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. Author manuscript; available in PMC: 2019 Nov 1.
Published in final edited form as: J Lat Psychol. 2018 Nov;6(4):276–290. doi: 10.1037/lat0000118

A Dyadic Data Analytic Primer: An Illustration with Mexican-origin Couples

Lorey A Wheeler 1, Kimberly A Updegraff 2, Adriana J Umaña-Taylor 3
PMCID: PMC6424517  NIHMSID: NIHMS986251  PMID: 30906676

Abstract

Dyadic matched-pairs (each person paired with one other person) research designs that include parallel data from both members of a relationship dyad provide a rigorous method for examining questions of interdependence. These designs require the use of analytic methods that account for statistical dependencies due to dyad member characteristics and environments. Using structural equation modeling, we illustrate two alternative analytic approaches for distinguishable (nonexchangeable) two-wave dyadic data: (a) a hybrid of the two-intercept and actor-partner interdependence models and (b) a difference model. Few studies have used these rigorous analytic approaches to analyze dyadic data with Latinos, despite demographic shifts in the U.S. and the cultural relevance of family values and relationship interdependence for this population. As such, our illustrative data were drawn from a larger longitudinal study of Mexican-origin families, with husbands and wives both reporting on somatic symptoms and marital negativity (N = 246 marital dyads). Results revealed that Mexican-origin spouses’ somatic symptoms related to increases in partners’ marital negativity five years later. Prior levels of wives’ marital negatively linked to more discrepancies in marital negativity five years later, whereas husbands’ marital negativity related to fewer discrepancies. We conclude by discussing the benefits of prospective dyadic data designs for researchers examining questions related to Latino populations.

Keywords: dyadic data, family relationships, Latino couples and families, marriage, structural equation modeling

As the largest minority group in the U.S., the growing Latino population marries young, has high marriage rates, places a high value on relationships and interdependence among family members, and experiences high rates of contextual stressors that can strain relationships (Helms, Supple, & Proulx, 2011; Monthly Labor Review, 2013; U.S. Census Bureau, 2017). Despite these patterns, recent reviews underscore the limited scholarly attention given to the study of relationships and marriage among Latino couples and families (Glick, 2010; Helms, 2013). In the leading psychology, marital, and family journals, less than 1% of publications have examined Latino family dynamics in the past several decades (Helms, 2013). Furthermore, even fewer have employed analytic approaches using data from both members of the dyad (for exceptions see Davidson & Cardemil, 2009; Falconier, 2013; Helms et al., 2014; Sarmiento & Cardemil, 2009; Wheeler, Updegraff, & Thayer, 2010). In part, this may be explained by the difficulty in recruiting dyads from this population or the challenges researchers perceive in conducting dyadic analyses. Thus, the current study provides a primer for using dyadic analytic approaches, with the goal of encouraging dyadic research among scholars interested in Latino families.

To serve as a resource, we briefly review some of the theoretical and methodological issues associated with using the perspectives of two individuals within a dyad. We begin by defining matched-pairs data and distinguishability, discussing the unit of analysis, and then addressing issues of statistical dependency. Matched-pairs designs include collecting data about the same constructs from both individuals within a dyad; each person is paired with one other person. In this case, the construct is measured at the individual level as each member has a score; this is in contrast to measurement at the dyad level, in which each dyad has one score (e.g., observer ratings of couple negativity; a difference score representing parent-child acculturation gap). Observations are grouped such that individuals are linked together by, in this case, a dyadic relationship (e.g., marriage, parent-child, sibling). An important question in relation to matched-pairs data is whether the dyad members are empirically distinguishable. Distinguishability refers to members having distinct roles in the dyad identified by a non-arbitrary variable such as sex or social role. In heterosexual couples, members can be distinguished by gender; in sibling dyads, two siblings can be distinguished by birth order. Conversely, in indistinguishable or exchangeable dyads, members cannot be naturally distinguished, such as same-sex friend dyads, identical twins, or homosexual couples. Analytic techniques appropriate for distinguishable dyads may not be appropriate for indistinguishable dyads.

