 41.57, p < .001, CFI = .99, RMSEA = .05). Then the set of increasingly constrained multi-sample confirmatory factor analyses, were estimated and tested. Table 2 shows the sequence of models and their differences to baseline (configural) model. The comparison of models yielded quite clear results. Metric invariance was pretty clear, as both statistical and practical approaches to model comparison agree that there were no statistically significant differences between configural and metric invariant models, and therefore the more parsimonious (invariant) model could be retained. Indeed practical fit indices remained extremely
Table 1 Items’ means, SD, and correlation matrix of the items for the total sample and female and male subjects. Items
SD
I1
I2
I3
I4
I5
Total sample I1 3.36 I2 2.99 I3 3.42 I4 3.12 I5 2.69
Mean
1.17 1.22 1.28 1.29 1.34
1 .287⁄⁄ .345⁄⁄ .288⁄⁄ .213⁄⁄
1 .509⁄⁄ .413⁄⁄ .292⁄⁄
1 .455⁄⁄ .342⁄⁄
1 .356⁄⁄
1
Women I1 I2 I3 I4 I5
3.35 3.10 3.40 3.19 2.68
1.18 1.20 1.29 1.30 1.36
1 .293⁄⁄ .359⁄⁄ .329⁄⁄ .234⁄⁄
1 .533⁄⁄ .429⁄⁄ .258⁄⁄
1 .490⁄⁄ .374⁄⁄
1 .376⁄⁄
1
Men I1 I2 I3 I4 I5
3.38 2.98 3.48 3.07 2.70
1.14 1.23 1.25 1.28 1.33
1 .283⁄⁄ .332⁄⁄ .249⁄⁄ .193⁄⁄
1 .490⁄⁄ .395⁄⁄ .323⁄⁄
1 .422⁄⁄ .311⁄⁄
1 .335⁄⁄
1
Table 2 Set of hierarchical models to test for measurement invariance. Model
SB
v2
df
DSBv2
Ddf
CFI
Gender invariance Configural 63.08 Metric 78.12 Scalar 116.08 Strict 142.26
10 14 18 23
7.79 31.76*
4 8 13
.989 .987 .986 .984
Age invariance Configural 100.34 Metric 145.59 Scalar 377.14 Strict 480.97
30 50 70 95
48.26* 189.8*
20 40 65
.983 .977 .978 .970
similar or even slightly improved (i.e. the RMSEA). When item intercepts were made invariant (scalar invariance) by gender the chi-square difference was statistically significant (p < .001), but differences in practical fit were minimum, less than .01 for the CFI, the most severe criteria. The same happened when strict invariance was tested, as practical differences in fit were irrelevant. Accordingly, the set of equivalences are considered tenable, and the SWLS may be considered equivalent by gender. Unstandardized and standardized factor loadings and intercepts in the retained model are presented in Table 3. The latent mean values were fixed to zero for males, making men the reference group. Latent mean value for women showed higher life satisfaction for them, although the effect size was low (a = 0.04, z = 2.74, p < .05, d = 0.08). 3.2. Age invariance With respect to age invariance, again previous to the invariance routine the one-factor model was separately tested in each age subsample. Again model fit was adequate for all samples: 14–17 years (v2(5) = 28.09, p < .001, CFI = .97, RMSEA = .04); 18–24 years (v2(5) = 30.14, p < .001, CFI = .98, RMSEA = .05); 25–34 years (v2(5) = 18.18, p = .002, CFI = .98, RMSEA = .05); 35–44 years (v2(5) = 13.59, p = .003, CFI = .98, RMSEA = .06); 45–55 years (v2(5) = 5.54, p = .36, CFI = .99, RMSEA = .02); 55–64 years (v2(5) = 5.67, p = .35, CFI = .99, RMSEA = .02). Given that the one-factor model fitted well in each separate sample, the set of models for the invariance routine was tested. Table 2 shows goodness-of-fit indices for the sequence of models and their differences to baseline (configural) model. Results were quite clear again. Both metric and scalar invariance seem reasonable. Although from a strict chi-square difference test both models were statistically worse than configural model, the practical fit indices were similar or even slightly improved (i.e. the RMSEA). Differences in practical fit were minimum, less than .01 for the CFI, the most severe criteria. As it was the case with gender invariance, a strict invariance model was also tested and considered tenable. Accordingly, the set of equivalences are considered tenable, and the SWLS may also be considered equivalent by age. Unstandardized and standardized factor loadings and intercepts in the retained model are presented in Table 3. The latent mean values were fixed to zero for the first age group (14–74 years), making this the reference group. Therefore, the mean differences are always the group of age considered against those 14–17 years old. All latent mean (differences) estimated for the other age group showed that the youngest group was more satisfied than the rest: 18–24 years (a = 0.261, z = 12.90, p < .01, d = 0.52); 25–34 years (a = 0.463, z = 16.25, p < .01, d = 0.85); 35–44 (a = 0.410, z = 12.46, p < .01, d = 0.80); 45–54 (a = 0.507, z = 13.08, p < .01, d = 0.96): 55–65 (a = 0.428, z = 9.05, p < .01, d = 0.76). The effect sizes may be considered moderate to large. 4. Discussion
DCFI
RMSEA
90% CI
.002 .003 .005
.043 .040 .041 .040
.033–.054 .032–.049 .033–.053 .033–.048
.006 .005 .013
.050 .045 .053 .053
.039–.061 .037–.054 .045–.062 .047–.060
Notes: SBv2 = Satorra–Bentler chi-square; df = degrees of freedom; D = differences. * p < .05.
