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RESEARCH ARTICLE |
a University of Guelph, Ontario, Canada
b University of Victoria, British Columbia, Canada
c Georgia Institute of Technology, Atlanta
Scott B. Maitland, Department of Family Relations & Applied Nutrition, University of Guelph, Guelph, ON, Canada N1G 2W1 E-mail: smaitlan{at}uoguelph.ca.
Decision Editor: Toni C. Antonucci, PhD
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Abstract |
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IMPORTANT questions arise when one attempts to measure psychological constructs like subjective beliefs, emotions, or psychological well-being. As previous reviewers have noted, measures of the subjective well-being construct attempt to capture a valid representation of a moving target (
Chamberlain 1988
;
Diener 1994;
Larson 1978;
McNeil, Stones, and Kozma 1986b). That is, previous researchers have used numerous measures of well-being to examine either (a) cross-sectional age differences in mean levels, or (b) longitudinal stability and mean-level change in the construct over time (e.g.,
Andrews 1991;
Chamberlain and Zika 1992;
Costa, Zonderman, McCrae, Cornoni-Huntley, Locke, and Barbano 1987;
McNeil, Stones, and Kozma 1986a;
Stacey and Gatz 1991).
However, for us to examine such differences and changes it is critical that measures of well-being have similar meaning to different groups of people and that this meaning remains equivalent over time (
Andrews 1991). Although the issue of equivalence of meaning has been explored in the literature, particularly with reference to gender (e.g.,
Liang and Bollen 1985) and age (e.g.,
Herzog and Rodgers 1981;
Liang 1985;
Ryff and Keyes 1995), the measurement equivalence of well-being scales has not been fully established.
The Bradburn Affect Balance scale (ABS;
Bradburn 1969) is a widely used measure of psychological well-being. It has frequently been employed to study well-being in adulthood, perhaps due to its availability in a number of longitudinal studies and archival data sets. Items from the ABS are commonly grouped into two related scales: positive affect and negative affect. In turn, these can be used to calculate an affect balance score (positive affect - negative affect;
Bradburn 1969). Such a score would be maximally valid if positive affect and negative affect are considered opposite poles of a bipolar factor, although this issue is still a matter of some controversy in the literature (see
Russell and Carroll 1999;
Van Schuur and Kruijtbosch 1995;
Watson and Tellegen 1985). This paper treats affect, as measured by the ABS, as comprising two correlated but distinct factors of positive and negative affect (see
Watson and Tellegen 1985, for further discussion). Previous studies using the two-factor ABS structure have examined cross-sectional differences and longitudinal change in well-being in older adults (
Stacey and Gatz 1991), scale validity in a sample of family caregivers (
Perkinson, Albert, Luborsky, Moss, and Glicksman 1994), the relationship of major life events with the ABS (
Stallings, Dunham, Gatz, Baker, and Bengtson 1997), and the genetic and environmental etiologies of positive and negative affect (
Baker, Cesa, Gatz, and Mellins 1992).
The most common comparisons employed when examining the Bradburn ABS have been gender, age group, and longitudinal changes in average observed well-being scores. Questions remain regarding the measurement properties of the ABS (e.g.,
Diener 1984,
Diener 1994;
Diener and Emmons 1985;
Stull 1987;
Van Schuur and Kruijtbosch 1995). Moreover, the longitudinal factor structure of well-being as measured by the ABS has not been examined.
The concept of measurement invariance refers to the assumption that the relationships of observed items to latent constructs are equivalent between groups or across time (
Baltes, Reese, and Nesselroade 1988;
Labouvie 1980). Measurement invariance is required to permit valid quantitative inferences about constructs such as well-being from empirical behavior of scales such as the ABS (e.g., the degree of stability in mean levels of well-being over time). Typically, appropriate evidence is generated from using structural equation modeling to test for invariance in construct-variable relationships (particularly, in item factor loadings) across different groups, time periods, or situations.
