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A measurement model for subjective marital solidarity: Invariance across time, gender, and life cycle stage
SOCIAL
SCIENCE
RESEARCH
19, 62-81 (I!?%)
A Measurement Model for Subjective Marital Solidarity: Invariance across Time, Gender, and Life Cycle Stage BARBARA
STANEK
University
FRANK Mississippi
KILBOURNE
of Texas-Dallas
HOWELL State
University
AND
PAULA University
ENGLAND of Arizona
We use LISREL to assess the measurement properties of a unidimensional indicator of subjective marital solidarity based on four questionnaire items. A rigorously assessed measure containing more than one, yet relatively few items, is solely needed for research on marriage; such a measure can combine high reliability with low cost. Using 1971 and 1978 waves of the Quality of American Life data, we evaluate a measure based on four items: how well the respondent thinks his or her spouse understands him or her, how well the respondent understands his or her spouse, the amount of time spouses spend together in companionate activities, and reported marital satisfaction. With one correlated error term, these items are found to be a unidimensional indicator and to show substantial invariance across gender, survey year, and life cycle stage. We rejected inclusion of an item on how much the couple agrees on finances because this item created invariance by gender and survey year. This item apparently changed its meaning during the 1970s when many women became wage earners. 0 1990 Academic
Press, Inc.
The data used in this study were made available by the Inter-University Consortium for Political and Social Research. The data for the Quality of American Life, 1971 and 1978, were collected by the Institute for Social Research, University of Michigan, under support from the National Science Foundation. Neither the original collectors nor the Consortium bear responsibility for the analyses or interpretations presented herein. Address correspondence and reprint requests to Barbara Stanek Kilbourne, School of Social Sciences. University of Texas-Dallas, Richardson, TX 750830688. 62 0049-089X?% $3 .OO Copyright All rights
0 1990 by Academic Press. Inc. of reproduction in any form reserved.
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The status of marriage is of much concern to social scientists and the public. This focus is well placed, for studies have shown that marriage is a central part of adult life. Campbell, Converse, and Rogers (1976) show that more adults rate a happy marriage as extremely important than any other domain of life, and their smallest-space analysis shows that items about marriage cluster nearer to the overall measure of subjective well-being than items on any other subject. Recent studies show that happiness with one’s marriage is the most important determinant of overall happiness (for the overall population, see Benine and Nienstedt, 1985; Glenn and Weaver, 1981; on blacks, see Zollar and Williams, 1987). Studies of family well-being have taken two major approaches, emphasizing either the objective or subjective solidarity of marriage. Some emphasize marital dissolution, operationalized as separation or divorce (e.g., Huber and Spitze, 1980; Morgan and Rindfuss, 1984). This is an appropriate measure of what we would call the objective solidarity of marriage, something that should be distinguished from the subjective experience of marriage (Lenthall, 1977; Lewis and Spanier, 1979). Marital dissolution is affected by individuals’ alternatives outside of marriage. An example of this is the relationship between women’s earnings and their probability of divorce (Cherlin, 1979; Ross and Sawhill, 1975). But the probability of marital dissolution is also affected by subjective marital solidarity (Lewis and Spanier, 1979:268). Thus, some marriages persist because of women’s economic dependence, even though subjective solidarity is low. Other marriages are dissolved because of low subjective solidarity. The subjective experience of marriage is important as a predictor of divorce as well as in its own right as an indicator of well-being. Measures of this construct (variously referred to as marital quality, adjustment, happiness, satisfaction or solidarity) are among the most frequently studied variables in the field of family research. Yet most research on the subject suffers from a lack of attention to the link between conceptualization and measurement (Lewis and Spanier, 1979), a problem common to many topics in the social sciences (Bohrnstedt and Borgatta, 1981). Many studies have used one or two item measures of the construct (e.g., Benin and Nienstedt, 1985; Glenn and McLanahan, 1982; Glenn and Weaver, 1981; Honeycutt, Wilson, and Parker, 1982; Ryan, 1981; Udry, 1983). The reliability of such measures is in doubt. Most other studies have used scales with many (often over 20) items (e.g., Bahr, Chappell, and Leigh, 1983; Belsky, Lang, and Rovine, 1985; Doherty, 1981; Madden and Janoff-Bulman, 1981; Roach, Frazier, and Bowden, 1980; Tiggle, Peters, Kelley, and Vincent, 1982; Vera, Berardo, and Berardo, 1985; White, 1983). Few studies provide discussion of the reliability or validity of the scales. When reliability is assessed, this is usually limited to use of Cronbach’s LY,which measures the intercorre-
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KILBOURNE,
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ENGLAND
lation of scale items (e.g., Abbott and Brody, 1985; Belsky et al., 1985; Davidson, Balswick, and Halverson, 1983; Doherty, 1981; Filsinger and Wilson, 1984; Hansen, 1981; Houseknecht and Macke, 1981; Madden and Janoff-Bulman, 1981; Pittman, Price-Bonham, and McKenry, 1983; Rhyne, 1981; Vera et al., 1985; White, 1983). While many studies add items to form a single scale in such a way that presumes a single dimension, very few studies provide a rigorous confirmatory factor analysis to justify their assumption about unidimensionality. (Otto, Spenner, and Featherman, 1980 are exceptional in this regard.) A rigorously assessed measure of subjective solidarity containing more than one, yet relatively few items, is sorely needed. One or two item measures are often unreliable. One scale containing 32 items, Spanier’s (1976) Dyadic Adjustment Scale, has been assessed for construct validity and reliability. Yet we believe many researchers will find it excessively expensive to include such a large number of items on surveys administered to large samples. Further, it will not be possible to get multiitem scales added to such ongoing national data resources as the National Opinion Research Center’s General Social Survey, whereas scales with only a few items could be incorporated. The use of many-item measures of subjective solidarity has gone hand in hand with the use of small samples that limit the costs of interviewing. But Spanier and Lewis (1980) identify the use of larger sample sizes as a major trend of research on marital quality since 1970. The use of large probability samples is long overdue in family research. In order that these efforts to lessen sampling error not increase measurement error. we suggest that, rather than shift to single-item measures, what is needed is a several-item measure of subjective solidarity that has undergone a rigorous test of psychometric properties. This will permit research to combine the merits of large probability samples with the merits of reliable measurement. One unresolved question is the dimensionality of measures of subjective marital solidarity. A commonly used scale by Orden and Bradburn (1968) presumes three dimensions-two of positive satisfactions (sociability and companionship) and one of negatively experienced tensions. Otto et al. (1980) use confirmatory factor analysis and find that a model with only two dimensions, one for satisfactions and one for tensions, fits satisfactorily. Menaghan (1983) has suggested splitting the concept into a dimension relating to equity and a second measuring affection fulfillment. The commonly used scale proposed by Spanier (1976) has several subscales established by factor analysis. Campbell et al. (1976) argue that the five Likert-type items we analyze in this paper divide into tW0 separate constructs, an affective construct measuring satisfaction (indexed by the item on marital satisfaction) and a causally prior cognitive construct that is an assessment of one’s marital relationship (indexed by the items on companionship, understanding, and disagreements about
MEASUREMENT
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MARITAL
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65
money). They base their argument for distinguishing two constructs on the fact that indices of the two “constructs” vary differently by life cycle and sex. However, to foreshadow our confirmatory factor analysis, while many researchers consider subjective marital solidarity to have two or more dimensions, we find that the items we assess represent a single factor. METHODS Samples
The Quality of American Life surveys are virtually replicate national probability surveys of the adult (18 years and over) U.S. population in 1971 (QAL71) and 1978 (QAL78). The two surveys did not use precisely the same geographical boundaries for the primary sampling areas incorporated into the cluster sampling procedure. This is because the QAL78 sample was revised to incorporate slightly different definitions of SMSAs (Campbell and Converse, 1980). But this small change in procedures should have no discernable effect on results. Household interviews were completed for 2164 individuals in the QAL71 survey and for 3692 individuals in the QAL78 survey. We restrict our analysis to white, married respondents with children. There were too few minorities or childless couples in the samples to allow us to test whether the measurement model fits these groups as well. (More details on the QAL surveys are found in Campbell et al., 1976; Campbell, Converse, and Rogers, 1975; Campbell and Converse, 1980; Campbell, 1981.) Measures
We begin with all nonredundant items on marriage that appeared in both the QAL71 and QAL78 surveys. Figure 1 shows the five Likertlike items and the scaling of each. One item (SPEND) deals with how much the couple disagrees about family finances. Berry and Williams (1987) have shown that agreement on spending affects satisfaction with one’s spouse, at least for men. Two items elicit feelings of mutuality. The first of these asks how well the respondent thinks his or her spouse understands him or her (UNDER). The second asks how well the respondent understands his or her spouse (RUNDER). The importance of such understanding to the subjective experience of marriage is suggested by studies showing effects on marital satisfaction of communication (Levinger and Senn, 1967; Navran, 1967; Snyder, 1979), self-disclosure (Jorgensen and Gaudy, 1980; Hendrick, 1981), and the ability to read nonverbal cues from the spouse (Gottman and Porterfield, 1981). A fourth item concerns the amount of time spouses spend together in companionate activities (COMPAN). The importance of this is suggested by Rhyne’s (1981) finding that how much one meets friendship needs through marriage is one of the top predictors of marital satisfaction. The final
66
KILBOURNE, Mnemonic
I.