Results have found strict invariance of the SWLS held across gender and age in a sample of more than five thousand Angolans. This strong invariance allowed for meaningful latent mean comparisons and here, again, results were clear. There were latent mean differences due to gender and age, but while gender differences were modest, the age differences were larger. How does the results accommodate within the existing evidence? With respect to gender invariance, among the six papers reviewed, three of them found evidence for scalar (strong) equivalence (Shevlin et al., 1998; Hultell & Gustavson, 2008; and Clench-Aas et al., 2014). Two papers found metric invariance
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J.M. Tomás et al. / Personality and Individual Differences 85 (2015) 182–186 Table 3 Unstandardized and standardized loadings and intercepts for scalar invariant models across age and gender. Gender
Age
Men
k1 k2 k3 k4 k5 m1 m2 m3 m4 m5
Women
14–17
18–24
25–34
35–44
45–54
55–65
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
1 1.5 1.8 1.6 1.2 3.3 3.0 3.4 3.1 2.7
.43 .65 .73 .62 .46
1 1.5 1.8 1.5 1.2 3.3 3.0 3.4 3.1 2.7
.46 .67 .76 .65 .48
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.38 .62 .67 .53 .40
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.43 .68 .72 .58 .45
1 1.5 1.7 1.4 1.1 3.5 3.3 3.8 3.4 2.9
.43 .68 .72 .59 .46
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.44 .68 .72 .59 .46
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.44 .69 .73 .60 .47
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.47 .71 .75 .63 .49
(Moksnes et al., 2014; Wu & Yao, 2006), but one of them did not tested for scalar invariance (Wu & Yao, 2006). Only one research failed to find scalar and/or metric invariance (Atienza et al., 2003). When mean differences were tested, they were either non-significant or of small magnitude. We could therefore conclude that our results are in line with most of the accumulated evidence. Regarding age invariance of the SWLS, our results also point out at a scalar invariance that allows for latent mean comparisons. This result is coincident with most of the literature that has also found evidence for scalar invariance across age groups (Blais et al., 1989; Durak, Senol-Durak, & Gencoz, 2010; Gouveia et al., 2009; Siedlecki, Tucker-Drob, Oishi, & Salthouse, 2008; Wu et al., 2009). Some studies on measurement invariance found weak equivalence but failed to test for scalar equivalence (Atienza et al., 2000; Glaesmer et al., 2011). However, there are also important studies that found a lack of scalar invariance for the SWLS (Clench-Aas et al. (2011); Hultell & Gustavson, 2008). Clench-Aas et al. (2011) study, in particular, was based on a large and representative sample of the Norwegian population that included the age range 14– 79 years old. Since in our study evidence of scalar invariance was found, we proceeded to compare the latent means of life satisfaction. There were differences between the youngest and the other groups, but latent means remained almost unchanged from 25 till 65 years old. Studies disagree about this point, with evidence in all directions: weak positive linear relation (e.g., Hansson et al., 2005), weak negative one (e.g., Chen, 2001); a curvilinear relationship, either with subjective well-being highest among those in middle age (e.g., Easterlin, 2006) or U-shaped in relation to age (Blanchflower & Oswald, 2004, 2008); or even no relationship at all (e.g., Diener & Suh, 1998). All studies that found an age effect on life satisfaction agreed that the effect was weak. The plateau we have observed in life satisfaction in most age groups could be explained because different ages may judge their life satisfaction as dependent on different factors, and this may moderate their perceptions. Oishi, Diener, Suh, and Lucas (1999) have, for example, proposed a value as moderator model which predicts that as individual’s age, changes in values lead to changes in the determinants of their life satisfaction. Therefore, further studies should shed light on this age effect, but before measurement invariance should be tested and ensured.