Measurement invariance of the ABS may be evaluated using methods described by
Alwin and Jackson 1979,
Horn, McArdle, and Mason 1983, and
Meredith 1993, among others. The sequence of testing measurement invariance involves comparisons of nested models of increasingly stringent invariance assumptions. Measurement models employed in the current paper include tests of configural invariance and metric invariance of the factor loadings.
Horn and colleagues 1983 suggested that configural invariance requires only that the same variables load on the same number and pattern of factors for different groups. A model with configural invariance provides evidence of qualitative but not quantitative similarity across groups. In contrast, metric invariance involves equivalence of metric (unstandardized) factor loadings between groups or across occasions. Metric invariance establishes comparable units of measurement for the variables and the factors. It therefore allows for meaningful quantitative comparisons of groups or across time (
Cunningham 1982,
Cunningham 1991;
Horn 1991;
Horn et al. 1983;
Horn and McArdle 1992).
Partial measurement invariance implies that some, but not all, of the configurally invariant items have equivalent metric factor loadings (
Byrne, Shavelson, and Muthen 1989). Tests of partial measurement invariance can be conducted at the individual factor, or observed variable level, even if models positing invariance of all factor loadings are rejected. Partial invariance can be imposed on subsequent models focusing on modeling latent variable relationships. Items that are demonstrated to be equivalent are constrained as such across groups or over time, whereas loadings which are significantly different between groups or over time are allowed to vary freely. Rather than disregarding quantitative inferences for a scale after rejection of the hypothesis of metric invariance for the complete set of factor loadings, this approach allows researchers to identify which items have variability in measurement properties and to adjust statistical analyses for these differences (see
Byrne et al. 1989;
Maitland, Intrieri, Schaie, and Willis 2000;
Schaie, Maitland, Willis, and Intrieri 1998). Such items could be dropped from scales; alternatively, a measurement model with partial measurement equivalence can be used to estimate quantitative age differences or age changes at the level of latent variable means.
The few tests of factorial invariance of the ABS have shown conflicting results. For example,
Benin, Stock, and Okun 1988 reported a lack of metric invariance of ABS items in a cross-sectional comparison of three age groups (20–39, 40–59, & 60–96 years). Factor loadings for the two younger groups were found to be equivalent; however, the oldest group differed from the other two groups. Unfortunately, the sequence of nested models did not test the hypothesis of equal factor loadings under the assumption of correlated affect factors.
Devins, Beiser, Dion, Pelletier, and Edwards 1997 conducted a test of cross-cultural measurement invariance of English-language and Asian-language versions of the ABS. This study established metric invariance of the positive and negative affect factors using a subset of 9 of the 10 ABS items.
Previous research on measurement equivalence of other measures of well-being in aging samples has also shown mixed results. For example,
Herzog and Rodgers 1981 found evidence for both similarities and differences in age-related structures of well-being across groups (25–75 years) in previously published data sets.
Usala and Hertzog 1989 found configural but not metric invariance in multiple age groups for adjective rating scales measuring multiple positive and negative affect constructs. Similarly, in a series of studies, Lawton and colleagues (e.g.,
Lawton, Kleban, Dean, Rajagopal, and Parmelee 1992;
Lawton, Kleban, Rajagopal, and Dean 1992;
Lawton, Kleban, and Dean 1993) addressed age-group invariance of well-being under different conditions and reported conflicting results.
Lawton, Kleban, Dean, and colleagues 1992 reported metric invariance of the factor loadings of 10 items from the Philadelphia Geriatric Center (PGC) Affect scales for three community-resident groups of older adults, whereas a comparison of a model distinguishing between state versus trait measures of well-being in older adults resulted only in a configural model. Additional group comparisons of the invariance of well-being include
Liang and Bollen 1985 test of gender equivalence using the PGC Morale scale. Whether invariance was found depended on which set of fit indexes was accepted. Likelihood ratio comparisons rejected gender equivalence of the factor loadings, whereas follow-up tests and alternative fit indexes suggested no gender differences.