(SPEND)
HOWELL,
AND ENGLAND
Item wording and metric “How often do you disagree with your husband/wife much money to spend on various things?” “Never” (=5) . “Very often” (= 1)
about how
2. (UNDER)
“How well do you think your husband/wife understands you . your feelings, your likes, and dislikes, and any problems you may have: Do you think he/she understands you .” “Very well” (=4) “Not well at all” (= 1)
3. (RUNDER)
“How well do you understand your husband/wife?” “Very well” (=4) . “Not well at all” (= I)
4. (COMPAN)
“How much companionship do you and your husband/wife how often do you do things together?” “All the time” (~5) . “Hardly ever” ( = I)
5. (SATMAR)
“All things considered, how satisfied are you with your marriage?” “Completely satisfied (=7) “Completely dissatisfied”
have-
(=
1)
FIG. 1. Item wording and scaling for marital solidarity scale: QAL71 and QAL78.
item is general, asking about marital satisfaction (SATMAR). Thus, four of the items refer to specific areas of marital life, whereas the fifth is concerned with a more global and affective assessment of subjective marital solidarity. We use life cycle stage, survey year, and gender as control variables. Specifically, we see if the factor structure of the solidarity items is invariant across categories of these variables. Family life cycle is important because cross-sectional research suggests that marital satisfaction varies in a U-shaped pattern across the life cycle (Aldous, 1978:202; Schram, 1979; Lupri and Frideres, 1981; Rollins and Cannon, 1974; Steinberg and Silverberg, 1987). (There is some question of whether this finding may be an artifact of cohort differences (Spanier and Lewis, 1980:829).) The possibility that subjective solidarity may change over the life cycle makes it all the more important that we have an instrument measuring the construct invariantly across the life cycle. We follow Simpson and England (1981) in classifying the life cycle into three stages: parents with at least one child less than six living at home; parents whose oldest child in the home is between 6 and 17 years; and postparental individuals whose youngest child is 18 years or over and no longer living life cycle stage because in these at home. We omit the “preparental” cross-sectional data, married persons who do not yet (but will) have children cannot be distinguished from those who cannot or have chosen not to have children. Controlling for the child status aspect of life cycle in this way is important because of the increasingly conclusive evidence
MEASUREMENT
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67
that children reduce marital satisfaction (Glenn and McLanahan, 1982; Michalos, 1986; Spanier and Lewis, 1980). It will be important for studies seeking to replicate this finding to know that they are using a measurement protocol that is reliable across child status categories. Invariance of the internal structure of the items between 1971 and 1978 is important because the 1970s were a time of significant social change in gender role beliefs (Cherlin and Walters, 1981; Mason, Czajka, and Arber, 1976). Finally, assessing whether the factor structure is invariant by gender is particularly important because a measure that is reliable for both men and women is necessary if the measure is to be used to explore gender differences in levels or correlates of solidarity. We are particularly concerned about this issue since Rollins and Feldman (1970) found sex differences in the factor structure of the scale they were using. The importance of gender invariance is underscored by the fact that since 1970 studies on marriage increasingly include men and investigate sex differences (Spanier and Lewis, 1980), perhaps in response to Bernard’s (1972 :4) observation that every marriage contains two marriages that may be quite distinct. Analysis The focus of our analysis is a confirmatory factor analysis developed by Joreskog and Sorbom (1979), illustrated for social survey situations by Alwin and Jackson (1980), and available under the LISREL V computer package. We specify a single underlying factor or unobserved construct-subjective marital solidarity-as accounting for the observed covariances of these five items. We test the fit of this specification to the observed data. However, we do not simply focus upon the “fit” of the unidimensional model at one point in time for a single population. Rather, we investigate several theoretically important measurement issues as well. Figure 2 presents a graphical display of the research design. We begin by estimating, for each of the four gender-year groups, a model in which there are only random errors among the five observed items. Then we test whether a theoretically important nonrandom error term between the mutuality items UNDER and RUNDER represents a significant improvement in the fit on the model. (The relation between the two error terms is shown in Fig. 2 as a 7r coefficient and a curved arrow between the 6 - 6 terms for these two items.) This shared covariance may represent the largely artifactual “testing effect” of the parallel wording and identical scaling metric for UNDER and RUNDER which is above and beyond what they hold in common because they each represent the unobserved construct, subjective marital solidarity. Alternately, it may reflect a “specific factor” resulting from an unspecified construct relating to interspouse understanding. It is plausible that those who engage in the disclosure that helps their spouse understand them
68
KILBOURNE,
HOWELL,
AND
ENGLAND
WOMEN 1971
MEN 1971
MEN 1978
1978
FIGURE
2.
are more likely to practice listening and empathy that help them understand their spouse. Or perhaps one spouse’s understanding encourages the others. In either case, there is a theoretical justification for taking advantage of the improvement in fit afforded by specifying the measurement model to take this correlated measurement error into account. (On the importance of using theoretical criteria for specifying correlated errors, see Alwin and Jackson. 1980; Hoelter, 1984.)
MEASUREMENT
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We then assess whether the same model, with one factor and correlated error terms for the mutuality items, is invariant across by gender and year, as sketched in Fig. 2. We then go on to examine factorial invariance for each of the three family life cycle groups (not shown in Fig. 2). Finally, we address an issue distinct from that of invariance. This involves the type of measurement model which most adequately describes these five items in terms of each item’s relationship to the construct (i.e., factor loadings, error variance, and true score variance of the construct itself). (See Alwin and Jackson, 1980; Parker, 1983.) Three types of psychometric models are tested: parallel measures (or items); T equivalent measures; and congeneric measures (Parker, 1983). A parallel measures model contains indicants which are of equal reliability (i.e., have equal factor loadings); thus, the proportion of true score variance in each indicant is due to the underlying construct. In addition, this model requires that the measurement error variance be equal across each indicant. A less restrictive model is one that is 7 equivalent. This model relaxes the assumption of equal error variances among the indicants. However, the equality of true score variances is maintained as an assumption. The third in this set of hierarchically related measurement models is the congeneric measures model. The most realistic assumption in current survey research is that construct indicants will differ in both their respective reliabilities and in their error variances. This specification makes the congeneric measures model equivalent to a common factor model when there is a single construct, as is the case here. To summarize this section, the results will be presented as follows: For each of the four gender and survey-year groups, the interitem correlation and descriptive statistics will be examined. The internal consistency reliability coefficient, Cronbach’s CY,will be computed as a lowerbound estimate of overall (unweighted) index reliability. The one-factor measurement model will be tested for “fit” in each gender-year group, and the invariance of the measurement model across gender-year categories will be evaluated using Joreskog’s (1971) hypothesis-testing framework. To foreshadow, we will present three one-factor models: one with all five items, one with the five items adding the assumption of correlated measurement error between UNDER and RUNDER for the reasons discussed above, and one deleting SPEND because it appears to be causing invariance of the measurement model by gender and year. The issue of invariance of the measurement model across stages of the family life cycle is then considered. Finally, the psychometric properties involving type of measurement model are investigated within each of the gender-year groups. RESULTS
The interitem correlations Table 1 for each gender-year
and descriptive statistics are presented in group. The high means are typical of survey
6.180 1.241
,333 .500 .317
1.000 SOS
(2)
(1)
3.427 ,668
,297 .215
l.ooO
I. (3) .391 ,628
QAL71
.454
3.434 .568
,321 ,262
1.000
QAL78
3.906 1.118
.323
l.CQO
(4) ,402 ,370 ,303
II = 511; Women-QAL71,
Cronbach’s (Y: men = .734: women = ,762
3.298 ,687
.331
..584 .428
1.000
(3) .337 ,585
II.
n = 597: Men-QAL78.
.993
3.691
1.000
(5) .302 ,285 ,252 ,294
3.679 ,969
,121 3.842
1.000
1.000
n = 750; Women-QAL78,
6.340 3.481 3.407 3.865 3.675
Mean
6.407 3.411 3.373 3.788 3.659
Mean
Group: QAL71-QAL78
(5) ,360 .376 ,346 ,265
(4) .413 .297 ,353
1.181 Cronbach’s a: men = .758: women = .738
1.220
.419 1.ooo .632 .329 .328
(2)
3.281 .758
6.166
.556 .437 .401 .282
1.000
(1)
TABLE I Means, and Standard Deviations for Marital Solidarity Items by Year-Gender
Note. Men above the diagonal, Women below. Men-QAL7l.
Mean SD
SATMAR UNDER RUNDER COMPAN SPEND
883.