The unit of analysis is a methodological term that refers to “what” or “who” is being studied (e.g., individuals, dyads). For example, treating the individual as the unit of analysis to examine married spouses’ own adjustment as related to their own perceived relationship experiences would result in the sample size representing the number of individuals (e.g., 200 couples with 2 partners = 400 individuals). With matched-pairs data, the dyad should be treated as the unit of analysis (N = number of pairs or N/2 individuals; e.g., N = 400/2 paired individuals = 200 couples) to represent the nested nature of the data. The problem with this approach relates to the assumption of independence (i.e., scores from units are all independent) underlying traditional statistical approaches (e.g., ANOVA or multiple regression). However, because dyadic data come from members in a relationship, members may influence one another, in part, because of shared experiences. Thus, information used in the analyses is not independent. Nonindependence exists when scores from two members of a dyad are more similar to (or more different from) each other than scores from two randomly paired individuals in a sample. When conventional statistical methods are used in their standard forms with matched-pairs dyadic data with the individual as the unit of analysis, statistical assumptions of independence are violated leading to biased standard errors and increased Type I error rates (Kenny, 1995).

Researchers can ask questions about individuals from a dyad as in the above example but should use an analytic technique that accounts for interdependence. For example, in our work with Mexican-origin couples we used multilevel analyses to examine the links between individual spouses’ own cultural values and conflict resolution strategies on their own reports of marital relationship quality (Wheeler et al., 2010). Davidson and Cardemil (2009) examined the links between dyadic parent-child communication and parent-child acculturation and enculturation gaps on child functioning. Alternatively (and the focus of the current paper), research using matched-pairs data can focus on understanding how the interplay of each partner’s experiences or attributes inform relationship experiences.

The Current Study

Building on other primers on dyadic data analysis (e.g., Maguire 1999; Ledermann & Kenny, 2017; Lyons & Sayer, 2005), the goal of this article was to detail the steps necessary to analyze data from matched-pairs distinguishable dyads over time within a structural equation modeling (SEM) framework with two approaches: (a) a hybrid model combing the two-intercept (Wendorf, 2002) and actor-partner interdependence (APIM; Kenny, Kashy, & Cook, 2006) models; and (b) a difference model (Newsom, 2002). We chose these two models for two reasons: (a) fit with our research questions of interest (described below); and (b) advantages of modeling dyadic data in an SEM framework (discussed briefly later). For simplification purposes, we focus on distinguishable dyads and analyses of two waves of data. Discussions of indistinguishable dyads (e.g., same-sex partners) and longitudinal analyses with more than two waves of data (e.g., growth curve models) are presented in Olsen and Kenny (2006) and Lyons and Sayer (2005), respectively.

We illustrated each model with couple data from husbands and wives of Mexican origin, examining the prospective association between spouses’ depressive symptoms (i.e., somatic symptoms) on marital quality (i.e., negativity) based on prior research supporting links between individual and marital functioning (Proulx, Helms, & Buehler, 2007). As guided by the stress generation model, there is evidence that increases in depressive symptoms lead to decreases in marital quality concurrently and longitudinally (Davila, Bradbury, Cohan, & Tochluk, 1997). There is a need to examine crossover effects between spouses’ depressive symptoms and marital quality, in general (Beach, Katz, Kim & Brody, 2003), and specifically among ethnic-racial minority samples (Glick, 2010; Helms, 2013). Furthermore, research guided by spousal discrepancy approaches suggests that individual differences are a risk factor for marital instability (Kurdek, 1993); thus, it is important to understand what might predict differences in marital quality. Here we examine individuals’ depressive symptoms as a predictor of spousal differences in marital quality. The current illustration contributes by examining these processes within long-term marriages among Mexican-origin families with adolescent offspring. Marital conflicts often increase when adolescents are present in the home (Hatch & Bulcroft, 2004); thus, this period of childrearing may be important. We also examined variation by gender (i.e., empirical test of distinguishability by gender) based on prior work suggesting differences in links between personal well-being and marital quality (Proulx et al., 2007).

We addressed three research questions using a hybrid of the two-intercept and the APIM: (a) What are the patterns of associations for marital negativity over time, controlling for marital duration?; (b) Do levels of individuals’ own (actor effect) and their partners’ (partner effect) somatic symptoms relate to marital negativity, controlling for prior levels of marital negativity and marital duration?; (c) Does the pattern of associations between spouses’ somatic symptoms and marital negativity vary by spouse gender (empirical distinguishability)? Using the difference model, we addressed two research questions: (a) Are couples’ average levels of marital negativity predicted by prior levels of husbands’ and wives’ marital negativity and somatic symptoms? (b) Are within-couple differences in marital negativity predicted by prior levels of husbands’ and wives’ marital negativity and somatic symptoms?

