Satisfaction With Life Scale: analysis of factorial invariance, mean structures and reliability

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Abstract

The purpose of this study was to test the factorial invariance of the Satisfaction With Life Scale (SWLS) across sexes. After establishing an appropriate baseline model a hierarchy of successively restrictive models relating to the measurement properties of the scale were specified and estimated. In addition, tests of intercept and factor mean differences were conducted. Data from 258 undergraduates from two British universities (173 males and 85 females) was analysed using the multi-sample procedures in LISREL8. Factor loadings, unique variances and factor variance were found to be invariant across the sexes and no differences were found for the intercepts and factor means. In addition, the scale was found to have high reliability.

Introduction

The construct of subjective well-being has been the focus of a growing body of research over recent years (Diener and Larsen, 1992; Pavot and Diener, 1993). Instruments such as the Affectometer (Kammann and Flett, 1983) and the Positive and Negative Affect Schedule (Watson et al., 1988) have generally been used to measure the affective component of subjective well-being. The Satisfaction With Life Scale (SWLS) was developed to measure levels of global life satisfaction (Diener et al., 1985) which is the cognitive component. The scale consists of five items and uses a Likert type response format.

Exploratory factor analytic studies have suggested that the scale is unidimensional. Using principal axis factor analysis Diener et al. (1985)found a single factor accounting for 66% of the variance, and similar findings have been reported by Pavot et al. (1991). A single factor structure was also found for translations in French (Blais et al., 1989) and Dutch (Arrindell et al., 1991). Confirmatory factor analyses have also supported a unidimensional structure (Shevlin and Bunting, 1994; Lewis et al., 1995). In terms of reliability the SWLS has been found to be internally consistent and temporally stable. Diener et al. (1985)found a coefficient alpha of 0.87 and a test-retest correlation coefficient of 0.82 with a two month interval. Similar findings were reported by Pavot et al. (1991)and Yardley and Rice (1991).

In the aforementioned studies reliability was commonly estimated using Cronbach’s alpha (Cronbach, 1951), and dimensionality established by exploratory factor analysis. Such procedures are common in the literature, but have several well documented statistical and theoretical limitations (Bollen, 1989; Pedhazur and Schmelkin, 1991). However, these procedures can be generalised and incorporated into a single statistical model. Tests of factorial invariance within a structural equation framework (Joreskog, 1971) allow for the simultaneous estimation of a confirmatory factor model across different groups, such as sex. The estimation of a confirmatory factor model allows a test of an a priori factor structure. The fit of the model can be assessed using the chi-square test, or other goodness of fit indices, and the reliability can be estimated from the model parameters (Bollen, 1989). In addition, the degree of similarity of the scale’s properties across different groups, factorial invariance, can be statistically tested. As the SWLS aims to measure levels of global life satisfaction as opposed to specific criteria, its content and applicability should be equally relevant for qualitatively different groups. Hoelter (1983)stressed the importance of testing factorial invariance to ensure comparative validity across groups. Furthermore, Cohen and Cohen (1983)discuss the possible moderator effects that can occur when a scale’s reliability differs across two groups. For example, if the factor structure of the SWLS is not invariant for males and females it may appear that the relationship with SWLS and other variables differs across sexes. However, the differences in correlation or regression coefficients with another variable may be due entirely to differential item functioning or differences in the scale as a whole.

Factorial invariance indicates that the structure and measurement of the underlying construct are equivalent across groups (Byrne et al., 1989). This study aims to test the SWLS for factorial invariance across sexes and estimate the scale’s reliability.

Prior to any invariance analysis being carried out it is necessary to establish a well fitting baseline model (Reise et al., 1993). On the basis of previous studies a suitable baseline model is a single factor congeneric measurement model. This specifies that the variances\covariances of the observed items can be explained in terms of a single underlying latent variable, labelled life satisfaction, and uncorrelated unique variances or measurement error. If the single factor model cannot be rejected in each group increasingly restrictive constraints can be imposed on the model. First, the invariance of the factor loadings across the groups can be tested. This tests the hypothesis that the regression coefficients relating the latent variable to the observed variables for males (Λ1) is equal to that for females (Λ2). Second, additional constraints on the unique variances can be imposed. This tests the hypothesis that, in addition to invariant factor loadings, the unique variances for each item are the same for males (Θ1) and females (Θ2). The third restriction imposes an equality constraint on the variance of the latent variable for males (Φ1) and females (Φ2). These tests of factorial invariance tests the equivalence of the psychometric properties of the SWLS across sexes. However, they do not provide information regarding the mean levels of life satisfaction across the two groups. Further restrictions in terms of intercepts (τ1 = τ2) and factor means (κ1 = κ2) can be imposed to provide information about invariance of mean structures.

Further details on the technical issues involved in the specification and estimation of models of factorial invariance and mean structures can be found in Joreskog (1971), Sorbom (1974), Alwin and Jackson (1981), Bollen (1989),and Byrne et al. (1989).

Section snippets

Sample and procedure

The 258 participants in the study were first year undergraduates from two British universities. There were 173 male participants with an age range of 18–57 and a mean age of 20.6 years (SD = 5.61) and 85 female participants with an age range of 18–46 and a mean age of 22.9 years (SD = 8.06). All participants completed the Satisfaction With Life Scale (Diener et al., 1985). The data was then separated for males and females.

Analysis

All analyses were conducted using LISREL8 (Joreskog and Sorbom, 1989).

Results

All analyses used the multi-sample procedures in LISREL8. An acceptable baseline model was found for both males and females. A one factor congeneric measurement model was an acceptable explanation for males (χ2 = 3.44; df = 5; P = 0.63) and females (χ2 = 1.15; df = 5; P = 0.95). Results of hypotheses 1–5 are reported in Table 2.

The common metric completely standardised factor loadings were all very high ranging from 0.92 to 0.98 with a mean of 0.964. Using the formula presented by Fleishman and

Discussion

A single factor congeneric measurement model was an acceptable description of the data for both males and females. This indicates that the SWLS has the same ‘form’ in each group, that is, the dimensionality of the SWLS is the same across the groups. In addition, the more restrictive model with equal factor loadings across groups (Hypothesis 1) was an acceptable description of the data. Factor loadings represent the relative importance of a particular item in terms of the latent variable, or

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