I. 2. 3. 4. 5.
Mean SD
1. SATMAR 2. UNDER 3. RUNDER 4. COMPAN 5. SPEND
Correlations,
n =
1.026 1.048
.601
,626
SD 1.081
I.164 1.022
,935 ,651 ,636
SD
%
9
u
:r $
2 P
f3
z F
4 0
MEASUREMENT
OF
MARITAL
SOLIDARITY
71
responses to questions about various domains of life satisfaction (Campbell et al., 1976). The correlations are fairly similar across the four groups, ranging from approximately .2 to .6 in size. The item about disagreements on family finances (SPEND) exhibits the lowest correlations with other items, foreshadowing a problem to which we return to below. The most global item, marital satisfaction (SATMAR), correlates moderately and consistently with the more specific items. Of particular note are the relatively high correlations between the two mutuality items of understanding (UNDER AND RUNDER). This is what we would expect under the hypothesis of a “testing” effect in which respondents respond similarly to UNDER and RUNDER because of the similarity in the wording and scaling of the two items or under the hypothesis of a real correlation between interspousal understanding. Using the conventional coefficient for internal consistency of an unweighted index, Cronbach’s (Y is in an acceptable .7-.8 range for all four groups. Using confirmatory factor analysis, Table 2 presents three single-factor models for each of the four gender-year groups. The models do not include any across-group constraints. The unstandardized results are used to compare across groups while the standardized coefficients represent the relative contributions of the unobserved construct to each observed item within a given group. Model I is specified to allow only random measurement error among the five items (not shown in Fig. 2), which is the conventional assumption in index construction. Using the x’ test statistic, this model does not fit the observed data, forcing a rejection of this specification for each of the four groups. Evaluating various aspects of the model, such as the normalized residual matrix and the modification indices (see Joreskog and Sorhom, 1983), suggests that freeing up several elements in the 8 - 6 (errorterm matrix would result in a substantially better fit. However, using solely statistical criteria to make a model “fit” is somewhat akin to the atheoretical use of stepwise regression to find a “best” model. Such procedures are ill-advised because they tend to produce nonreplicable findings by capitalizing upon the idiosyncracies of the data instead of generating a theoretically based understanding of the data. (See Hoelter’s 1984 arguments on the misuse of covariance structure models.) In this case, UNDER and RUNDER are the only items for which we have a theoretical reason to expect correlated errors, as discussed above. For this reason, Model II allows only the covariance of the UNDER and RUNDER 8 - 6 terms and retains all five items. This specification results in a significantly improved fit within each gender-year group. Indeed, we cannot reject this model on statistical grounds using any Type 1 probability less than .Ol , although the QAL71 women’s results can be rejected at the .05 level. The standardized factor-loading coefficients show that marital solidarity is dominated by the marital satisfaction item (SATMAR) in all but one of the
72
KILBOURNE.
HOWELL,
AND
ENGLAND
:f P
1.000* S80 ,512 1.010 .128
Note. See Fig. 1 for item ” U, unstandardized. b S, standardized. * Fixed parameter.
SATMAR UNDER RUNDER COMPAN n23 2
wording
0.78 1 = .376
and legend
,713 s93 .537 ,579 .241
Model 1 .ooo* ,524 ,370 ,591 ,130 1.62 I = ,204
III:
Nonrandom ,811 ,771 .548 ,495 .233
error 1 .ooo* ,540 ,399 .806 ,098 0.86 1 = ,353
,695 ,648 ,499 ,578 ,197
1 .OOo* ,478 .273 .775 ,111 2.27 I =.131
,763 ,659 .455 ,656 .217
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ENGLAND
subgroups (males in 1971). This domination makes sense, given that the SATMAR item is the most global in its semantic referent. Examination of the factor loadings in Table 2 also shows a convergence between the sexes in the importance of disagreements about spending. The sex differences in 1971 are striking, with disagreements about spending much more important to men than to women in contribution to marital solidarity. But by 1978, the sexes were converging, with the salience of spending issues dropping for men and increasing for women. We conjecture that this results from a newly found sense of entitlement to participate in decisions about spending as increasing numbers of women became employed outside the home during the 1970s. Because SPEND is contributing to invariance of the measurement model by gender and year, Table 2 also includes Model III which drops SPEND and reestimates the measurement model (retaining the assumption of correlated error for UNDER and RUNDER introduced in Model II). This model fits better by statistical criteria. Using the .05 level, the model cannot be rejected for any of the four gender-year groups. More importantly, Model III shows greater invariance by year and sex. Thus, we recommend dropping SPEND from future analyses of marital solidarity because of its lack of invariance across gender and year. These differences among the four gender-year groups are more formally investigated through tests of invariance, summarized in Table 3. As the covariance matrix comparisons below the table show, when we test the null hypothesis that the variance-covariance matrices are equal, all the comparisons indicate that there are indeed subgroup differences, to which we now turn. The “unconstrained” model shown in the first column of Table 3 reports measurement model parameters estimated for each group with no across-group constraints in effect. As such, the xZ value from this unconstrained model serves as a baseline against which we may compare the across-group constraints that are shown in the remainder of the table. The first test is summarized in the second column and constrains the factor loadings to be equal across groups (e.g., for men and women in 1971). The resulting difference in the two x2 is the test statistic which evaluates the null hypothesis of equal factor loadings or, more substantively, equal “constructs” being measured across the two groups. The following tests sequentially examine the added equality constraints of true score variance and item error variance. These are summarized in the last three columns of Table 3. On statistical grounds alone, three of the four subgroup comparisons suggest that factorial invariance should be rejected. Only for men across time can the null hypothesis of equal “constructs” not be rejected. However, a careful comparison of test statistics indicates the group which differs most from the others is women in 1971. This was found in Table
MEASUREMENT
OF MARITAL
TABLE 3 Summary of Factorial Invariance across Year-Gender Scale: QAL7 1-QAL78 Unconstrained Aa+
Groups QAL71 men vs womena
QAL78 men vs womenb
X2 df Ax’ Adj P
Zf Ax’ Adf P
QAL71-78 men’
-
0.312 3.12 2 ,210
10.29 5 7.17 3 <.I0
21.77 6 11.48 1 <.OOl
18.53 10 8.24 5 c.01
-
1.64 2
6.19 6 0.12 1 >.90
-
33.22 II 27.03 5 <.001
19.63 6 0.31 1 >.90
-
48.21 II 28.58 5 <.OOl
-
Ax’
3.88 2 0.144
19.32 5 15.32 3 <.OlO
P
AaM
31.41 IO 14.11 5 <.02
0.440
Mf
Constrained parameters A0 A@ 32.60 6 15.29 1 <.OOl
P QAL71-78 wornend
Groups on Marital Solidarity
17.31 5 14.98 3 <.Ol
2.33 2
6.03 5 4.39 3 >.lO
if A$
Adf
y
A
75
SOLIDARITY
-
-
Note. Covariance matrix comparisons: “x’ = 56.29, P < .OO1;h~Z = 27.29. P < .OOl; = 31.15, P < .001;y = 45.10, P < ,001.
2, as well; the differences in Model III factor loadings between men and women in 1971 subside somewhat by 1978 and the over time comparisons for women themselves show that their factor loadings change significantly over time. Given the large sample size and the fact that only one genderyear group deviates from the overall pattern, we think that statistically significant subgroup differences shown in Table 3 are not substantively meaningful, with the single exception of comparisons involving women in 1971. Turning to the remaining invariance tests, it also seems that (item) error and true score variance differ significantly across groups. From a substantive viewpoint, however, it again seems that the primary source of these departures from invariance is the 1971 subgroup of women. In terms of the structure of subjective marital solidarity, it appears that the gender role change of the 1970s made women more like men by 1978. This suggests that research using data from later time periods or from new investigations can consider this measure invariant by gender.
76
KILBOURNE.
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Table 4 summarizes results of the same hypothesis tests for life cycle differences within each sex and survey year. Testing the hypothesis that the covariance-variance matrices for each sex and survey year are equal across life cycle stages, we find that this null hypothesis cannot be rejected for either gender in 1978. These comparisons are shown below Table 4. Although the covariance-variance matrices for the later time period do not differ across the three stages, we nonetheless include the results of further tests for these groups. In all four gender-survey year groups, the unconstrained model fits reasonably well and this x2 value serves as a baseline for the subsequent comparisons. In every case, the invariance of factor loadings cannot be rejected (P > . 100). Results from the next test, of across-group equality in measurement error, shown in column 2, suggest that there are indeed differences by the life cycle stage for the 1971 subgroups, but not for the 1978 subgroups. Factor (true score) variances differ only for 1971 females. Despite differences for this one gender-year group. the invariance by family life cycle wihin the TABLE 4 Summary of Factorial Invariance across Life Cycle (FLC) Stage By Gender and Survey Year: QAL71-QAL-78 FLC comparison group QAL71 males”
Unconstrained A
2 2f
Ax’ Adf QAL71 female?