SEM Approaches for Analyzing Matched-Pairs Dyadic Data

SEM is a multivariate (e.g., can include multiple outcome or endogenous variables) analytic technique combining path analysis and factor analysis, including measured and unmeasured (i.e., latent) variables, procedures for handling missing data, and indices of model fit (see Bollen, 1989 for advanced details; for novice users, see Kenny, 2016; Kline, 2005). The SEM analytic framework offers flexibility in answering questions using dyadic data (for an introduction see Kenny, 2015; Kenny et al., 2006; Ledermann & Kenny, 2017). In approaching any research question, scholars must make two decisions prior to proceeding with analyses. First is the choice of the unit of analysis. When using matched-pairs dyadic data in a SEM framework, the unit of analysis should be the dyad (N = number of pairs; 2N individuals). The second series of steps concerns the choice of model specification (parameterization) and the resulting identification (i.e., paths or parameters specified in model can be uniquely estimated), estimation, and testing of that model. This series of steps relates to determining the nature or links between the constructs of interest and translating that research question into a testable statistical model. In Table 1, we provide a brief overview of statistical approaches that can be used with matched-pairs dyadic data, along with the approaches that are the focus of the remainder of this paper. Ultimately, the theory being tested and research question under investigation should drive the choice of the SEM model specification. Of note, as guided by SEM nomenclature, the term exogenous refers to variables without a ‘cause’ included in the model [i.e., independent variables in ANOVA or predictors in regression; X]. The term endogenous refers to variables that are effects of other variables [i.e., dependent variables in ANOVA or criterions in regression; Y].

Table 1.

Overview of Analytic Approaches to use with Matched-Pairs Dyadic Distinguishable Data

Analytic Approaches Essential Measured Variables Analysis Example Research Questions
Actor-Partner Interdependence Model
(Kenny et al., 2006; Ledermann & Kenny, 2017; Van Dulmen, & Goncy, 2010)		 Y1a, Y1b

X1a, X1b
  • -

    Captures mutual influence

  • -

    Actor effects: regression paths from X1a to Y1a and X1b to Y1b

  • -

    Partner effects: regression paths from X1a to Y1b and X1b to Y1a
  • -

    Does mothers’ (person a) acculturative stress relate to mothers’ perceptions of parent-child relationship quality (actor effect) and child perceptions of relationship quality (partner effect)?

  • -

    Does child’s (person b) acculturative stress relate to child’s perceptions of parent-child relationship quality (actor effect) and mothers’ perceptions of relationship quality (partner effect)?
-Two-Intercept Model
(Barnett et al., 1993; Wendorf, 2002)		 Y1a, Y1b

X1
  • -

    Creation and prediction of latent outcome variables for each dyad member

  • -

    Regression path from X1 to Y1a and Y1b
  • -

    Does the parent-child acculturation gap relate to mothers’ and children’s perceptions of parent-child relationship quality?
Difference Model
(Newsom, 2002)		 Y1a, Y1b

X1
  • -

    Prediction of difference term

  • -

    Regression path from X1 variable to latent difference of Y1a and Y1b
  • -

    Do mothers’ and children’s acculturative stress associate with differences in mothers’ and children’s perceptions of parent-child relationship quality?
Common Fate Model
(Cook, 1998; Ledermann, & Kenny, 2011)		 Y1a, Y1b

X1a, X1b
  • -

    Group members are influenced by common relational or external factors

  • -

    Regression paths from Xa, Xb (specified at the individual- and dyad-level) to Y1a, Y1b
  • -

    Does dyad-level and individual-level reports of neighborhood safety relate to mothers’ and children’s perceptions of parent-child relationship quality?
Mutual Influence / Dyadic Feedback Model
(Cook, 1998)		 Y1a, Y1b

X1a, X1b
  • -

    Captures reciprocity between members

  • -

    Regression paths from X1a to Y1a and X1b to Y1b

  • -

    Regression paths from Y1a to Y1b and Y1b to Y1a

  • -

    Link between X1a and Y1b mediated by Y1a (for person a; and the same for person b)
  • -

    Do mothers’ (person a) perceptions of parent-child relationship quality mediate the link between maternal acculturative stress on children’s (person b) perceptions of relationship quality?