5. Conclusions The main aim of this research was to study the invariance of psychometric properties of the Portuguese version of the SWLS in Angola. Conclusions are simple to summarize. Strict invariance of the SWLS held across gender and age in a sample of more than five thousand Angolans. This strong invariance allowed for meaningful
latent mean comparisons and here, again, results were clear. The direct implication of this finding is that the SWLS may confidently been used in Angola, both across gender and age, and meaningful comparisons among groups are possible. Current research has some limitations, the incidental sampling and the cross-sectional nature of the design being the most obvious. Most of the evidence about the relationship between age and subjective well-being is based on cross-sectional studies, asking different people of different ages to report their life satisfaction or happiness. Unfortunately, data following the same person over the years is seldom considered in studies of the relationship between subjective well-being and ageing. Only a handful of studies that have longitudinal data have focused on the stability of subjective wellbeing over time (e.g., Baird, Lucas, & Donnellan, 2010). This is again a line for future research. Finally, another limitation of current results that points out for future research, has been the focus on a unidimensional measure of life satisfaction. Other authors have advocated for the multidimensional nature of life satisfaction (for example Huebner, 1994), and results could well vary with respect to those found in this research if domain-specific life satisfaction is analyzed across gender and age. References Anaby, D., Jarus, T., & Zumbo, B. D. (2010). Psychometric evaluation of the hebrew language version of the satisfaction with life scale. Social Indicators Research, 96, 267–274. Arrindell, W. A., Heesink, J., & Feij, J. A. (1999). The satisfaction with life scale (SWLS): Appraisal with 1700 health young adults in the Netherlands. Personality and Individual Differences, 26, 815–826. Atienza, F. L., Balaguer, I., & García-Merita, M. L. (2003). Satisfaction with life scale: Analysis of factorial invariance across sexes. Personality and individual Differences, 35, 1255–1260. Atienza, F. L., Pons, D., Balaguer, I., & García-Merita, M. L. (2000). Satisfaction with life scale: Analysis of factorial invariance for adolescents and elderly persons. Perceptual and Motor Skills, 87, 519–529. Baird, B. M., Lucas, R. E., & Donnellan, M. B. (2010). Life satisfaction across the lifespan: Findings from two nationally representative panel studies. Social Indicators Research, 99, 183–203. Blais, M. R., Vallerand, R. J., Pelletier, L. G., & Briere, N. M. (1989). The satisfaction with life scale: Canadian-French validation of the satisfaction with life scale (L’Echelle de satisfaction de vie: Validation Canadienne-Francaise du ‘‘satisfaction with life scale’’). Canadian Journal of Behavioral Science, 21, 210–223. Blanchflower, D. G., & Oswald, A. J. (2004). Well-being over time in Britain and the USA. Journal of Public Economics, 88, 1359–1386. Blanchflower, D. G., & Oswald, A. J. (2008). Is well-being U-shaped over the life cycle? Social Science and Medicine, 66, 1733–1749. Chen, C. (2001). Aging and life satisfaction. Social Indicators Research, 54, 57–79. Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing MI. Structural Equation Modeling, 9, 235–255. Clench-Aas, J., Nes, R. B., Dalgard, O. D., & Aarø, L. E. (2011). Dimensionality and measurement invariance in the satisfaction with life scale in Norway. Quality of Life Research, 20, 1307–1317. Diener, E. (2009). Introduction the science of well-being: Reviews and theoretical articles by Ed Diener. In E. Diener (Ed.), The science of well-being: The collected works of Ed Diener (pp. 1–10). Dordrecht, New York: Springer.