P 2 Zf
Ax’
1.44
,695 4.39
-
Mf QAL78 males’
P 2
2f
Ax’
Wf P
QAL78 females“
,222 1.88
S98 1.81
,612
Constrained parameters A@ A0
6.06 9 4.62 6 >.I00
32.38 19 22.22 10 c.025
9.32 II 3.26 2 >.OOl
10.06 9 5.67 6 >.I00
39.55 19 29.49 10 c.001
14.02 II 3.96 2 2.100
7.79 9 5.67 6 >.lOO
17.60 19 9.81 10 >.lOO
11.24 11 3.45 2 >.lOO
5.28 9 3.47 6 >.lOO
22.30 19 17.02 10 <.I0
9.14 11 3.86 i >.I00
Note. Covariance matrix comparisons: “x’ = 39.07. df = 20. P = .007; *x2 = 43.08. df = 20, P = .002; ‘x’ = 21.99. df = 20. P = ,341: ‘xZ = 25.57. df = 20. P = ,180.
MEASUREMENT
OF MARITAL
77
SOLIDARITY
other three gender-year groups suggests that the item set measures the same construct across family life cycle stages, particularly in recent years. Table 5 examines the type of measurement model that best describes these items. Others have found that the assumption of a congeneric model seems most warranted for contempory social survey data (Alwin and Jackson, 1980; Parker, 1983), and we make this conclusion about the subjective marital solidarity items here. In each subgroup the parallel and 7 equivalent models are handily rejected on a statistical basis. However, we cannot reject the congeneric model. And the adjusted goodnessof-fit index (AGFI) reaches a desirable level for this model, especially in comparison to the more rigorous measurement assumptions of the parallel and T equivalent models. SUMMARY AND CONCLUSION
Over a decade ago, Otto (1975) suggested that research on marriage and the family should improve the rigor of its conceptualization, measurement, and methods. One important part of this effort is the application of new analytical methods to problems of measurement (Bohrnstedt and Borgatta, 1981). In this spirit, we have provided a discussion TABLE 5 Summary of Analysis of Alternative Models for Marital Solidarity by Year-Gender Subgroup: QAL71-QAL78 Model” Parallel r equivalent Congeneric-Common Parallel r equivalent Congeneric-Common Parallel r equivalent Congeneric-Common Parallel r equivalent Congeneric-Common
x%f
AGFIh
factor
345.09 75.88 1.62
I. QAL71-Women 7 49.30 4 18.97 I 1.62
,756 ,855 ,987
factor
251.34 29.33 .78
II. 7 4 1
QAL71-Men 35.91 7.33 .78
,749 ,929 ,992
factor
680.89 194.27 2.27
III. QAL78-Women 7 97.27 4 48.57 1 2.27
.673 ,738 .987
factor
401.87 69.68 .86
X2
df
IV. 7 4 1
QAL78-Men 57.41 17.42 .86
y For a single-factor model, the congeneric and common factor specifications equivalent. b AGFI, adjusted goodness of fit index (see Joreskog and Sorbom, 1983).
,766 ,902 ,994 are
78
KILBOURNE,
HOWELL.
AND ENGLAND
of the measurement properties of a set of five Likert-type items available in two national replicate surveys in an attempt to provide a sound measure of subjective marital solidarity for use in future research. We have focused on the (internal consistency) reliability of the items and their factorial invariance across time, gender, and family life cycle stage. Our analysis suggests that two things are necessary to turn these items into a measurement protocol that “fits” as a single factor and is relatively invariant across gender, time, and life cycle stage. For fit, we need to allow the error terms for feeling understood by one’s spouse and understanding one’s spouse (UNDER AND RUNDER) to be correlated, as both substantive and measurement theory suggest they would be. We found that dropping the item on how much the couple disagrees on spending (SPEND) substantially improves the invariance of the measurement model. This item has changed its meaning during the period when so many women became wage earners. We conclude that these four items form an appropriate linear composite of subjective marital solidarity, that the measurement is a clear advance over single-item indicators, and that the modest number of items makes this protocol feasible to put on large multipurpose surveys. We have focused on reliability: future work should examine the criterion and construct validity of the measure we propose. If this unidimensional measure is found to correlate highly with only one factor of scales that have been conceptualized as multidimensional, this will delineate the discriminant validity of the measure and show the theoretical limits of its applicability. Alternatively, if the measure is highly correlated with the overall score from scales containing dozens of items, it can become a cost-effective replacement for multi-item scales. REFERENCES Abbott, D. A., and Brody. G. H. (1985). “The relation of child age, gender, and number of children to the marital adjustment of wives,” Journal of Marriage and the Family 47, 77-84.
Aldous, J. (1978). Family Careers: Development Change in Families, Wiley, New York. Alwin, D. F., and Jackson, D. J. (1980). “Measurement models for response errors in surveys: Issues and applications,” in Sociological Methodology (K. F. Schuessler, Ed.), Jossey-Bass, San Francisco. Bahr, S. J., Chappell, C. B.. and Leigh, G. K. (1983). “Age at marriage, role enactment. role consensus, and marital satisfaction,” Journal of Marriage and Family 45, 795803.
Belsky, J.. Lang, M. E., and Rovine, M. (1985). “Stability and change in marriage across Journal of Marriage and the Family the transition to parenthood: A second study,” 47, 855-865.
Benin, M. H., and Nienstedt, B. C. (1985). “Happiness in single and dual-earner families: The effects of marital happiness, job satisfaction, and life cycle,” Journal of Marriage and the Family 47, 975-984. Bernard. J. (1972). The Future of Marriage, Bantam Books, New York. Berry, R. E.. and Williams, F. L. (1987). “Assessing the relationship between quality of
MEASUREMENT
OF MARITAL
SOLIDARITY
79
life and marital and income satisfaction: A path analytic approach,” Journal of Marriage and the Family 49, 107-l 16. Bohmstedt, G. W., and Borgatta, E. F. (1981). Social Measurement: Current Issues, Sage, Beverly Hills. Campbell, A. (1981). The Sense of Well-Being in America. McGraw-Hill, New York. Campbell, A., and Converse, P. E. (1980). The Quality of American Life 1978, Institute for Social Research, University of Michigan, Ann Arbor, MI. Campbell, A., Converse, P. E., and Rogers, W. L. (1975). The Quality of American Life 1971, Institute for Social Research, University of Michigan, Ann Arbor, MI. Campbell, A., Converse, P. E., and Rogers, W. L. (1976). The Quality of American Life, McGraw-Hill, New York. Cherlin, A. (1979). “Work Life and Marital Dissolution,” in Divorce and Separation, (G. Levinger, and 0. C. Moles, Eds.), Basic Books, New York. Cherlin, A., and Walters, P. B. (1981). “Trends in United States men’s and women’s sexrole attitudes: 1972-1978,” American Sociological Review 46, 453-460. Davidson, B., Balswick, J., and Halverson, C. (1983). “Affective self-disclosure and marital adjustment: A test of equity theory,” Journal of Marriage and the Family 45, 93-102. Doherty, W. J. (1981). “Locus of control differences and marital dissatisfaction,” Journal of Marriage and the Family 43, 369-377. Filsinger, E. E., and Wilson, M. R. (1984). “Religiosity. socioeconomic rewards, and family development: Predictors of marital adjustment,” Journal of Marriage and the Family 46, 663-670. Glenn, N. D., and McLanahan, S. (1982). “Children and marital happiness: A further specification of the relationship,” Journal of Marriage and the Family 44, 63-72. Glenn, N. D., and Weaver, C. N. (1981). “The contribution of marital happiness to global happiness.” Journal of Marriage and the Family 43, 161-168. Gottman, J. M., and Porterheld. A. L. (1981). “Communicative competence in the nonverbal behavior of married couples,” Journal of Marriage and the Family 43, 817824. Hansen, G. L. (1981). “Marital adjustment and conventionalization: A re-examination,” Journal of Marriage and the Family 43, 855-863. Hendrick. S. S. (1981). “Self-disclosure and marital satisfaction,” Journal of Personality and Social Psychology 40, 1150-l 159. Hoelter, J. W. (1984). Uses and Misuses of Joreskog’s Covariance Structure (JCS) Models, Paper presented at the annual meetings of the Southern Sociological Society meetings, Knoxville. Honeycutt. J. M., Wilson, C., and Parker, C. (1982). “Effects of sex and degrees of happiness on perceived styles of communication in and out of the marital relationship,” Journal of Marriage and the Family 44, 395-406. Houseknecht. S. K.. and Macke, A. S. (1981). “Combining marriage and career: The marital adjustment of professional women,” Journal of Marriage and the Family 43, 651-661. Huber, J., and Spitze, G. (l980). “Considering divorce: An expansion of Becker’s theory of marital instability,” American Journal of Sociology 86, 75-89. Joreskog, K. G. (1971). “Simultaneous factor analysis in several populations.” Psychometrika 36, 409-426. Joreskog, K. G., and Sorbom, D. (1979). Advances in Factor Analysis and Structural Equation Models, Abt Books. Cambridge, MA. Joreskog, K. G.. and Sorbom, D. (1983). LISREL V: Analysis of Linear Structural Relationship by Maximum Likelihood and Least Squares Methods, International Educational Resources, Chicago. Jorgensen, S. R., and Gaudy, J. C. (1980). “Self-disclosure and satisfaction in marriage: The relation examined,” Family Relations 29, 281-287.