  • -

    Do children’s (person b) perceptions of parent-child relationship quality mediate the link between child acculturative stress on mothers’ (person a) perceptions of relationship quality?
Dyadic Growth Curve Model
(Kurdek, 2003; Lyons & Sayer, 2005)		 Y1a, Y1b over at least four times
  • -

    Starting level (intercept) and growth terms (slope) for each dyad member (using Y11a, Y12a, Y13a, Y14a; Y11b, Y12b, Y13b, Y14b); can include predictors (X) of intercept and slope
  • -

    Does acculturative stress relate to covariation in wives’ and husbands’ perceptions of marital relationship quality over time?
Cluster / Latent Class / Mixture Models
(Whiteman & Loken, 2006)		 Multiple Y variables for each dyad member
  • -

    Classification of a sample into subpopulation groups based on Y variables (measured for both dyad members)

  • -

    Use classification variable to predict or can predict membership in groups
  • -

    Are there varying profiles of parent and child acculturation (measures of cultural values, orientations, behaviors)?

  • -

    Do varying acculturation profiles relate to differences in perceptions of parent-child relationship quality?
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Note. X = predictor or independent or exogenous variable. Y = outcome or dependent or endogenous variable. a = dyad member a. b = dyad member b. MLM = multilevel modeling framework. SEM = structural equation modeling framework. Basic models are presented, but most of these models can be extended to more complex versions – see noted citations for extensions.

Hybrid Two-Intercept Actor-Partner Interdependence Model

The two-intercept APIM model combines components from the standard APIM model and the standard two-intercept model. We present the standard components of each model first, starting with the APIM, the two-intercept model, and then discuss the hybrid model. By far the most common conceptual and statistical model for dyadic data is the APIM (Kenny et al., 2006). The primary focus of the APIM is to answer questions of mutual influence between individual dyad members, assessing dyadic processes. In the simplest version of the APIM, the association between a dyad member’s (Person a) own behavior or trait (Xa) and his or her own outcome (Ya) is referred to as an actor effect (e.g., wives’ marital negativity predicted by wives’ somatic symptoms; Kenny et al., 2006). The association with the partner’s (Person b) outcome (Xa → Yb) is referred to as a partner effect (e.g., husbands’ marital negativity predicted by wives’ somatic symptoms). In a model including at least two waves of data, an actor effect denotes the relation between a person’s current behavior or trait and his or her own past behavior or trait, representing a measure of stability in that behavior or trait [Kenny et al.; e.g., association between wives’ earlier (X11a) and later marital negativity (Y12a)]. Partner effects quantify the cross-over effects between partners over time [e.g., links between husbands’ earlier marital negativity (X11b) and wives’ later marital negativity (Y12a)].

The two-intercept model (Wendorf, 2002) is a general SEM analytic strategy adapted from multilevel modeling (MLM) approaches for analyzing matched-pairs dyadic data (Barnett, Marshall, Raudenbush, & Brennan, 1993). The two-intercept model requires only the inclusion of two latent endogenous variables measured with reports from both dyad members on a construct, thus resulting in two intercepts estimated in the model. Thus, the two-intercept model is adaptable as to what other constructs are included in the model, which facilitates flexibility in the types of questions that researchers can answer. The two-intercept model readily allows for the consideration of multiple contextual, intrapersonal, and intrapersonal dimensions and perspectives observed for individuals and dyads. For example, the two-intercept approach can answer questions about contextual factors (observed for the dyad) that associate with interpersonal relationships (as perceived by individual dyad members), such as “Is couple socioeconomic status (X11) associated with changes in wives’ (Y12a) and husbands’ (Y12b) marital quality over time?” Alternatively, the two-intercept approach can answer questions about the association between intrapersonal factors and interpersonal relationships observed by each individual, such as “Are wives’ (X11a) and husbands’ (X11b) depressive symptoms associated with changes in wives’ (Y12a) and husbands’ (Y12b) marital quality over time?”