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Measurement invariance of the Satisfaction With Life Scale (SWLS) by gender and age in Angola J.M. Tomás a,⇑, M. Gutiérrez b, P. Sancho c, I. Romero d a
Department of Methodology for the Behavioral Sciences, Faculty of Psychology, University of Valencia, Spain Department of Educational and Developmental Psychology, Faculty of Psychology, University of Valencia, Spain c Department of Education, Faculty of Social Sciences and Communication, Catholic University of Saint Anthony, Murcia, Spain d Departamento de Ciências da Educação, Instituto Superior de Ciências da Educação, Universidade Katyavala Bwila, Benguela, Angola b
a r t i c l e
i n f o
Article history: Received 3 December 2014 Received in revised form 2 May 2015 Accepted 4 May 2015
Keywords: Well-being Measurement equivalence Latent mean differences Confirmatory factor analyses
a b s t r a c t Subjective well-being is a research arena that has grown almost exponentially: over the last 20 years, the number of publications on subjective well-being has increased approximately 16-fold (Diener, 2009). The cognitive aspect of subjective well-being or life satisfaction is referred to a conscious cognitive judgment of life (Diener, Emmons, Larsen, & Griffin 1985), in which person’s quality of life is globally assessed (Shin & Johnson, 1978). The Satisfaction With Life Scale (SWLS, Diener et al., 1985) is the most widely used instrument for its measurement. A reliable, valid and invariant measurement is critical for meaningful comparisons. The aim of this study is to examine the configural, metric and scalar invariance across age in the Portuguese version of the SWLS with a sample of 5630 Angolans. A standard measurement invariance procedure has been applied both across gender and age. Results shown that scalar invariance of the SWLS held across gender and age. This strong invariance allowed for meaningful latent mean comparisons. There were latent mean differences due to gender and age, but while gender differences were modest, the age differences were larger. Results are discussed in their relation with existing literature. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Subjective well-being (SWB) research is a non-trivial task that touches on many areas of social and health sciences. Its interest has grown almost exponentially: over the last 20 years, the number of publications on well-being has increased approximately 16-fold (Diener, 2009), and articles on SWB have recently been published in journals such as Science (Oswald & Wu, 2010). Simply put, SWB aims to study and understand what makes people feel well in relation to their own values and standards (Diener, Oishi, & Lucas, 2003). Diener and Emmons (1984) distinguished two parts of SWB: an affective and a cognitive component (life satisfaction). Life satisfaction is referred to a conscious cognitive judgment of life (Diener, Emmons, Larsen, & Griffin, 1985), in which person’s quality of life is globally assessed according to his/her chosen criteria (Shin & Johnson, 1978). Life satisfaction has mostly been considered to be a state variable, something present and contextual (Hultell & Gustavson, 2008). However, other authors have found that life ⇑ Corresponding author at: Department of Methodology for the Behavioral Sciences, Faculty of Psychology, University of Valencia, Av. Blasco Ibañez, 21, Valencia 46010, Spain. E-mail address: [email protected] (J.M. Tomás). http://dx.doi.org/10.1016/j.paid.2015.05.008 0191-8869/Ó 2015 Elsevier Ltd. All rights reserved.
satisfaction may also reflect habitual judgment strategies that are closer to a trait. For example, Lucas (2007) provided evidence that around 34–38% of the variance in life satisfaction is trait variance. The stability of scores across the life span can be considered evidence of this trait-alike behavior of life satisfaction. A widely used measure of life satisfaction is the Satisfaction With Life Scale (SWLS, Diener et al., 1985). It aims at measuring a single trait of life satisfaction that could be used across the life-span. The scale has been validated across countries and areas of research. The bulk of validation studies have used the English version of the scale, among others: Diener et al., 1985; Lucas, Diener, & Suh, 1996; Pavot, Diener, Colvin, & Sandvick, 1991; or Shevlin & Bunting, 1994. Nevertheless, the scale has also been translated and validated in numerous countries and languages: French (Blais, Vallerand, Pelletier, & Briere, 1989); Spanish (Atienza, Pons, Balaguer, & García-Merita, 2000); Dutch (Arrindell, Heesink, & Feij, 1999); Chinese (Sachs, 2004); Hebrew (Anaby, Jarus, & Zumbo, 2010); Portuguese (Gouveia, Milfont, da Fonseca, & Coelho, 2009; Sancho, Galiana, Gutiérrez, Francisco, & Tomás, 2014); or German (Glaesmer, Grande, Braehler, & Roth, 2011). Most of this research has found a solid one-factor structure. Measurement invariance of the SWLS has also deserved careful and extensive attention. Tucker, Ozer, Lyubomirsky, and Boehm
J.M. Tomás et al. / Personality and Individual Differences 85 (2015) 182–186