In summary, previous studies of cross-sectional factorial invariance of well-being have shown support for the configural invariance of item factor loadings, often with minimal evidence of identical factor loadings across age groups (e.g.,
Lawton, Kleban, Rajagopal et al. 1992;
Lawton et al. 1993). Few studies have found metric invariance of well-being items (
Herzog and Rodgers 1981;
Liang and Bollen 1985;
Devins et al. 1997;
Lawton, Kleban, Dean et al. 1992;
Usala and Hertzog 1989), and studies specifically examining equivalence of the entire complement of 10 items from the ABS are almost nonexistent.
In our study we also focused on the longitudinal invariance of factor structure in the ABS in an adult sample. Given that most studies of well-being that used the ABS focused on stability of means or stability of individual differences in the scale scores, it is important to explicitly examine the longitudinal measurement equivalence of the ABS to determine whether such comparisons across time are justified. This approach also allowed us to correct estimates of stability in positive and negative affect for both random and systematic sources of measurement error that can contaminate estimates of stability taken from the scale scores themselves (e.g.,
Nesselroade, Pruchno, and Jacobs 1986). We employed data from the Victoria Longitudinal Study (VLS) to examine measurement invariance in the ABS across age groups, gender groups, and longitudinal occasions.
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Methods |
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for VLS1 and
Dixon and colleagues in press for VLS2. The present sample was derived by combining data from the first two waves of VLS1 with the first two waves of VLS2. This allowed for large-sample (n = 678) longitudinal analysis of factorial equivalence of the ABS. For age-group analyses, the sample was divided into two groups with the following characteristics at the initial wave. The young–old age group ranged from 54 to 70 years (M = 64.12; SD = 4.01; n = 452), whereas the old–old group was 71 to 87 years (M = 75.05; SD = 3.70; n = 226). Women comprised 60.4% of the young–old and 66.4% of the old–old adults. The sample was generally well-educated (years of education: MYO = 14.70, SD = 3.00; MOO = 14.09, SD = 3.17). The sample was also divided into two groups for gender analyses with the following characteristics at the initial wave. Women ranged from 54 to 87 years of age (M = 67.83; SD = 6.80; n = 423), whereas men's ages ranged from 55 to 84 years (M = 67.65; SD = 5.90; n = 255). Both genders had comparable levels of education (years of education: MW = 14.26, SD = 2.90; MM = 14.89, SD = 3.30).
Analyses examining attrition from the longitudinal samples have been conducted separately for VLS1 (
Hultsch et al. 1998) and VLS2 (
Dixon et al. in press). Reasons for attrition were similar for the two VLS samples and included: lack of interest or time, personal illness, geographical relocation, family health problems, death, and loss of contact with researchers. As expected, returning participants tended to be demographically (e.g., younger, healthier) and cognitively (e.g., word and text recall, vocabulary) superior to participants who did not return. Additionally, attrition analyses examined differences in well-being and found a significant main effect for attrition status; returning participants reported higher levels of positive affect than those who dropped out: F(1,953) = 14.23, p < .001; Mreturn = 4.09, Mattrite = 3.76, whereas no differences were noted for negative affect F(1,953) = .14, p = .715; Mreturn = .85, Mattrite = .81.
Measures
The Bradburn ABS was used to measure psychological well-being. It is comprised of 10 items, 5 measuring positive affect and the remaining 5 measuring negative affect. Positive affect items include: (a) particularly interested in something, (b) proud because someone complimented you on something you had done, (c) pleased about having accomplished something, (d) on top of the world, and (e) that things were going your way. Negative affect items include: (a) so restless you couldn't sit long in a chair, (b) very lonely or remote from other people, (c) bored, (d) depressed or very unhappy, and (e) upset because someone criticized you. The italicized word in each item represents the one-word label for each variable in this report. Participants were asked whether or not they had experienced feelings relevant to each question during the previous month.
Cross-sectional analyses of internal consistency for positive affect by age group were 
= .62 and = .65 respectively for the younger and older groups. Cronbach's alpha for the negative affect scales for young–old and old–old adults were YO = .62 and OO = .63. Internal consistency was similar for women and men for both negative affect (W = .65, M = .57) and for positive affect (W = .61, M = .67). Internal consistency statistics such as represent lower-bound estimates, with true reliability often being greater than that estimated by . These estimates of internal consistency are not high but are consistent with others reported in the ABS scales. Given that low internal consistency can result from factorial heterogeneity (
McDonald 1981), these estimates support the need for factor analysis of the ABS items.