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Lenthall, G. (1977). “Marital satisfaction and marital stability,” Journal of Marriage and Family Counseling 3, 25-32. Lewis, R. A., and Spanier, G. B. (1979). “Theorizing about the quality and stability of marriage,” in Contemporary Theories About the Family: Research-Based Theories, (W. R. Burr, R. Hill, F. I. Nye, and I. L. Reiss, Eds.), Vol. I. Free Press, New York. Levinger, G., and Senn, K. J. (1967). “Disclosure of feelings in marriage,” Merrill-Palmer Quarterly 13, 237-249. Lupri, E., and Frideres, J. (1981). “The quality of marriage and the passage of time: Marital satisfaction over the family life cycle,” Canadian Journal of Sociology 6, 283305. Madden, M. E., and Bulman, R. J. (1981). “Blame, control, and marital satisfaction: Wifes’ attributions for conflict in marriage,” Journal of Marriage and the Family 43, 663674. Mason, K. O., Czajka, J. L., and Arber, S. (1976). “Change in U.S. women’s sex-role attitudes: 1964-1974,” American Sociological Review 41, 573-596. Menaghan, E. (1983). “Marital stress and family transitions: A panel analysis,” Journal of Marriage and the Family, 45, 371-386. Michalos, A. C. (1986). “Job satisfaction, marital satisfaction, and the quality of life: A review and a preview,” in Research on the quality of life, (F. M. Andrews, Ed.), Institute for Social Research, University of Michigan, Ann Arbor, MI. Morgan, S. P., and Rindfuss, R. R. (1984). “Marital disruption: Structural and temporal dimensions,” American Journal of Sociology 90, 1055-1077. Navran, L. (1967). “Communication and adjustment in marriage,” Family Process, 6, 173184. Orden, S., and Bradburn, N. M. (1968). “Dimensions of marriage happiness,” American Journal of Sociology 73, 715-731. Otto, L. B. (1975). ‘Class and status in family research,” Journal of Marriage and the Family 37, 315-32. Otto, L. B., Spenner, K. I., and Featherman, D. L. (1980). The Structure of the Marital State Fitting Measurement to Theory, paper presented at the annual meeting of the American Sociological Association, New York, August 27-31, 1980. Parker, R. N. (1983). “Measuring social participation,” American Sociological Review 48, 864-873. Pittman, J. F., Jr., Price-Bonham, S., and McKenry, P. C. (1983). “Marital cohesion: A path model,” Journal of Marriage and the Family 45, 521-531. Rhyne, D. (1981). “Bases of marital satisfaction among men and women,” Journal of Marriage and the Family 43, 941-955. Roach, A. J., Frazier, L. P., and Bowden, S. R. (1980). “The marital satisfaction scale: Development of a measure for intervention research,” Journal of Marriage and the Family 43, 537-546. Rollins, B. C., and Cannon, K. L. (1974). Journal of Marriage and the Family 36, 27l282. Rollins, B. C., and Feldman, H. (1970). “Marital satisfaction over the family life cycle,” Journal of Marriage and the Family 32, 20-27. Ross, H. L., and Sawhill, I. V. (1975). Time of Transition: The Growth of Families Headed by Women. Urban Institute, Washington, DC. Ryan, J. (1981). “Marital status, happiness, and anemia,” Journal of Marriage and the Family 43, 643-649. Schram, R. W. (1979). “Marital satisfaction over the family life cycle: A critique and proposal,” Journal of Marriage and the Family 41, 7-12. Simpson, I. H., and England, P. (1981). “Conjugal work roles and marital solidarity,” Journal of Family Issues 1, 147-171.
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Snyder, D. K. (1979). “Multidimensional assessment of marital satisfaction,” Journal of Marriage and the Family 41, 813-823. Spanier, G. B., and Cole, C. L. (1976). “Measuring dyadic adjustment: New scales for assessing the quality of marriage and similar dyads,” Journal of Marriage and the Family 38, 15-28. Spanier, G. B., and Lewis, R. A. (1980). “Marital quality: A review of the seventies,” Journal of Marriage and the Family 42, 813-823. Steinberg, L., and Silverberg, S. B. (1987). “Influences on marital satisfaction during the middle stages of the life cycle,” Journal of Marriage and the Family 49, 751-760. Tiggle, R. B., Peters, M. D., Kelley, H. H., and Vincent, J. (1982). “Correlational and discrepancy indices of understanding and their relation to marital satisfaction,” Journal of Marriage and the Family 44, 209-215. Udry, J. R. (1983). “The maritai happiness/disruption relationship by level of marital alternatives,” Journal of Marriage and the Family 45, 221-230. Vera, H., Berardo, D.H., and Berardo, F.M. (1985). “Age heterogamy in marriage,” Journal of Marriage and the Family 47, 553-566. White, L. K. (1983). “Determinants of spousal interaction: Marital structure or marital happiness,” Journal of Marriage and the Family 45, 511-519. Zollar, A. C., and Williams, J. S. (1987). “The contribution of marriage to the life satisfaction of black adults,” Journal of Marriage and the Family 49, 87-92.
SCIENCE
RESEARCH
19, 62-81 (I!?%)
A Measurement Model for Subjective Marital Solidarity: Invariance across Time, Gender, and Life Cycle Stage BARBARA
STANEK
University
FRANK Mississippi
KILBOURNE
of Texas-Dallas
HOWELL State
University
AND
PAULA University
ENGLAND of Arizona
We use LISREL to assess the measurement properties of a unidimensional indicator of subjective marital solidarity based on four questionnaire items. A rigorously assessed measure containing more than one, yet relatively few items, is solely needed for research on marriage; such a measure can combine high reliability with low cost. Using 1971 and 1978 waves of the Quality of American Life data, we evaluate a measure based on four items: how well the respondent thinks his or her spouse understands him or her, how well the respondent understands his or her spouse, the amount of time spouses spend together in companionate activities, and reported marital satisfaction. With one correlated error term, these items are found to be a unidimensional indicator and to show substantial invariance across gender, survey year, and life cycle stage. We rejected inclusion of an item on how much the couple agrees on finances because this item created invariance by gender and survey year. This item apparently changed its meaning during the 1970s when many women became wage earners. 0 1990 Academic
Press, Inc.
The data used in this study were made available by the Inter-University Consortium for Political and Social Research. The data for the Quality of American Life, 1971 and 1978, were collected by the Institute for Social Research, University of Michigan, under support from the National Science Foundation. Neither the original collectors nor the Consortium bear responsibility for the analyses or interpretations presented herein. Address correspondence and reprint requests to Barbara Stanek Kilbourne, School of Social Sciences. University of Texas-Dallas, Richardson, TX 750830688. 62 0049-089X?% $3 .OO Copyright All rights
0 1990 by Academic Press. Inc. of reproduction in any form reserved.