(2006) tested measurement invariance in Russia and North America. Gouveia et al. (2009) tested invariance in five Brazilian subpopulations, founding configural invariance. However, metric or scalar invariance were not tested. Sex differences have always been of great interest, and therefore it is not a surprise that gender invariance of the SWLS has been extensively studied (as a clue for its importance, a search of sex measurement invariance in the web of science from 2005 to now retrieved 526 entries). Shevlin, Brunsden, and Miles (1998) tested measurement invariance across sexes in a sample of British undergraduates and found evidence for strict invariance without latent mean differences. Atienza, Balaguer, and García-Merita (2003) surveyed Spanish high-school students and tested for sex invariance: they found a lack of metric invariance for two items, but failed to test for scalar equivalence. Wu and Yao (2006) also studied gender invariance of Taiwanese undergraduates. Their results showed factor loadings and uniquenesses equivalence, but failed to test for equal intercepts and therefore strict invariance was lacked. 2966 Swedish students for becoming teachers were also surveyed and SWLS gender and age invariance tested (Hultell & Gustavson, 2008). Gender scalar invariance was achieved. This same result held for a large and representative sample of Norwegian (Clench-Aas, Nes, Dalgard, & Aarø, 2011). Indeed, gender strict invariance was tenable across sexes. Finally, Moksnes, Løhre, Byrn, and Haugan (2014) also tested measurement equivalence in Norwegian adolescents, and found support only for metric invariance. An extremely interesting issue in the field of subjective wellbeing is how life satisfaction changes during the life-span (Blanchflower & Oswald, 2008; Easterlin, 2006), and several authors have also considered age potential differences and factorial invariance. For example, Wu, Tsai, and Chen (2009) examined longitudinal measurement invariance of students and found evidence for scalar equivalence over a period of several months. Atienza et al. (2000) studied the scale in two Spanish samples of elderly and students, but only tested for configural and metric equivalence. Clench-Aas et al. (2011) explored the dimensionality and measurement equivalence of the SWLS, across age, in a representative sample of Norwegians. They found partial measurement invariance. The German version of the scale was tested for age measurement equivalence across the life-span by Glaesmer et al. (2011). They found evidence for both gender and age equivalence, but they only tested for configural and metric invariance, not for scalar one, which would allow for meaningful mean comparisons. The findings on the age and life satisfaction relationship have been rather inconsistent (Pinquart & Sorensen, 2000), with some studies reporting a weak positive linear relation (e.g., Hansson, Hillerås, & Forsell, 2005), others a weak negative one (e.g., Chen, 2001), and still others a curvilinear relationship, either with subjective well-being highest among those in middle age (e.g., Easterlin, 2006) or U-shaped in relation to age (Blanchflower & Oswald, 2004, 2008). Finally, some studies have found no relationship at all (e.g., Diener & Suh, 1998). Therefore, previous research has found somehow conflicting results, with samples been mainly young people and university students from developed countries. Additionally, several of these studies have not tested the full range of equivalence restrictions. Thus, this field needs further scrutiny (Realo & Dobewell, 2011). The aim of this study is to examine the whole range of invariance restrictions in the Portuguese version of the SWLS in Angola. 2. Method 2.1. Participants and procedure The participants in this study come from three independent cross-sectional surveys made in Angola within 2013–2014: school
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and high-school students, young adults, and adults. For the purposes of this study the samples were aggregated into a single one with some socio-demographic variables and the items of the SWLS. The sample consisted of 5630 Angolans with ages ranging from 14 years up to 65 years old. 50.8% were men (N = 2860), while women were 49.2% (N = 2770). Six age groups were considered, each group consisting of 10 years with the exception of the two first groups to divide in those under age majority (less than 18 years old) and young adults. The groups and their sample sizes were then: 34.4% (N = 1937) were 14–17 years old; 30.08% (N = 1694) were 18–24 years old; 17.2% (N = 966) were in the range 25–34; 8.5% (N = 476) were 34–44; 6% (N = 338) were 45–54; and 3.9% (N = 219) were in the range 55–65 years old. 2.2. Measures The surveys included socio-demographic variables and other scales, but the one of interest is the SWLS, composed of five items ranging from 1 (=totally disagree) to 5 (=totally agree). Author’s Portuguese version of the SWLS was used (Diener, 2009). 2.3. Statistical analyses A standard measurement invariance routine using a set of Confirmatory Factor Analyses estimated in EQS 6 was applied, with ML estimation with robust corrections. Establishing measurement invariance involves running a set of increasingly constrained confirmatory factor analyses, and testing whether differences between these models are significant, either from a statistical or a practical point of view (van de Schoot, Lugtig, & Hox, 2012). First, a one-factor model was separately tested on each group. After the determination of good fit for each group, a configural model was tested simultaneously for the groups and established as the baseline model. This model tested configural equivalence, or same factor structure holding for all groups. Then, factor loading were constrained across groups (metric invariance). Metric invariance tests whether respondents across groups attribute the same meaning to the latent construct under study. Then, a model with constrained item intercepts tested for scalar invariance which implies that the meaning and the levels of the underlying items (intercepts) are equal across groups, and accordingly groups