Longitudinal stability and independence of the positive and negative affect factors were initially examined by computing correlations among the composite positive and negative affect scales. Positive and negative affect scale scores were moderately stable across three years (r = .44 and r = .45, respectively). The correlations between positive and negative affect scales at each wave were r = -.13 and r = -.10 (ps < .05). Small negative correlations have been used in prior research to demonstrate the independence of the two well-being factors, as well as to support the necessity for two separate affect factors.
Statistical Procedures
All structural analyses were conducted using EQS 5.6 (
Bentler 1995). Additional descriptive analyses were completed using SPSS Version 8 (
SPSS 1997). To establish the basic measurement model for the ABS, a split-half design was tested. The cross-sectional sample for first time of measurement (n = 949) was randomly divided into two halves, and participants were randomly assigned to one of two samples (ns = 475, 474). As expected, these samples were similar in age and gender composition. Mean ages for the two samples were 68.37 years (range 54–89) and 68.66 years (range 55–87). The first half-sample consisted of 63.8% women and the second half was 61.4% women. The measurement model was established in the first half-sample and validated by testing it in the second half-sample. Once the measurement model was established, confirmatory factor analyses were used to examine two levels of measurement invariance, namely, configural and metric invariance. Analyses were conducted on covariance matrices, with the factor pattern identification established by fixing one loading on each factor to a value of 1.0. A 20 x 20 covariance matrix of the 10 Bradburn items at two time points was tested for all longitudinal models. All longitudinal models also allowed for autocorrelation of the unique variances to account for the nonindependent nature of repeated measures data (
Sorbom 1975;
Wiley and Wiley 1970).
Several criteria were used to determine model fit to the data and to evaluate improvement in fit between subsequent models. The nonnormed fit index (NNFI;
Bentler and Bonnet 1980), the comparative fit index (CFI;
Bentler 1990), the root mean square error of approximation (RMSEA;
Steiger 1990;
Steiger and Lind 1980), the goodness of fit index (GFI;
Joreskog and Sorbom 1993) and the Z ratio (
2/df;
Bollen 1989) were all used to determine model fit. Furthermore, comparisons of nested models, essential to tests of measurement invariance, were conducted using the difference in model 2 (
Joreskog and Sorbom 1979). For current purposes, we accepted a 2 difference significant at or beyond the 1% level of confidence as indicating a significant decrease in model fit. Accordingly, the model with fewer constraints on parameters following a significant loss of fit was retained. All comparisons of unstandardized factor loadings were conducted using a z test and a critical value of ± 2.58, p < .01.
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fit the data for the first half-sample relatively well (2 = 99.22, df = 34, p < .001, GFI = .96, CFI = .89). All ABS items loaded significantly onto their expected factors. The validation half-sample replicated the measurement model with a similar fit (2 = 91.13, df = 34, p < .001, GFI = .96, CFI = .90).
Overall Longitudinal Comparison
A test of longitudinal measurement equivalence for the entire sample followed. This model served as a precursor to the age and gender tests of measurement invariance. The configural model fit well across the 3-year period (2 = 360.63, df = 154, p < .001, GFI = .95, CFI = .90). All factor loadings and factor variances were statistically significant. All uniqueness terms, correlated across time, were statistically significant with the exception of depressedt1 with depressedt2. A test of metric invariance of the factor loadings across time was examined (2 = 384.51, df = 162, p < .001, GFI = .95, CFI = .89; 
2 = 23.88, df = 8, p < .01). Whereas all factor loadings remained statistically significant, the failure to accept the hypothesis of metric invariance indicated that not all ABS items could be constrained to be equivalent across the 3-year period. Statistical comparison of the unstandardized factor loadings revealed only the pleased item on the positive affect scale differed between time points (Z = 2.85, p < .01), with more positive endorsement of this item for Time 1 than Time 2.