MEASUREMENT
OF MARITAL
SOLIDARITY
63
The status of marriage is of much concern to social scientists and the public. This focus is well placed, for studies have shown that marriage is a central part of adult life. Campbell, Converse, and Rogers (1976) show that more adults rate a happy marriage as extremely important than any other domain of life, and their smallest-space analysis shows that items about marriage cluster nearer to the overall measure of subjective well-being than items on any other subject. Recent studies show that happiness with one’s marriage is the most important determinant of overall happiness (for the overall population, see Benine and Nienstedt, 1985; Glenn and Weaver, 1981; on blacks, see Zollar and Williams, 1987). Studies of family well-being have taken two major approaches, emphasizing either the objective or subjective solidarity of marriage. Some emphasize marital dissolution, operationalized as separation or divorce (e.g., Huber and Spitze, 1980; Morgan and Rindfuss, 1984). This is an appropriate measure of what we would call the objective solidarity of marriage, something that should be distinguished from the subjective experience of marriage (Lenthall, 1977; Lewis and Spanier, 1979). Marital dissolution is affected by individuals’ alternatives outside of marriage. An example of this is the relationship between women’s earnings and their probability of divorce (Cherlin, 1979; Ross and Sawhill, 1975). But the probability of marital dissolution is also affected by subjective marital solidarity (Lewis and Spanier, 1979:268). Thus, some marriages persist because of women’s economic dependence, even though subjective solidarity is low. Other marriages are dissolved because of low subjective solidarity. The subjective experience of marriage is important as a predictor of divorce as well as in its own right as an indicator of well-being. Measures of this construct (variously referred to as marital quality, adjustment, happiness, satisfaction or solidarity) are among the most frequently studied variables in the field of family research. Yet most research on the subject suffers from a lack of attention to the link between conceptualization and measurement (Lewis and Spanier, 1979), a problem common to many topics in the social sciences (Bohrnstedt and Borgatta, 1981). Many studies have used one or two item measures of the construct (e.g., Benin and Nienstedt, 1985; Glenn and McLanahan, 1982; Glenn and Weaver, 1981; Honeycutt, Wilson, and Parker, 1982; Ryan, 1981; Udry, 1983). The reliability of such measures is in doubt. Most other studies have used scales with many (often over 20) items (e.g., Bahr, Chappell, and Leigh, 1983; Belsky, Lang, and Rovine, 1985; Doherty, 1981; Madden and Janoff-Bulman, 1981; Roach, Frazier, and Bowden, 1980; Tiggle, Peters, Kelley, and Vincent, 1982; Vera, Berardo, and Berardo, 1985; White, 1983). Few studies provide discussion of the reliability or validity of the scales. When reliability is assessed, this is usually limited to use of Cronbach’s LY,which measures the intercorre-
64
KILBOURNE,
HOWELL,
AND
ENGLAND
lation of scale items (e.g., Abbott and Brody, 1985; Belsky et al., 1985; Davidson, Balswick, and Halverson, 1983; Doherty, 1981; Filsinger and Wilson, 1984; Hansen, 1981; Houseknecht and Macke, 1981; Madden and Janoff-Bulman, 1981; Pittman, Price-Bonham, and McKenry, 1983; Rhyne, 1981; Vera et al., 1985; White, 1983). While many studies add items to form a single scale in such a way that presumes a single dimension, very few studies provide a rigorous confirmatory factor analysis to justify their assumption about unidimensionality. (Otto, Spenner, and Featherman, 1980 are exceptional in this regard.) A rigorously assessed measure of subjective solidarity containing more than one, yet relatively few items, is sorely needed. One or two item measures are often unreliable. One scale containing 32 items, Spanier’s (1976) Dyadic Adjustment Scale, has been assessed for construct validity and reliability. Yet we believe many researchers will find it excessively expensive to include such a large number of items on surveys administered to large samples. Further, it will not be possible to get multiitem scales added to such ongoing national data resources as the National Opinion Research Center’s General Social Survey, whereas scales with only a few items could be incorporated. The use of many-item measures of subjective solidarity has gone hand in hand with the use of small samples that limit the costs of interviewing. But Spanier and Lewis (1980) identify the use of larger sample sizes as a major trend of research on marital quality since 1970. The use of large probability samples is long overdue in family research. In order that these efforts to lessen sampling error not increase measurement error. we suggest that, rather than shift to single-item measures, what is needed is a several-item measure of subjective solidarity that has undergone a rigorous test of psychometric properties. This will permit research to combine the merits of large probability samples with the merits of reliable measurement. One unresolved question is the dimensionality of measures of subjective marital solidarity. A commonly used scale by Orden and Bradburn (1968) presumes three dimensions-two of positive satisfactions (sociability and companionship) and one of negatively experienced tensions. Otto et al. (1980) use confirmatory factor analysis and find that a model with only two dimensions, one for satisfactions and one for tensions, fits satisfactorily. Menaghan (1983) has suggested splitting the concept into a dimension relating to equity and a second measuring affection fulfillment. The commonly used scale proposed by Spanier (1976) has several subscales established by factor analysis. Campbell et al. (1976) argue that the five Likert-type items we analyze in this paper divide into tW0 separate constructs, an affective construct measuring satisfaction (indexed by the item on marital satisfaction) and a causally prior cognitive construct that is an assessment of one’s marital relationship (indexed by the items on companionship, understanding, and disagreements about
MEASUREMENT
OF
MARITAL
SOLIDARITY
65
money). They base their argument for distinguishing two constructs on the fact that indices of the two “constructs” vary differently by life cycle and sex. However, to foreshadow our confirmatory factor analysis, while many researchers consider subjective marital solidarity to have two or more dimensions, we find that the items we assess represent a single factor. METHODS Samples
The Quality of American Life surveys are virtually replicate national probability surveys of the adult (18 years and over) U.S. population in 1971 (QAL71) and 1978 (QAL78). The two surveys did not use precisely the same geographical boundaries for the primary sampling areas incorporated into the cluster sampling procedure. This is because the QAL78 sample was revised to incorporate slightly different definitions of SMSAs (Campbell and Converse, 1980). But this small change in procedures should have no discernable effect on results. Household interviews were completed for 2164 individuals in the QAL71 survey and for 3692 individuals in the QAL78 survey. We restrict our analysis to white, married respondents with children. There were too few minorities or childless couples in the samples to allow us to test whether the measurement model fits these groups as well. (More details on the QAL surveys are found in Campbell et al., 1976; Campbell, Converse, and Rogers, 1975; Campbell and Converse, 1980; Campbell, 1981.) Measures
We begin with all nonredundant items on marriage that appeared in both the QAL71 and QAL78 surveys. Figure 1 shows the five Likertlike items and the scaling of each. One item (SPEND) deals with how much the couple disagrees about family finances. Berry and Williams (1987) have shown that agreement on spending affects satisfaction with one’s spouse, at least for men. Two items elicit feelings of mutuality. The first of these asks how well the respondent thinks his or her spouse understands him or her (UNDER). The second asks how well the respondent understands his or her spouse (RUNDER). The importance of such understanding to the subjective experience of marriage is suggested by studies showing effects on marital satisfaction of communication (Levinger and Senn, 1967; Navran, 1967; Snyder, 1979), self-disclosure (Jorgensen and Gaudy, 1980; Hendrick, 1981), and the ability to read nonverbal cues from the spouse (Gottman and Porterfield, 1981). A fourth item concerns the amount of time spouses spend together in companionate activities (COMPAN). The importance of this is suggested by Rhyne’s (1981) finding that how much one meets friendship needs through marriage is one of the top predictors of marital satisfaction. The final
66
KILBOURNE, Mnemonic
I.
(SPEND)
HOWELL,
AND ENGLAND
Item wording and metric “How often do you disagree with your husband/wife much money to spend on various things?” “Never” (=5) . “Very often” (= 1)
about how
2. (UNDER)
“How well do you think your husband/wife understands you . your feelings, your likes, and dislikes, and any problems you may have: Do you think he/she understands you .” “Very well” (=4) “Not well at all” (= 1)
3. (RUNDER)
“How well do you understand your husband/wife?” “Very well” (=4) . “Not well at all” (= I)
4. (COMPAN)
“How much companionship do you and your husband/wife how often do you do things together?” “All the time” (~5) . “Hardly ever” ( = I)
5. (SATMAR)
“All things considered, how satisfied are you with your marriage?” “Completely satisfied (=7) “Completely dissatisfied”
have-
(=
1)
FIG. 1. Item wording and scaling for marital solidarity scale: QAL71 and QAL78.
item is general, asking about marital satisfaction (SATMAR). Thus, four of the items refer to specific areas of marital life, whereas the fifth is concerned with a more global and affective assessment of subjective marital solidarity. We use life cycle stage, survey year, and gender as control variables. Specifically, we see if the factor structure of the solidarity items is invariant across categories of these variables. Family life cycle is important because cross-sectional research suggests that marital satisfaction varies in a U-shaped pattern across the life cycle (Aldous, 1978:202; Schram, 1979; Lupri and Frideres, 1981; Rollins and Cannon, 1974; Steinberg and Silverberg, 1987). (There is some question of whether this finding may be an artifact of cohort differences (Spanier and Lewis, 1980:829).) The possibility that subjective solidarity may change over the life cycle makes it all the more important that we have an instrument measuring the construct invariantly across the life cycle. We follow Simpson and England (1981) in classifying the life cycle into three stages: parents with at least one child less than six living at home; parents whose oldest child in the home is between 6 and 17 years; and postparental individuals whose youngest child is 18 years or over and no longer living life cycle stage because in these at home. We omit the “preparental” cross-sectional data, married persons who do not yet (but will) have children cannot be distinguished from those who cannot or have chosen not to have children. Controlling for the child status aspect of life cycle in this way is important because of the increasingly conclusive evidence
MEASUREMENT
OF
MARITAL
SOLIDARITY
67
that children reduce marital satisfaction (Glenn and McLanahan, 1982; Michalos, 1986; Spanier and Lewis, 1980). It will be important for studies seeking to replicate this finding to know that they are using a measurement protocol that is reliable across child status categories. Invariance of the internal structure of the items between 1971 and 1978 is important because the 1970s were a time of significant social change in gender role beliefs (Cherlin and Walters, 1981; Mason, Czajka, and Arber, 1976). Finally, assessing whether the factor structure is invariant by gender is particularly important because a measure that is reliable for both men and women is necessary if the measure is to be used to explore gender differences in levels or correlates of solidarity. We are particularly concerned about this issue since Rollins and Feldman (1970) found sex differences in the factor structure of the scale they were using. The importance of gender invariance is underscored by the fact that since 1970 studies on marriage increasingly include men and investigate sex differences (Spanier and Lewis, 1980), perhaps in response to Bernard’s (1972 :4) observation that every marriage contains two marriages that may be quite distinct. Analysis The focus of our analysis is a confirmatory factor analysis developed by Joreskog and Sorbom (1979), illustrated for social survey situations by Alwin and Jackson (1980), and available under the LISREL V computer package. We specify a single underlying factor or unobserved construct-subjective marital solidarity-as accounting for the observed covariances of these five items. We test the fit of this specification to the observed data. However, we do not simply focus upon the “fit” of the unidimensional model at one point in time for a single population. Rather, we investigate several theoretically important measurement issues as well. Figure 2 presents a graphical display of the research design. We begin by estimating, for each of the four gender-year groups, a model in which there are only random errors among the five observed items. Then we test whether a theoretically important nonrandom error term between the mutuality items UNDER and RUNDER represents a significant improvement in the fit on the model. (The relation between the two error terms is shown in Fig. 2 as a 7r coefficient and a curved arrow between the 6 - 6 terms for these two items.) This shared covariance may represent the largely artifactual “testing effect” of the parallel wording and identical scaling metric for UNDER and RUNDER which is above and beyond what they hold in common because they each represent the unobserved construct, subjective marital solidarity. Alternately, it may reflect a “specific factor” resulting from an unspecified construct relating to interspouse understanding. It is plausible that those who engage in the disclosure that helps their spouse understand them
68
KILBOURNE,
HOWELL,
AND
ENGLAND
WOMEN 1971
MEN 1971
MEN 1978
1978
FIGURE
2.
are more likely to practice listening and empathy that help them understand their spouse. Or perhaps one spouse’s understanding encourages the others. In either case, there is a theoretical justification for taking advantage of the improvement in fit afforded by specifying the measurement model to take this correlated measurement error into account. (On the importance of using theoretical criteria for specifying correlated errors, see Alwin and Jackson. 1980; Hoelter, 1984.)