may be compared on their scores on the factor. Finally a test of strict invariance, equal errors, was also proposed, although it is a very stringent test that it is not really needed for mean comparisons (Millsap & Olivera-Aguilar, 2012). The plausibility of the models was assessed using several fit criteria: (a) chi-square statistic; (b) the comparative fit index (CFI) and (c) the root mean squared error of approximation (RMSEA). Hu and Bentler (1999) suggested that a CFI of at least .90, and a RMSEA less than .06 together, would indicate a good fit. Nevertheless, cut-off criteria established in Hu and Bentler (1999) should also be taken with caution as they depend on sample size (Fan & Sivo, 2005). With larger sample sizes (N > 250) RMSEA lower the .05 and CFI of more than .95 are probably needed to stablish good baseline models to start the invariance routine. Models in the invariance routine are nested, and may therefore be compared with two rationales, the statistical and the modeling one. The statistical employs v2 differences (Dv2) to compare constrained to unconstrained models, with non-significant values suggesting multigroup equivalence. This statistical approach has been criticized (Cheung & Rensvold, 2002), recommending the modeling approach that uses practical fit indices to determine the overall adequacy of a fitted model. From this point of view, if a parsimonious model (such as the ones that posit invariance) evinces adequate levels of practical fit, then the sets of equivalences are considered a reasonable approximation to the data. Usually, CFI
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differences (DCFI) are used to evaluate measurement invariance. CFI differences lower than .01 (Cheung & Rensvold, 2002) are usually employed as cut-off criteria. 3. Results Table 1 shows descriptive statistics for the overall sample and the correlation matrix for the total sample and also for female and male groups. The alpha for the scale in the overall sample was adequate (a = .73). 3.1. Gender invariance Previous to the multi-group analyses, the one-factor model was separately tested in men and women. The model adequately fitted in both samples: men (v2(5) = 21.66, p = .001, CFI = .99, RMSEA = .03) and women (v2(5) = 41.57, p < .001, CFI = .99, RMSEA = .05). Then the set of increasingly constrained multi-sample confirmatory factor analyses, were estimated and tested. Table 2 shows the sequence of models and their differences to baseline (configural) model. The comparison of models yielded quite clear results. Metric invariance was pretty clear, as both statistical and practical approaches to model comparison agree that there were no statistically significant differences between configural and metric invariant models, and therefore the more parsimonious (invariant) model could be retained. Indeed practical fit indices remained extremely
Table 1 Items’ means, SD, and correlation matrix of the items for the total sample and female and male subjects. Items
SD
I1
I2
I3
I4
I5
Total sample I1 3.36 I2 2.99 I3 3.42 I4 3.12 I5 2.69
Mean
1.17 1.22 1.28 1.29 1.34
1 .287⁄⁄ .345⁄⁄ .288⁄⁄ .213⁄⁄
1 .509⁄⁄ .413⁄⁄ .292⁄⁄
1 .455⁄⁄ .342⁄⁄
1 .356⁄⁄
1
Women I1 I2 I3 I4 I5
3.35 3.10 3.40 3.19 2.68
1.18 1.20 1.29 1.30 1.36
1 .293⁄⁄ .359⁄⁄ .329⁄⁄ .234⁄⁄
1 .533⁄⁄ .429⁄⁄ .258⁄⁄
1 .490⁄⁄ .374⁄⁄
1 .376⁄⁄
1
Men I1 I2 I3 I4 I5
3.38 2.98 3.48 3.07 2.70
1.14 1.23 1.25 1.28 1.33
1 .283⁄⁄ .332⁄⁄ .249⁄⁄ .193⁄⁄
1 .490⁄⁄ .395⁄⁄ .323⁄⁄
1 .422⁄⁄ .311⁄⁄
1 .335⁄⁄
1
Table 2 Set of hierarchical models to test for measurement invariance. Model
SB
v2
df
DSBv2
Ddf
CFI
Gender invariance Configural 63.08 Metric 78.12 Scalar 116.08 Strict 142.26
10 14 18 23
7.79 31.76*
4 8 13
.989 .987 .986 .984
Age invariance Configural 100.34 Metric 145.59 Scalar 377.14 Strict 480.97
30 50 70 95
48.26* 189.8*
20 40 65
.983 .977 .978 .970
similar or even slightly improved (i.e. the RMSEA). When item intercepts were made invariant (scalar invariance) by gender the chi-square difference was statistically significant (p < .001), but differences in practical fit were minimum, less than .01 for the CFI, the most severe criteria. The same happened when strict invariance was tested, as practical differences in fit were irrelevant. Accordingly, the set of equivalences are considered tenable, and the SWLS may be considered equivalent by gender. Unstandardized and standardized factor loadings and intercepts in the retained model are presented in Table 3. The latent mean values were fixed to zero for males, making men the reference group. Latent mean value for women showed higher life satisfaction for them, although the effect size was low (a = 0.04, z = 2.74, p < .05, d = 0.08). 3.2. Age invariance With respect to age invariance, again previous to the invariance routine the one-factor model was separately tested in each age subsample. Again model fit was adequate for all samples: 14–17 years (v2(5) = 28.09, p < .001, CFI = .97, RMSEA = .04); 18–24 years (v2(5) = 30.14, p < .001, CFI = .98, RMSEA = .05); 25–34 years (v2(5) = 18.18, p = .002, CFI = .98, RMSEA = .05); 35–44 years (v2(5) = 13.59, p = .003, CFI = .98, RMSEA = .06); 45–55 years (v2(5) = 5.54, p = .36, CFI = .99, RMSEA = .02); 55–64 years (v2(5) = 5.67, p = .35, CFI = .99, RMSEA = .02). Given that the one-factor model fitted well in each separate sample, the set of models for the invariance routine was tested. Table 2 shows goodness-of-fit indices for the sequence of models and their differences to baseline (configural) model. Results were quite clear again. Both metric and scalar invariance seem reasonable. Although from a strict chi-square difference test both