The two-intercept approach was initially designed to overcome difficulties inherent to modeling dyadic data within a MLM framework. More specifically, with only two members per group, there is not enough information to obtain all of the parameters specified in MLM (Barnett et al., 1993); in SEM terms, this is known as underidentification. Barnett and colleagues’ MLM two-intercept model estimated each dyad member’s endogenous (dependent) variable in a separate regression equation in the same model to account for the dependence of observations. Wendorf extended this two-intercept model by converting the MLM version into a similar, though not identical, identified model estimated in the SEM framework. This model requires only the inclusion of two latent factors: one for each endogenous variable of interest (Ya, Yb) measured by dyad member reports on the same construct (e.g., observed reports of marital satisfaction). The resulting two-intercept SEM parameterization can take the form of a measurement model (e.g., dyadic confirmatory factor analysis) or a structural model including any number of exogenous explanatory variables (Xa, Xb related to Ya, Yb).

Within the context of SEM, a hybrid of the two-intercept model and the APIM can be estimated. This hybrid model combines the actor and partner effects from the APIM with the latent endogenous variables from the two-intercept model. This model may also be referred to as a latent version of the APIM. In the context of this illustration, we refer to this model as a hybrid for the purpose of exposing researchers to both types of analytic approaches - giving researchers additional approaches to use in answering research questions related to Latino populations.

Difference Model

A second technique for analyzing matched-pairs data is Newsom’s (2002) SEM that extends work on statistical techniques used for longitudinal analysis of individual growth curves (e.g., Bryk & Raudenbush, 1987). The goal of Newsom’s model is to allow for tests of sophisticated causal models of relational behavior that use dyadic data and incorporate latent factors and complex error structures. This dyadic approach ranges in complexity from the simplest just-identified model (i.e., a single observed measure for each dyad member as indicators of an endogenous latent factor) to complex second-order factor models (i.e., multiple observed measures for each dyad member as indicators of latent factors). This approach can incorporate exogenous variables (X) observed for an individual or dyad.

For the purposes of illustration, we focus on one specific parameterization of Newsom’s SEM, the difference model. Specifically, this model provides a test of, on average, the difference between dyad members on a particular relationship outcome. We focus on this approach to offer researchers an alternative to using a difference score (calculated from the absolute or quadratic difference between dyad members’ scores; Griffin, Murray, & Gonzalez, 1999) as it offers the statistical advantages of SEM (e.g., comparison of models) in addition to improved psychometric properties. The difference model builds on concepts derived from individual growth curve modeling to dyadic data by incorporating two latent factors (i.e., a latent intercept and slope) defined by a single indicator for each dyad member that represents the endogenous variables (Ya, Yb). The average latent intercept (η1) represents the average on the endogenous outcome variable across the dyad using effect coding, hereinafter referred to as the couple average. For example, researchers may be interested in examining whether wives’ (X11a) and husbands’ (X11b) somatic symptoms are associated with couples’ average levels of marital negativity (η1). The average latent slope (η2) represents the difference between dyad members on the outcome variable, referred to here as within-couple difference or the coefficient for the difference between partners. In this case, researchers may be interested in testing whether somatic symptoms for each dyad member (X11a, X11b) are associated with husband-wife differences in marital negativity (η2). Both of these coefficients (i.e., couple average - η1; within-couple difference - η2) can be predicted from exogenous variables (X). Thus, the difference model offers a flexible approach to answer substantive questions that are distinct from those answered by the two-intercept model. Researchers can also answer questions including dyad-level measured exogenous variables, such as “Is an observational measure of couples’ marital conflict (X1) associated with differences in levels of husbands’ and wives’ marital satisfaction (η2)?”

Illustration: Somatic Symptoms and Marital Negativity among Mexican-Origin Couples

Data came from a longitudinal study of Mexican-origin two-parent families with two adolescent offspring recruited from schools in a southwestern metropolitan area (see Updegraff, McHale, Whiteman, Thayer, & Delgado, 2005 for additional details; N = 246). Data included in-home interviews at Times 1 (T1) and 2 (T2; five years later) with 75% of the original Mexican-origin families (n = 185). At T1, wives and husbands averaged 39 (SD = 4.63) and 41 (SD = 5.77) years of age, respectively, and had an average of 10 years of education (wives: M = 10.33, SD = 3.73; husbands: M = 9.87, SD = 4.37). Annual median family income was $40,000. Most (70%) spouses were born outside the U.S. Interviews were conducted in Spanish (67%) or English (33%).