MEASUREMENT
OF MARITAL
SOLIDARITY
69
We then assess whether the same model, with one factor and correlated error terms for the mutuality items, is invariant across by gender and year, as sketched in Fig. 2. We then go on to examine factorial invariance for each of the three family life cycle groups (not shown in Fig. 2). Finally, we address an issue distinct from that of invariance. This involves the type of measurement model which most adequately describes these five items in terms of each item’s relationship to the construct (i.e., factor loadings, error variance, and true score variance of the construct itself). (See Alwin and Jackson, 1980; Parker, 1983.) Three types of psychometric models are tested: parallel measures (or items); T equivalent measures; and congeneric measures (Parker, 1983). A parallel measures model contains indicants which are of equal reliability (i.e., have equal factor loadings); thus, the proportion of true score variance in each indicant is due to the underlying construct. In addition, this model requires that the measurement error variance be equal across each indicant. A less restrictive model is one that is 7 equivalent. This model relaxes the assumption of equal error variances among the indicants. However, the equality of true score variances is maintained as an assumption. The third in this set of hierarchically related measurement models is the congeneric measures model. The most realistic assumption in current survey research is that construct indicants will differ in both their respective reliabilities and in their error variances. This specification makes the congeneric measures model equivalent to a common factor model when there is a single construct, as is the case here. To summarize this section, the results will be presented as follows: For each of the four gender and survey-year groups, the interitem correlation and descriptive statistics will be examined. The internal consistency reliability coefficient, Cronbach’s CY,will be computed as a lowerbound estimate of overall (unweighted) index reliability. The one-factor measurement model will be tested for “fit” in each gender-year group, and the invariance of the measurement model across gender-year categories will be evaluated using Joreskog’s (1971) hypothesis-testing framework. To foreshadow, we will present three one-factor models: one with all five items, one with the five items adding the assumption of correlated measurement error between UNDER and RUNDER for the reasons discussed above, and one deleting SPEND because it appears to be causing invariance of the measurement model by gender and year. The issue of invariance of the measurement model across stages of the family life cycle is then considered. Finally, the psychometric properties involving type of measurement model are investigated within each of the gender-year groups. RESULTS
The interitem correlations Table 1 for each gender-year
and descriptive statistics are presented in group. The high means are typical of survey
6.180 1.241
,333 .500 .317
1.000 SOS
(2)
(1)
3.427 ,668
,297 .215
l.ooO
I. (3) .391 ,628
QAL71
.454
3.434 .568
,321 ,262
1.000
QAL78
3.906 1.118
.323
l.CQO
(4) ,402 ,370 ,303
II = 511; Women-QAL71,
Cronbach’s (Y: men = .734: women = ,762
3.298 ,687
.331
..584 .428
1.000
(3) .337 ,585
II.
n = 597: Men-QAL78.
.993
3.691
1.000
(5) .302 ,285 ,252 ,294
3.679 ,969
,121 3.842
1.000
1.000
n = 750; Women-QAL78,
6.340 3.481 3.407 3.865 3.675
Mean
6.407 3.411 3.373 3.788 3.659
Mean
Group: QAL71-QAL78
(5) ,360 .376 ,346 ,265
(4) .413 .297 ,353
1.181 Cronbach’s a: men = .758: women = .738
1.220
.419 1.ooo .632 .329 .328
(2)
3.281 .758
6.166
.556 .437 .401 .282
1.000
(1)
TABLE I Means, and Standard Deviations for Marital Solidarity Items by Year-Gender
Note. Men above the diagonal, Women below. Men-QAL7l.
Mean SD
SATMAR UNDER RUNDER COMPAN SPEND
883.
I. 2. 3. 4. 5.
Mean SD
1. SATMAR 2. UNDER 3. RUNDER 4. COMPAN 5. SPEND
Correlations,
n =
1.026 1.048
.601
,626
SD 1.081
I.164 1.022
,935 ,651 ,636
SD
%
9
u
:r $
2 P
f3
z F
4 0
MEASUREMENT
OF
MARITAL
SOLIDARITY
71
responses to questions about various domains of life satisfaction (Campbell et al., 1976). The correlations are fairly similar across the four groups, ranging from approximately .2 to .6 in size. The item about disagreements on family finances (SPEND) exhibits the lowest correlations with other items, foreshadowing a problem to which we return to below. The most global item, marital satisfaction (SATMAR), correlates moderately and consistently with the more specific items. Of particular note are the relatively high correlations between the two mutuality items of understanding (UNDER AND RUNDER). This is what we would expect under the hypothesis of a “testing” effect in which respondents respond similarly to UNDER and RUNDER because of the similarity in the wording and scaling of the two items or under the hypothesis of a real correlation between interspousal understanding. Using the conventional coefficient for internal consistency of an unweighted index, Cronbach’s (Y is in an acceptable .7-.8 range for all four groups. Using confirmatory factor analysis, Table 2 presents three single-factor models for each of the four gender-year groups. The models do not include any across-group constraints. The unstandardized results are used to compare across groups while the standardized coefficients represent the relative contributions of the unobserved construct to each observed item within a given group. Model I is specified to allow only random measurement error among the five items (not shown in Fig. 2), which is the conventional assumption in index construction. Using the x’ test statistic, this model does not fit the observed data, forcing a rejection of this specification for each of the four groups. Evaluating various aspects of the model, such as the normalized residual matrix and the modification indices (see Joreskog and Sorhom, 1983), suggests that freeing up several elements in the 8 - 6 (errorterm matrix would result in a substantially better fit. However, using solely statistical criteria to make a model “fit” is somewhat akin to the atheoretical use of stepwise regression to find a “best” model. Such procedures are ill-advised because they tend to produce nonreplicable findings by capitalizing upon the idiosyncracies of the data instead of generating a theoretically based understanding of the data. (See Hoelter’s 1984 arguments on the misuse of covariance structure models.) In this case, UNDER and RUNDER are the only items for which we have a theoretical reason to expect correlated errors, as discussed above. For this reason, Model II allows only the covariance of the UNDER and RUNDER 8 - 6 terms and retains all five items. This specification results in a significantly improved fit within each gender-year group. Indeed, we cannot reject this model on statistical grounds using any Type 1 probability less than .Ol , although the QAL71 women’s results can be rejected at the .05 level. The standardized factor-loading coefficients show that marital solidarity is dominated by the marital satisfaction item (SATMAR) in all but one of the
72
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:f P
1.000* S80 ,512 1.010 .128
Note. See Fig. 1 for item ” U, unstandardized. b S, standardized. * Fixed parameter.