models were statistically worse than configural model, the practical fit indices were similar or even slightly improved (i.e. the RMSEA). Differences in practical fit were minimum, less than .01 for the CFI, the most severe criteria. As it was the case with gender invariance, a strict invariance model was also tested and considered tenable. Accordingly, the set of equivalences are considered tenable, and the SWLS may also be considered equivalent by age. Unstandardized and standardized factor loadings and intercepts in the retained model are presented in Table 3. The latent mean values were fixed to zero for the first age group (14–74 years), making this the reference group. Therefore, the mean differences are always the group of age considered against those 14–17 years old. All latent mean (differences) estimated for the other age group showed that the youngest group was more satisfied than the rest: 18–24 years (a = 0.261, z = 12.90, p < .01, d = 0.52); 25–34 years (a = 0.463, z = 16.25, p < .01, d = 0.85); 35–44 (a = 0.410, z = 12.46, p < .01, d = 0.80); 45–54 (a = 0.507, z = 13.08, p < .01, d = 0.96): 55–65 (a = 0.428, z = 9.05, p < .01, d = 0.76). The effect sizes may be considered moderate to large. 4. Discussion
DCFI
RMSEA
90% CI
.002 .003 .005
.043 .040 .041 .040
.033–.054 .032–.049 .033–.053 .033–.048
.006 .005 .013
.050 .045 .053 .053
.039–.061 .037–.054 .045–.062 .047–.060
Notes: SBv2 = Satorra–Bentler chi-square; df = degrees of freedom; D = differences. * p < .05.
Results have found strict invariance of the SWLS held across gender and age in a sample of more than five thousand Angolans. This strong invariance allowed for meaningful latent mean comparisons and here, again, results were clear. There were latent mean differences due to gender and age, but while gender differences were modest, the age differences were larger. How does the results accommodate within the existing evidence? With respect to gender invariance, among the six papers reviewed, three of them found evidence for scalar (strong) equivalence (Shevlin et al., 1998; Hultell & Gustavson, 2008; and Clench-Aas et al., 2014). Two papers found metric invariance
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J.M. Tomás et al. / Personality and Individual Differences 85 (2015) 182–186 Table 3 Unstandardized and standardized loadings and intercepts for scalar invariant models across age and gender. Gender
Age
Men
k1 k2 k3 k4 k5 m1 m2 m3 m4 m5
Women
14–17
18–24
25–34
35–44
45–54
55–65
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
UN
ST
1 1.5 1.8 1.6 1.2 3.3 3.0 3.4 3.1 2.7
.43 .65 .73 .62 .46
1 1.5 1.8 1.5 1.2 3.3 3.0 3.4 3.1 2.7
.46 .67 .76 .65 .48
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.38 .62 .67 .53 .40
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.43 .68 .72 .58 .45
1 1.5 1.7 1.4 1.1 3.5 3.3 3.8 3.4 2.9
.43 .68 .72 .59 .46
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.44 .68 .72 .59 .46
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.44 .69 .73 .60 .47
1 1.6 1.8 1.4 1.2 3.5 3.3 3.8 3.4 2.9
.47 .71 .75 .63 .49
(Moksnes et al., 2014; Wu & Yao, 2006), but one of them did not tested for scalar invariance (Wu & Yao, 2006). Only one research failed to find scalar and/or metric invariance (Atienza et al., 2003). When mean differences were tested, they were either non-significant or of small magnitude. We could therefore conclude that our results are in line with most of the accumulated evidence. Regarding age invariance of the SWLS, our results also point out at a scalar invariance that allows for latent mean comparisons. This result is coincident with most of the literature that has also found evidence for scalar invariance across age groups (Blais et al., 1989; Durak, Senol-Durak, & Gencoz, 2010; Gouveia et al., 2009; Siedlecki, Tucker-Drob, Oishi, & Salthouse, 2008; Wu et al., 2009). Some studies on measurement invariance found weak equivalence but failed to test for scalar equivalence (Atienza et al., 2000; Glaesmer et al., 2011). However, there are also important studies that found a lack of scalar invariance for the SWLS (Clench-Aas et al. (2011); Hultell & Gustavson, 2008). Clench-Aas et al. (2011) study, in particular, was based on a large and representative sample of the Norwegian population that included the age range 14– 79 years old. Since in our study evidence of scalar invariance was found, we proceeded to compare the latent means of life satisfaction. There were differences between the youngest and the other groups, but latent means remained almost unchanged from 25 till 65 years old. Studies disagree about this point, with evidence in all directions: weak positive linear relation (e.g., Hansson et al., 2005), weak negative one (e.g., Chen, 2001); a curvilinear relationship, either with subjective well-being highest among those in middle age (e.g., Easterlin, 2006) or U-shaped in relation to age (Blanchflower & Oswald, 2004, 2008); or even no relationship at all (e.g., Diener & Suh, 1998). All studies that found an age effect on life satisfaction agreed that the effect was weak. The plateau we have observed in life satisfaction in most age groups could be explained because different ages may judge their life satisfaction as dependent on different factors, and this may moderate their perceptions. Oishi, Diener, Suh, and Lucas (1999) have, for example, proposed a value as moderator model which predicts that as individual’s age, changes in values lead to changes in the determinants of their life satisfaction. Therefore, further studies should shed light on this age effect, but before measurement invariance should be tested and ensured.