The exogenous variables were T1 husbands’ and wives’ depressive symptoms (Radloff, 1977; 7 items from the somatic symptoms subscale; wives’ α = .75, husbands’ α = .71). The endogenous variables were T2 husbands’ and wives’ marital negativity (5 items; Braiker & Kelley, 1979; wives’ α = .68, .76 and husbands’ α = .69, .72 at T1 and T2, respectively). Covariates were T1 marital negativity and duration (i.e., wife report of number of years of marriage) based on evidence linking duration to poorer marital quality (e.g., Proulx et al., 2007). Poverty (an auxiliary variable) was created from a ratio of T1 family income to census poverty thresholds (reverse coded), such that high scores indicated higher levels of poverty. The Institutional Review Board approved the study.

We used Mplus 7.3 (Muthén & Muthén, 1998–2014) to estimate all models. Data were configured in a “repeated measures” format (dyad design; i.e., separate records for each couple, each record contained husbands’ and wives’ variables entered as separate variables with different names). We used full information maximum likelihood (FIML) estimation with auxiliary variables to retain all cases in our sample (N = 246). On average, predictor variables were missing for 1% and outcome variables were missing for 40% of our total sample cases, which is less than the amount of missing data that simulation studies show FIML can handle without added bias (i.e., up to 50%; Enders, 2010). The use of the auxiliary command in Mplus is one method of improving the accuracy of estimation with missing data (Enders). In an attempt to satisfy the missing at random assumption (i.e., missingness is dependent on other observed variables), we used poverty as an auxiliary variable; it was most highly related to T2 attrition compared to maternal education, also related to missingness. There were no other differences between participating and non-participating couples on demographic or study variables. We determined adequate model fit by a nonsignificant chi-square statistic, a root mean square error of approximation (RMSEA) ≤ .08, a comparative fit index (CFI) ≥ .90, and a standardized root mean square residual (SRMR) ≤ .10. Effect sizes (ES) reported are based on the R2 (small ≥ .0196, medium ≥ .1304, large ≥ .2592; Cohen, 1992). See Table 2 for descriptive statistics.

Table 2.

Correlations and Descriptive Statistics for Study Variables (N = 246 Mexican-Origin Couples)

Variables 1 2 3 4
1. T1 marital duration in years - −.09 −.09 −.06
2. T1 somatic symptoms −.09 .26*** .39*** .36***
3. T1 marital negativity −.10 .29*** .33*** .56***
4. T2 marital negativity −.04 .18* .52*** .29***
Husbands’ M (SD) 17.52 (5.34) 1.79a (.51) 3.97a (1.63) 3.46a (1.58)
Wives’ M (SD) 17.52 (5.34) 1.83a (.56) 4.43b (1.69) 4.24b (1.77)
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Note. Correlations among wives are above the diagonal. Correlations among husbands are below the diagonal. The diagonal depicts the correlations between wives and husbands. The marital duration variable is the same for wives and husbands. Means in columns with different subscripts (a,b) are significantly different at p < .05.

***

p < .001.

*

p < .05.

Hybrid Two-Intercept Actor-Partner Interdependence Model

We used two estimation steps. Step 1 estimated a measurement model that confirmed the latent factor structure of the endogenous variables of marital negativity, measured separately for husbands and wives. To account for the nested nature of the scores, the measurement model requires the inclusion of the estimation of the covariance of item residuals between spouses (e.g., wives’ Item 1 correlated with husbands’ Item 1). The results of Step 1 indicated that the measurement model adequately fit the data, χ2(36) = 63.61, p < .01, RMSEA = .06, CFI = .92, SRMR = .11. Based on modification indices to improve model fit, we correlated the residuals of two wife items that had similar wording.