SATMAR UNDER RUNDER COMPAN n23 2
wording
0.78 1 = .376
and legend
,713 s93 .537 ,579 .241
Model 1 .ooo* ,524 ,370 ,591 ,130 1.62 I = ,204
III:
Nonrandom ,811 ,771 .548 ,495 .233
error 1 .ooo* ,540 ,399 .806 ,098 0.86 1 = ,353
,695 ,648 ,499 ,578 ,197
1 .OOo* ,478 .273 .775 ,111 2.27 I =.131
,763 ,659 .455 ,656 .217
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subgroups (males in 1971). This domination makes sense, given that the SATMAR item is the most global in its semantic referent. Examination of the factor loadings in Table 2 also shows a convergence between the sexes in the importance of disagreements about spending. The sex differences in 1971 are striking, with disagreements about spending much more important to men than to women in contribution to marital solidarity. But by 1978, the sexes were converging, with the salience of spending issues dropping for men and increasing for women. We conjecture that this results from a newly found sense of entitlement to participate in decisions about spending as increasing numbers of women became employed outside the home during the 1970s. Because SPEND is contributing to invariance of the measurement model by gender and year, Table 2 also includes Model III which drops SPEND and reestimates the measurement model (retaining the assumption of correlated error for UNDER and RUNDER introduced in Model II). This model fits better by statistical criteria. Using the .05 level, the model cannot be rejected for any of the four gender-year groups. More importantly, Model III shows greater invariance by year and sex. Thus, we recommend dropping SPEND from future analyses of marital solidarity because of its lack of invariance across gender and year. These differences among the four gender-year groups are more formally investigated through tests of invariance, summarized in Table 3. As the covariance matrix comparisons below the table show, when we test the null hypothesis that the variance-covariance matrices are equal, all the comparisons indicate that there are indeed subgroup differences, to which we now turn. The “unconstrained” model shown in the first column of Table 3 reports measurement model parameters estimated for each group with no across-group constraints in effect. As such, the xZ value from this unconstrained model serves as a baseline against which we may compare the across-group constraints that are shown in the remainder of the table. The first test is summarized in the second column and constrains the factor loadings to be equal across groups (e.g., for men and women in 1971). The resulting difference in the two x2 is the test statistic which evaluates the null hypothesis of equal factor loadings or, more substantively, equal “constructs” being measured across the two groups. The following tests sequentially examine the added equality constraints of true score variance and item error variance. These are summarized in the last three columns of Table 3. On statistical grounds alone, three of the four subgroup comparisons suggest that factorial invariance should be rejected. Only for men across time can the null hypothesis of equal “constructs” not be rejected. However, a careful comparison of test statistics indicates the group which differs most from the others is women in 1971. This was found in Table
MEASUREMENT
OF MARITAL
TABLE 3 Summary of Factorial Invariance across Year-Gender Scale: QAL7 1-QAL78 Unconstrained Aa+
Groups QAL71 men vs womena
QAL78 men vs womenb
X2 df Ax’ Adj P
Zf Ax’ Adf P
QAL71-78 men’
-
0.312 3.12 2 ,210
10.29 5 7.17 3 <.I0
21.77 6 11.48 1 <.OOl
18.53 10 8.24 5 c.01
-
1.64 2
6.19 6 0.12 1 >.90
-
33.22 II 27.03 5 <.001
19.63 6 0.31 1 >.90
-
48.21 II 28.58 5 <.OOl
-
Ax’
3.88 2 0.144
19.32 5 15.32 3 <.OlO
P
AaM
31.41 IO 14.11 5 <.02
0.440
Mf
Constrained parameters A0 A@ 32.60 6 15.29 1 <.OOl
P QAL71-78 wornend
Groups on Marital Solidarity
17.31 5 14.98 3 <.Ol
2.33 2
6.03 5 4.39 3 >.lO
if A$
Adf
y
A
75
SOLIDARITY
-
-
Note. Covariance matrix comparisons: “x’ = 56.29, P < .OO1;h~Z = 27.29. P < .OOl; = 31.15, P < .001;y = 45.10, P < ,001.
2, as well; the differences in Model III factor loadings between men and women in 1971 subside somewhat by 1978 and the over time comparisons for women themselves show that their factor loadings change significantly over time. Given the large sample size and the fact that only one genderyear group deviates from the overall pattern, we think that statistically significant subgroup differences shown in Table 3 are not substantively meaningful, with the single exception of comparisons involving women in 1971. Turning to the remaining invariance tests, it also seems that (item) error and true score variance differ significantly across groups. From a substantive viewpoint, however, it again seems that the primary source of these departures from invariance is the 1971 subgroup of women. In terms of the structure of subjective marital solidarity, it appears that the gender role change of the 1970s made women more like men by 1978. This suggests that research using data from later time periods or from new investigations can consider this measure invariant by gender.
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Table 4 summarizes results of the same hypothesis tests for life cycle differences within each sex and survey year. Testing the hypothesis that the covariance-variance matrices for each sex and survey year are equal across life cycle stages, we find that this null hypothesis cannot be rejected for either gender in 1978. These comparisons are shown below Table 4. Although the covariance-variance matrices for the later time period do not differ across the three stages, we nonetheless include the results of further tests for these groups. In all four gender-survey year groups, the unconstrained model fits reasonably well and this x2 value serves as a baseline for the subsequent comparisons. In every case, the invariance of factor loadings cannot be rejected (P > . 100). Results from the next test, of across-group equality in measurement error, shown in column 2, suggest that there are indeed differences by the life cycle stage for the 1971 subgroups, but not for the 1978 subgroups. Factor (true score) variances differ only for 1971 females. Despite differences for this one gender-year group. the invariance by family life cycle wihin the TABLE 4 Summary of Factorial Invariance across Life Cycle (FLC) Stage By Gender and Survey Year: QAL71-QAL-78 FLC comparison group QAL71 males”
Unconstrained A
2 2f
Ax’ Adf QAL71 female?
P 2 Zf
Ax’
1.44
,695 4.39
-
Mf QAL78 males’
P 2
2f
Ax’
Wf P
QAL78 females“
,222 1.88
S98 1.81
,612
Constrained parameters A@ A0
6.06 9 4.62 6 >.I00
32.38 19 22.22 10 c.025
9.32 II 3.26 2 >.OOl
10.06 9 5.67 6 >.I00
39.55 19 29.49 10 c.001
14.02 II 3.96 2 2.100
7.79 9 5.67 6 >.lOO
17.60 19 9.81 10 >.lOO
11.24 11 3.45 2 >.lOO
5.28 9 3.47 6 >.lOO
22.30 19 17.02 10 <.I0
9.14 11 3.86 i >.I00
Note. Covariance matrix comparisons: “x’ = 39.07. df = 20. P = .007; *x2 = 43.08. df = 20, P = .002; ‘x’ = 21.99. df = 20. P = ,341: ‘xZ = 25.57. df = 20. P = ,180.
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77
SOLIDARITY
other three gender-year groups suggests that the item set measures the same construct across family life cycle stages, particularly in recent years. Table 5 examines the type of measurement model that best describes these items. Others have found that the assumption of a congeneric model seems most warranted for contempory social survey data (Alwin and Jackson, 1980; Parker, 1983), and we make this conclusion about the subjective marital solidarity items here. In each subgroup the parallel and 7 equivalent models are handily rejected on a statistical basis. However, we cannot reject the congeneric model. And the adjusted goodnessof-fit index (AGFI) reaches a desirable level for this model, especially in comparison to the more rigorous measurement assumptions of the parallel and T equivalent models. SUMMARY AND CONCLUSION
Over a decade ago, Otto (1975) suggested that research on marriage and the family should improve the rigor of its conceptualization, measurement, and methods. One important part of this effort is the application of new analytical methods to problems of measurement (Bohrnstedt and Borgatta, 1981). In this spirit, we have provided a discussion TABLE 5 Summary of Analysis of Alternative Models for Marital Solidarity by Year-Gender Subgroup: QAL71-QAL78 Model” Parallel r equivalent Congeneric-Common Parallel r equivalent Congeneric-Common Parallel r equivalent Congeneric-Common Parallel r equivalent Congeneric-Common
x%f
AGFIh
factor
345.09 75.88 1.62
I. QAL71-Women 7 49.30 4 18.97 I 1.62
,756 ,855 ,987
factor
251.34 29.33 .78
II. 7 4 1
QAL71-Men 35.91 7.33 .78
,749 ,929 ,992
factor
680.89 194.27 2.27
III. QAL78-Women 7 97.27 4 48.57 1 2.27
.673 ,738 .987
factor
401.87 69.68 .86
X2
df
IV. 7 4 1
QAL78-Men 57.41 17.42 .86
y For a single-factor model, the congeneric and common factor specifications equivalent. b AGFI, adjusted goodness of fit index (see Joreskog and Sorbom, 1983).
,766 ,902 ,994 are
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of the measurement properties of a set of five Likert-type items available in two national replicate surveys in an attempt to provide a sound measure of subjective marital solidarity for use in future research. We have focused on the (internal consistency) reliability of the items and their factorial invariance across time, gender, and family life cycle stage. Our analysis suggests that two things are necessary to turn these items into a measurement protocol that “fits” as a single factor and is relatively invariant across gender, time, and life cycle stage. For fit, we need to allow the error terms for feeling understood by one’s spouse and understanding one’s spouse (UNDER AND RUNDER) to be correlated, as both substantive and measurement theory suggest they would be. We found that dropping the item on how much the couple disagrees on spending (SPEND) substantially improves the invariance of the measurement model. This item has changed its meaning during the period when so many women became wage earners. We conclude that these four items form an appropriate linear composite of subjective marital solidarity, that the measurement is a clear advance over single-item indicators, and that the modest number of items makes this protocol feasible to put on large multipurpose surveys. We have focused on reliability: future work should examine the criterion and construct validity of the measure we propose. If this unidimensional measure is found to correlate highly with only one factor of scales that have been conceptualized as multidimensional, this will delineate the discriminant validity of the measure and show the theoretical limits of its applicability. Alternatively, if the measure is highly correlated with the overall score from scales containing dozens of items, it can become a cost-effective replacement for multi-item scales. REFERENCES Abbott, D. A., and Brody. G. H. (1985). “The relation of child age, gender, and number of children to the marital adjustment of wives,” Journal of Marriage and the Family 47, 77-84.
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