LaGrangian Multiplier tests were evaluated to determine whether additional factor loadings would improve the fit of the model. There was no indication of possible model improvement through freeing fixed zero factor loadings. It would have been possible to improve the fit by adding a few residual covariances between specific item residuals, but in no case did these residual covariances seem theoretically interpretable and compelling. Hence we opted to use the 10-item, 2-factor model as specified in our main analysis of age and gender differences and age changes in the factor structure of the ABS.
Therefore, the ABS items displayed longitudinal measurement equivalence with the exception of a single marker on the positive affect scale. The next models tested for differential measurement properties of the ABS items in longitudinal comparisons of older adults and genders.
Longitudinal Age Group Comparisons
A multiple age-group, longitudinal configural invariance model was tested to examine fit of the measurement model for young–old and old–old adults (2 = 537.51, df = 308, p < .001, GFI = .93, CFI = .89). This model demonstrated that the measurement model fitted the data well for both age groups and across the 3-year interval. All factor loadings, longitudinal stabilities for positive and negative affect, and the correlations between affect factors were statistically different from zero. The satisfactory fit established configural invariance for the ABS items. To examine the next level of measurement equivalence, two initial models of metric invariance were tested. The first model tested age-group invariance of the factor loadings by constraining the factor loadings between the two age groups. This model allowed factor loadings to vary freely across the two time points. This model resulted in a nonsignificant loss of fit over the configural model (2 = 563.44, df = 324, p < .001, GFI = .92, CFI = .89; 2 = 25.93, df = 16, p > .01). Thus, age-group invariance of the factor loadings was deemed acceptable. Second, factor loadings were constrained across time within both age groups, but were allowed to vary freely between age groups. To test the hypothesis of time invariance, this time invariance model was also compared against the configural model. The time invariance model resulted in a significant loss of model fit and revealed a lack of metric invariance of the two-affect factor's loadings across the two occasions (2 = 575.29, df = 324, p < .001, GFI = .92, CFI = .88; 2 = 37.78, df = 16, p < .01).
Because age-group invariance was considered tenable, whereas time invariance was not, we evaluated individual longitudinal constraints on ABS item factor loadings. The loading of the ABS pleased variable on the positive affect factor for the young–old subjects could not be constrained across time (Z = 3.06, p < .01). Furthermore, the ABS upset variable was not time invariant for the old–old subjects (Z = -3.05, p < .01). Relaxing the equality constraint for time on the upset variable produced a nonsignificant factor loading at Time 1 for old–old participants. Analogous to results obtained from analysis of variance approaches, the omnibus test of age-group invariance was accepted. However, additional post hoc comparisons of the factor loadings were conducted to examine differences between age groups. The only significant result was that the ABS upset item demonstrated a statistically significant difference between the young–old and old–old participants but only for the first time of measurement (Z = 2.81, p < .01). These modifications were tested as a partial invariance model and provided acceptable fit when compared to the configural model (2 = 565.58, df = 330, p < .001, GFI = .92, CFI = .89; 2 = 28.07, df = 22, p > .01). This model was accepted as the best fitting longitudinal age group solution. Because a partially invariant model was accepted as best fitting the data, a more stringent model constraining factor loadings across age group and time simultaneously would be expected to fit the data markedly worse, and indeed it did (see Table 1 ). Standardized and unstandardized factor loadings from the accepted age group model are provided in Table 2 . All factor loadings were equivalent between age groups with the upset variable at Time 1 the only exception.
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positive = .55, negative = .54) and old–old adults (positive = .68, negative = .67). The age differences among these correlations were not significantly different. The factor correlations between positive and negative factors at each time point were small but statistically significant for young–old (time1 = -.20, time2 = -.24) and old–old participants (time1 = -.34) with one exception (time2 = -.23). No significant differences were found for these factor correlations when tested between groups, or across time within groups. Furthermore, no age-group differences or changes across time were noted in the factor variances of positive and negative affect.
