6 Journal of Marriage and Family for this research because they collected infor- income in each time period.Moreover,results mation on respondents'age at first marriage of analyses using wages and salaries were (the census)or whether respondents married substantively the same as those using the total within the past 12 months (the ACS),number income. of times married,and total personal income for Incomes in the 2008-2012 5-year ACS data the previous year.Thus,both data sets allowed file were inflated to 2012 dollars.To perform me to examine newly contracted first marriages log-linear analysis,I have to recode the continu- and to obtain information on both spouses ous income measure into a categorical measure. education and income at the time of marriage. To reduce zero cells while preserving adequate Given the focus on income,I limited my detail in spouses'income (Schwartz,2010), sample to working-age adults.In addition, I classified each individual's income by the as marriage patterns may differ between decile he or she occupied in the income dis- native-borns and immigrants,I only included tribution of the 1980 and 2008-2012 analytic couples in which both spouses were U.S.born. samples,respectively.In other words,income In sum,I used a sample of U.S.-born couples in deciles were defined by ranking all people in which both the husband and wife were aged 18 the period-specific analytic samples by their to 55 years and married for the first time within income.Thus,spouses were classified by time approximately 1 year prior to the census or period based on their income relative to other ACS.Sensitivity analysis (available on request) people irrespective of gender. confirmed that the results did not change if I Similar to prior research (e.g.,Qian,1997; included immigrants or used alternative age Qian Lichter,2007;Schwartz Mare,2012), ranges.After excluding 462 couples in which classified each spouse into one of the four either spouse had negative income or both education levels-less than high school,high spouses had zero income,the final sample sizes school,some college,and college degrees and were 38,016 couples in 1980 and 37,686 couples above.As a robustness check,I experimented in2008-2012. with different classifications of educational More than 80%of newlyweds were non- and income levels (e.g.,income quintiles and Hispanic White couples,and supplementary five education levels)and obtained results analyses of White couples only yielded substan- similar to those reported next.Taken together, tively identical results to those reported next. I produced a five-way table with 3,200 cells Assortative mating patterns might be different (10 Income deciles for husbands x 10 Income for racial or ethnic minority couples considering deciles for wives x4 Education levels for hus- the differences across racial or ethnic groups bands x4 Education levels for wives x2 Time in the gender gap in education,the retreat from periods). marriage,the availability of economically suit- able men,and the marriage pool influenced by the large influx of recent immigrants(Cherlin, Analytical Approach 2010;DiPrete Buchmann,2013;Qian I used log-linear models to examine educa- Lichter,2007,2011:Schoen Cheng,2006). tional and income assortative mating.The chief Sample sizes were too small to separately exam- advantage of log-linear models lies in their abil- ine racial or ethnic minority couples,so I leave ity to estimate associations between spouses' this task to future research.The goal of this characteristics (e.g.,education or income)while article is to provide a general account of gender controlling for husband-wife differences in the asymmetry in assortative mating patterns among marginal distributions of these characteristics U.S.newlyweds. as well as shifts in the marginal distributions Following Cancian and Reed (1999),I (Kalmijn,2010:Qian Lichter,2007,2011; defined an individual's income as his or her total Schwartz Mare,2005;but see Rosenfeld, pretax personal income from all sources for 2005,for a critique of log-linear models).The the previous year.I examined spouses'income first set of models included only educational from all sources rather than their annual wage pairing of spouses.The second set of log-linear and salary earnings because the total income models added associations between spouses' reflects individuals'overall economic quality. income.Finally,I examined how education On average,individuals'wages and salaries interacts with income to shape assortative constituted more than 90%of their own total mating patterns
6 Journal of Marriage and Family for this research because they collected information on respondents’ age at first marriage (the census) or whether respondents married within the past 12 months (the ACS), number of times married, and total personal income for the previous year. Thus, both data sets allowed me to examine newly contracted first marriages and to obtain information on both spouses’ education and income at the time of marriage. Given the focus on income, I limited my sample to working-age adults. In addition, as marriage patterns may differ between native-borns and immigrants, I only included couples in which both spouses were U.S. born. In sum, I used a sample of U.S.