5. Conclusions The main aim of this research was to study the invariance of psychometric properties of the Portuguese version of the SWLS in Angola. Conclusions are simple to summarize. Strict invariance of the SWLS held across gender and age in a sample of more than five thousand Angolans. This strong invariance allowed for meaningful
latent mean comparisons and here, again, results were clear. The direct implication of this finding is that the SWLS may confidently been used in Angola, both across gender and age, and meaningful comparisons among groups are possible. Current research has some limitations, the incidental sampling and the cross-sectional nature of the design being the most obvious. Most of the evidence about the relationship between age and subjective well-being is based on cross-sectional studies, asking different people of different ages to report their life satisfaction or happiness. Unfortunately, data following the same person over the years is seldom considered in studies of the relationship between subjective well-being and ageing. Only a handful of studies that have longitudinal data have focused on the stability of subjective wellbeing over time (e.g., Baird, Lucas, & Donnellan, 2010). This is again a line for future research. Finally, another limitation of current results that points out for future research, has been the focus on a unidimensional measure of life satisfaction. Other authors have advocated for the multidimensional nature of life satisfaction (for example Huebner, 1994), and results could well vary with respect to those found in this research if domain-specific life satisfaction is analyzed across gender and age. References Anaby, D., Jarus, T., & Zumbo, B. D. (2010). Psychometric evaluation of the hebrew language version of the satisfaction with life scale. Social Indicators Research, 96, 267–274. Arrindell, W. A., Heesink, J., & Feij, J. A. (1999). The satisfaction with life scale (SWLS): Appraisal with 1700 health young adults in the Netherlands. Personality and Individual Differences, 26, 815–826. Atienza, F. L., Balaguer, I., & García-Merita, M. L. (2003). Satisfaction with life scale: Analysis of factorial invariance across sexes. Personality and individual Differences, 35, 1255–1260. Atienza, F. L., Pons, D., Balaguer, I., & García-Merita, M. L. (2000). Satisfaction with life scale: Analysis of factorial invariance for adolescents and elderly persons. Perceptual and Motor Skills, 87, 519–529. Baird, B. M., Lucas, R. E., & Donnellan, M. B. (2010). Life satisfaction across the lifespan: Findings from two nationally representative panel studies. Social Indicators Research, 99, 183–203. Blais, M. R., Vallerand, R. J., Pelletier, L. G., & Briere, N. M. (1989). The satisfaction with life scale: Canadian-French validation of the satisfaction with life scale (L’Echelle de satisfaction de vie: Validation Canadienne-Francaise du ‘‘satisfaction with life scale’’). Canadian Journal of Behavioral Science, 21, 210–223. Blanchflower, D. G., & Oswald, A. J. (2004). Well-being over time in Britain and the USA. Journal of Public Economics, 88, 1359–1386. Blanchflower, D. G., & Oswald, A. J. (2008). Is well-being U-shaped over the life cycle? Social Science and Medicine, 66, 1733–1749. Chen, C. (2001). Aging and life satisfaction. Social Indicators Research, 54, 57–79. Cheung, G. W., & Rensvold, R. B. (2002). Evaluating goodness-of-fit indexes for testing MI. Structural Equation Modeling, 9, 235–255. Clench-Aas, J., Nes, R. B., Dalgard, O. D., & Aarø, L. E. (2011). Dimensionality and measurement invariance in the satisfaction with life scale in Norway. Quality of Life Research, 20, 1307–1317. Diener, E. (2009). Introduction the science of well-being: Reviews and theoretical articles by Ed Diener. In E. Diener (Ed.), The science of well-being: The collected works of Ed Diener (pp. 1–10). Dordrecht, New York: Springer.
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