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2 = 520.30, df = 308, p < .001, GFI = .93, CFI = .90). A model constraining factor loadings to be equivalent between genders was examined, concurrently allowing factor loadings to be freely estimated across time (2 = 562.85, df = 324, p < .001, GFI = .92, CFI = .89; 2 = 42.55, df = 16, p < .01). Gender invariance of all ABS items was rejected as a plausible hypothesis. Next, a model constraining factor loadings to be equivalent across time but allowing them to be freely estimated between gender groups was tested and demonstrated time invariance of the factor loadings when compared to the configural model (2 = 550.96, df = 324, p < .001, GFI = .93, CFI = .89; 2 = 30.66, df = 16, p > .01). Because time invariance of factor loadings was accepted, whereas gender invariance was not, we evaluated individual items to determine the source for the lack of gender invariance. Results indicated that the way variable on the positive affect factor was different for men and women at both time points (Time 1: Z = 3.66, p < .01; Time 2: Z = 2.87, p < .01). Also on the positive affect factor, the top item showed gender differences for both time points (Time 1: Z = 2.91, p < .01; Time 2: Z = 5.47, p < .01). Additional post hoc comparisons of the factor loadings were conducted to examine differences across time. Only the pleased item was important, having a significantly smaller loading at Time 2 than at Time 1. This pattern is similar to the overall sample results; however, it only decreased over time for men (Z = 2.90, p < .01). All factor loadings were time-invariant for women. Because a partially invariant model best fit the data, a metric invariance model must fit worse and is reported in Table 1 for comparison.
These modifications resulted in the accepted partial measurement invariance gender model (2 = 538.49, df = 328, p < .001, GFI = .93, CFI = .90; 2 = 18.19, df = 20, p > .01). Factor stability was moderate for positive and negative affect factors over three years for both men (positive = .51, negative = .68) and women (positive = .67, negative = .53). Stability of positive affect for women was significantly greater than for men (Z = -2.81, p < .01), although no gender difference in stability of negative affect was found. The correlations between positive and negative factors were statistically significant for women ( = -.36 at both time points) and nonsignificant for men ( = -.05 at both time points). Finally, gender differences favoring women for the factor variances of positive affect were noted for both time points (Time 1: Z = -3.14, p < .01; Time 2: Z = -3.62, p < .01). No gender differences were noted in factor variances for negative affect. These results indicate that items of the ABS relate to one another and to their latent constructs in differential fashion across time and between genders. Standardized and unstandardized factor loadings from the accepted gender invariance solution are provided in Table 4 . Factor correlations for both gender groups are provided in Table 5 .
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Discussion |
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We began by demonstrating that the basic 10-item, 2-factor model of psychological well-being could be identified in a large sample of older adults. The structure of the ABS provided a good representation of positive and negative affect factors. Unlike the work of previous researchers (e.g.,
Devins et al. 1997;
Liang 1985), which excluded at least one item from the analyses, all ten ABS items were included in the present results. Comparison of the two randomly constituted groups found acceptable fit for all ten items as measured by statistically significant factor loadings (p < .01).
Longitudinal comparisons revealed a lack of measurement equivalence for the pleased item in the overall sample; however, this result could be localized to young–old and male groups. A lack of longitudinal invariance was also noted for the upset item for the old–old participants only. Removing the equality constraint over time for the upset variable led to a nonsignificant factor loading at the first measurement occasion for the old–old. This was the only occurrence of a nonsalient loading for the 10 ABS items across four comparison groups and two longitudinal measurements. Furthermore, we noted age group and gender differences in the upset, top, and way variables. This supports the work of
Benin and colleagues 1988 who reported difficulty with the pleased and upset items during examination of age-group invariance.