-born couples in which both the husband and wife were aged 18 to 55 years and married for the first time within approximately 1 year prior to the census or ACS. Sensitivity analysis (available on request) confirmed that the results did not change if I included immigrants or used alternative age ranges. After excluding 462 couples in which either spouse had negative income or both spouses had zero income, the final sample sizes were 38,016 couples in 1980 and 37,686 couples in 2008–2012. More than 80% of newlyweds were nonHispanic White couples, and supplementary analyses of White couples only yielded substantively identical results to those reported next. Assortative mating patterns might be different for racial or ethnic minority couples considering the differences across racial or ethnic groups in the gender gap in education, the retreat from marriage, the availability of economically suitable men, and the marriage pool influenced by the large influx of recent immigrants (Cherlin, 2010; DiPrete & Buchmann, 2013; Qian & Lichter, 2007, 2011; Schoen & Cheng, 2006). Sample sizes were too small to separately examine racial or ethnic minority couples, so I leave this task to future research. The goal of this article is to provide a general account of gender asymmetry in assortative mating patterns among U.S. newlyweds. Following Cancian and Reed (1999), I defined an individual’s income as his or her total pretax personal income from all sources for the previous year. I examined spouses’ income from all sources rather than their annual wage and salary earnings because the total income reflects individuals’ overall economic quality. On average, individuals’ wages and salaries constituted more than 90% of their own total income in each time period. Moreover, results of analyses using wages and salaries were substantively the same as those using the total income. Incomes in the 2008–2012 5-year ACS data file were inflated to 2012 dollars. To perform log-linear analysis, I have to recode the continuous income measure into a categorical measure. To reduce zero cells while preserving adequate detail in spouses’ income (Schwartz, 2010), I classified each individual’s income by the decile he or she occupied in the income distribution of the 1980 and 2008–2012 analytic samples, respectively. In other words, income deciles were defined by ranking all people in the period-specific analytic samples by their income. Thus, spouses were classified by time period based on their income relative to other people irrespective of gender. Similar to prior research (e.g., Qian, 1997; Qian & Lichter, 2007; Schwartz & Mare, 2012), I classified each spouse into one of the four education levels—less than high school, high school, some college, and college degrees and above. As a robustness check, I experimented with different classifications of educational and income levels (e.g., income quintiles and five education levels) and obtained results similar to those reported next. Taken together, I produced a five-way table with 3,200 cells (10 Income deciles for husbands × 10 Income deciles for wives × 4 Education levels for husbands × 4 Education levels for wives × 2 Time periods). Analytical Approach I used log-linear models to examine educational and income assortative mating. The chief advantage of log-linear models lies in their ability to estimate associations between spouses’ characteristics (e.g., education or income) while controlling for husband–wife differences in the marginal distributions of these characteristics as well as shifts in the marginal distributions (Kalmijn, 2010; Qian & Lichter, 2007, 2011; Schwartz & Mare, 2005; but see Rosenfeld, 2005, for a critique of log-linear models). The first set of models included only educational pairing of spouses. The second set of log-linear models added associations between spouses’ income. Finally, I examined how education interacts with income to shape assortative mating patterns
Educational and Income Assortative Marriage 1 To begin,my basic model is as follows: log ()=Model 1 + 1og(/）=+EY+Er +层+， (2) ++增+m "iit where r is a set of parameter estimates for homogamy of each educational group +r, (1) (0=1 when i=k=1,...,0=4 when i=k=4, and =0otherwise),and is the educa- where HE is husband's education (i=1,...4). tion hypogamy parameter (P=1 when i<k WE is wife's education (k=1,...,4),HI is hus- and 0 otherwise )and estimate band's income category (j=1,...,10).WI is changes in the odds of educational homogamy wife's income category (I=1,...,10),and Y and hypogamy,respectively,between 1980 is period (t=1,2).Thus,kr is the expected and 2008-2012,net of shifts in the marginal number of marriages between men with educa- distributions of husbands'and wives'education. tion i in income decile j and women with edu- Building on the best-fitting model with edu- cation k in income decile in period t.This cational assortative mating parameters,I added model includes variations in the distributions additional parameters to model income assor- of husband's and wife's education and income tative mating to test Hypothesis 2.Similar to by year (yy).the associ- educational homogamy parameters,I modeled income homogamy by adding variable diago- ations between education and income for both husbands and wives and their variations by year nal parameters.To model gender asymmetry AwEwI Y AwEwry).and all lower in income assortative mating,I constrained the cells in which wives were in a lower income order terms. decile than husbands into one income hyper- The 1980 census is self-weighting,whereas gamy parameter.The model becomes the ACS 2008-2012 5-year sample contains weights to ensure that the multiyear sample is log (/)Model ++2 representative of the population during the entire 5-year period.I incorporated the weights by ++6号 9 (3) an offset ti which is the inverse of the total weighted frequency of the cell divided by the where is a set of parameter estimates for unweighted cell count (Agresti,2002,p.391). homogamy of each income decile group (S=I To preserve the original sample size in the ACS when j=l =1,...S=10 when j=/=10,and sample,I rescaled the original weights so that S=0 otherwise).and is an income hyper- the sum of the weights equaled the sample size gamy parameter (O=1 when j>I and 0 oth- (Schwartz Mare,2005).In 14.25%of cells with counts of 0(i.e.,456 of 3,200),I settikr to 1 erwise).and represent changes in the odds of income homogamy and hypergamy. (Schwartz Mare,2005).Empty cells need not respectively,between 1980 and 2008-2012,net be problematic in log-linear analyses (Agresti, of shifts in the marginal distributions of hus- 2002).As a robustness check,I added 0.5 to bands'and wives'income deciles. each cell and obtained substantively the same Finally,to test Hypotheses 3a,3b,4a,and results. 