Combined with evidence from previous studies (
Baker et al. 1992;
Bradburn 1969;
Diener and Emmons 1985;
Lawton 1984;
Stacey and Gatz 1991;
Stallings et al. 1997), the current results support a 2-factor theory of psychological well-being as measured by the ABS. Past research has also made strong arguments concerning the independence of positive and negative affect factors (e.g.,
Baker et al. 1992;
Bradburn 1969;
Diener and Emmons 1985;
Hilleras, Jorm, Herlitz, and Winblad 1998;
Lawton 1984;
Stacey and Gatz 1991;
Stallings et al. 1997;
Watson and Tellegen 1985). In the present study, the correlations between the positive and negative affect factors were statistically significant and consistent in magnitude and direction with
Benin and associates 1988. We also noted differential patterns of relationships between the positive and negative affect factors for men and women. Traditionally, small negative correlations between the positive and negative affect factors have been interpreted as supporting the notions of independence between the two dimensions (but see
Diener 1984;
Diener and Iran-Nejad 1986;
Van Schuur and Kruijtbosch 1995).
Another important finding concerns the differences in stability estimates obtained as either Pearson correlations of ABS scales for positive and negative affect or estimated factor correlations provided by EQS. Stabilities were consistently higher from the measurement model than for the standard additive scales due to correction of measurement error. Factor correlations provide more definitive information about stability, because they will approach their true upper bound of 1.0 if there is a near-perfect stability of individual differences (
Hertzog and Nesselroade 1987). Factor correlations in the current study demonstrated only moderate stability across three years indicating substantial individual differences in change in affect over the three-year interval.
The magnitude of the three-year stability coefficients for positive and negative affect was consistent with other studies showing only moderate stability of affect over short longitudinal intervals in older populations. For example,
Usala and Hertzog 1991 reported that a state anxiety factor produced a two-year stability coefficient of .66, in contrast to a stability coefficient of .90 for a trait anxiety factor. The latter coefficient was consistent with reports of high stability of trait neuroticism (e.g.,
Conley 1985;
McCrae and Costa 1990;
Small, Hertzog, Hultsch, and Dixon 1999). Hence the positive and negative affect factors of the ABS behave more like psychological states than psychological traits in terms of stability of individual differences over time (see
Nesselroade 1986).
The inability to constrain all factor loadings to be equivalent leads us to conclude that only partial measurement invariance exists for the ABS. Therefore, the normal strategy of creating summative scales from all 10 positive and negative affect items from the ABS is somewhat problematic for older populations and for longitudinal measurements because quantitative scale differences could be produced by the shifting of measurement properties of some items rather than by changes in the affect constructs themselves.
These results do not, however, equate to a lack of support for use of the ABS. The lack of invariance appeared to be restricted to a few ABS items. Had we been unable to accept equivalence constraints across the majority of loadings on the positive and negative factors, we would have been forced to conclude that the ABS items have questionable validity and utility for quantitative comparisons of well-being using the ABS. To the contrary, the partial measurement equivalence (
Byrne et al. 1989;
Maitland, et al. 2000;
Schaie, et al. 1998) observed in this study suggests instead that ABS items can be used to make meaningful group or longitudinal comparisons of positive and negative affect, provided that items with differential measurement properties are identified and appropriate adjustments for these items are made. For example,
Schaie, Willis, Hertzog, and Schulenberg 1987, and
Byrne and colleagues 1989 have suggested that researchers encountering partial metric invariance should conduct quantitative comparisons of means for latent variables instead of summated scale scores, as is more typical in the literature. To the extent that the ABS is representative of other commonly used multiple-factor measures of affect, the present results suggest that studies of affect in older populations might best be conducted with latent variables. Alternatively, use of reduced scales using only those items demonstrating measurement invariance could be contemplated (e.g.,
Benin et al. 1988).
In summary, the current study demonstrates partial, but not complete, invariance for longitudinal models of well-being scale items. Notably, some items of the ABS have differential measurement properties between genders and age groups and across a 3-year period. Although the 2-factor model of affect was supported, the partial invariance pattern raises the possibility that what is known about aging with regard to positive or negative affect from earlier research may be contaminated by age differences or longitudinal changes in item measurement properties. Without identification of an equivalent factorial (qualitative) structure, group or mean-level (quantitative) comparisons must be conducted carefully.
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Acknowledgments |
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Received for publication March 22, 1999. Accepted for publication June 14, 2000.
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