4b,I examined how the gender asymmetry in To test Hypothesis 1,I modeled the associa- income assortative mating differed by the educa- tions between husbands'and wives'education. tional pairing of spouses.I included interaction I modeled the odds of educational homogamy terms between the income assortative mating and hypogamy relative to the odds of educational parameters and the educational homogamy and hypergamy by adding variable diagonal param- hypogamy parameters as well as changes in eters (Qian,1997)and a hypogamy parameter these interaction terms by year.The model is that was coded 1 if the wife had more educa- tion than the husband.Then I added interaction log ()Model3+ terms between the year and the variable diag- onal parameters and between the year and the ++层 hypogamy parameter to model changes in edu- cational assortative mating.The model becomes + (4)
Educational and Income Assortative Marriage 7 To begin, my basic model is as follows: log ( 𝜇ijklt∕tijklt) = 𝜆 + 𝜆HEY it + 𝜆WEY kt + 𝜆HIY jt + 𝜆WIY lt + 𝜆HEHIY ijt + 𝜆WEWIY klt , (1) where HE is husband’s education (i=1, …, 4), WE is wife’s education (k =1, …, 4), HI is husband’s income category (j=1, …, 10), WI is wife’s income category (l=1, …, 10), and Y is period (t =1, 2). Thus, 𝜇ijklt is the expected number of marriages between men with education i in income decile j and women with education k in income decile l in period t. This model includes variations in the distributions of husband’s and wife’s education and income by year (𝜆HEY it , 𝜆WEY kt , 𝜆HIY jt , 𝜆WIY lt ), the associations between education and income for both husbands and wives and their variations by year (𝜆HEHI ij , 𝜆WEWI kl , 𝜆HEHIY ijt , 𝜆WEWIY klt ), and all lower order terms. The 1980 census is self-weighting, whereas the ACS 2008–2012 5-year sample contains weights to ensure that the multiyear sample is representative of the population during the entire 5-year period. I incorporated the weights by an offset tijklt, which is the inverse of the total weighted frequency of the cell divided by the unweighted cell count (Agresti, 2002, p. 391). To preserve the original sample size in the ACS sample, I rescaled the original weights so that the sum of the weights equaled the sample size (Schwartz & Mare, 2005). In 14.25% of cells with counts of 0 (i.e., 456 of 3,200), I set tijklt to 1 (Schwartz & Mare, 2005). Empty cells need not be problematic in log-linear analyses (Agresti, 2002). As a robustness check, I added 0.5 to each cell and obtained substantively the same results. To test Hypothesis 1, I modeled the associations between husbands’ and wives’ education. I modeled the odds of educational homogamy and hypogamy relative to the odds of educational hypergamy by adding variable diagonal parameters (Qian, 1997) and a hypogamy parameter that was coded 1 if the wife had more education than the husband. Then I added interaction terms between the year and the variable diagonal parameters and between the year and the hypogamy parameter to model changes in educational assortative mating. The model becomes log ( 𝜇ijklt∕tijklt) = Model 1 + 𝛾O ik + 𝛾P p + 𝛾O ik𝜆Y t + 𝛾P p 𝜆Y t , (2) where 𝛾O ik is a set of parameter estimates for homogamy of each educational group (O =1 when i=k =1, …, O =4 when i=k =4, and O =0 otherwise), and 𝛾P p is the education hypogamy parameter (P=1 when i<k and 0 otherwise ). 𝛾O ik𝜆Y t and 𝛾P p 𝜆Y t estimate changes in the odds of educational homogamy and hypogamy, respectively, between 1980 and 2008–2012, net of shifts in the marginal distributions of husbands’ and wives’ education. Building on the best-fitting model with educational assortative mating parameters, I added additional parameters to model income assortative mating to test Hypothesis 2. Similar to educational homogamy parameters, I modeled income homogamy by adding variable diagonal parameters. To model gender asymmetry in income assortative mating, I constrained the cells in which wives were in a lower income decile than husbands into one income hypergamy parameter. The model becomes log ( 𝜇ijklt∕tijklt) = Model 2 + 𝛿S jl + 𝛿Q q + 𝛿S jl𝜆Y t + 𝛿Q q 𝜆Y t , (3) where 𝛿S jl is a set of parameter estimates for homogamy of each income decile group (S =1 when j=l =1, …, S =10 when j=l=10, and S =0 otherwise), and 𝛿Q q is an income hypergamy parameter (Q =1 when j>l and 0 otherwise). 𝛿S jl𝜆Y t and 𝛿Q q 𝜆Y t represent changes in the odds of income homogamy and hypergamy, respectively, between 1980 and 2008–2012, net of shifts in the marginal distributions of husbands’ and wives’ income deciles. Finally, to test Hypotheses 3a, 3b, 4a, and 4b, I examined how the gender asymmetry in income assortative mating differed by the educational pairing of spouses. I included interaction terms between the income assortative mating parameters and the educational homogamy and hypogamy parameters as well as changes in these interaction terms by year. The model is log ( 𝜇ijklt∕tijklt) = Model 3 + 𝛾O ik 𝛿S jl𝜆Y t + 𝛾P p 𝛿S jl𝜆Y t + 𝛾O ik 𝛿Q q 𝜆Y t + 𝛾P p 𝛿Q q 𝜆Y t , (4)