Step 2 included estimating a series of nested structural models to determine if husbands and wives should be treated as being empirically distinguishable. This is an important consideration in dyadic analysis (Kenny et al., 2006), examining whether dyad members are distinct based on the non-arbitrary linking variable, such as social role (e.g., husbands versus wives). Starting with the final measurement model from Step 1, the structural model included T2 husbands’ and wives’ marital negativity latent factors as endogenous variables, T1 husbands’ and wives’ somatic symptoms as endogenous variables, and T1 marital duration and T1 marital negativity as covariates. Actor (e.g., T1 husbands’ somatic symptoms → T2 husbands’ marital negativity) and partner (e.g., T1 husbands’ somatic symptoms → T2 wives’ marital negativity) effects were estimated. To account for the nested nature of the scores, the covariance among the exogenous variables and among the residuals for husbands’ and wives’ T2 marital negativity latent factors were estimated. A series of nested models were compared using chi-square difference tests to determine the model that fit the data the best [i.e., (a) unconstrained model – all parameters freely estimated across husbands and wives (gender); (b) actor and partner effects constrained equal across gender; (c) covariate paths; latent factor loadings, intercepts, and residual variances; and manifest indicator residual variances constrained equal across gender].

Results for Step 2, starting with the comparison of the nested models, indicate that husbands and wives are empirically nondistinguishable (i.e., no variation by gender; third research question). Specifically, the models partially constrained by gender (actor and partner paths), Δχ2 (4) = 3.91; p = .42, and fully constrained by gender (all paths, factors loadings, intercepts, variance, and residuals), Δχ2 (17) = 24.12; p = .11, fit the data equally as well as the unconstrained model. As illustrated in Figure 1, the results indicate that the final structural model had adequate fit and explained a large amount of variation in T2 marital negativity. Results from tests of our first research question revealed that for actors, but not partners, T1 and T2 marital negativity were positively associated, indicating relative stability in actors’ marital negativity over time. Results addressing our second research question revealed that partners’, but not actors’, higher T1 somatic symptoms were related to higher T2 marital negativity.

Figure 1.

Figure 1.

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Marital negativity results for the constrained two-intercept APIM approach (final model estimated).

Note. N = 246 Mexican-origin couples. We present unstandardized coefficients (standard errors) from the fully constrained model across gender (i.e., all model parameters including factor loadings for the negativity latent factor and actor and partner effects were constrained across husbands and wives). For simplification purposes, the figure presented was simplified to represent the constrained model; exogenous covariance parameters are not presented. Subscript a refers to actor. Subscript p refers partner. Covariance between husbands’ and wives’ T2 marital negativity = .15 (.15). Model fit: χ2(93) = 116.47, p = .05; RMSEA = .03; 90% CI [.00, .05]; CFI = .95; SRMR = .09. Husbands’ R2 = .40 (.06), p < .001. Wives’ R2 = .42 (.06), p < .001. *p < .05.

Difference Model

We used two estimation steps. In Step 1, we estimated a measurement model including two latent factors, a latent intercept and a latent slope. We used the observed variables (i.e., T2 husbands’ and wives’ marital negativity) as indicators of the latent factors. Using a similar model specification to that for latent growth curve models, our parameterization fixed the factor loadings of the latent factors to specific values for interpretation purposes. For the latent intercept, the factor loadings were fixed to 1 to represent the couple average on T2 marital negativity. For the latent slope, effect coding was used to fix the loadings to −.5 (husbands) and .5 (wives) to represent the within-couple difference on T2 marital negativity. The mean structure was estimated to obtain the averages for the latent intercept and slope. To identify the model (because the latent factors are fully determined by only two observed indicators): (a) the measurement residual variances (i.e., for the observed indicators) were constrained to be equal across husbands and wives – this provides a single estimate of within-couple variability; (b) intercepts for the observed indicators were set to 0; and (c) variance of the latent slope was set to 0. The purpose of Step 1 was two-fold. First, we confirmed the measurement structure; model fit was adequate, χ2 (1) = 1.96, p > .10, RMSEA = .06, CFI = .91, SRMR = .11. The couple average (M = 3.865, SE = .10, p = .000) and within-couple difference (M = .84, SE = .16, p = .000) for T2 marital negativity were significantly different from zero. Second, the model estimated the degree to which dyad members had similar scores on the dependent variable. The latent intercept variance corresponds to the standardized between-couple variation (Ψ00 = .81, SE = .25; p = .001). The measurement residual variance corresponds to the within-couple variation (Θe = 2.01, SE = .24; p = .000). There was greater variation within than between couples. The intraclass correlation coefficient (i.e., a ratio of the between-couple variation relative to the total variation; ρ = .29) revealed the proportion of variance explained by the couple was close to 30%.

In Step 2, we estimated a structural model that incorporated the measurement model from Step 1, by adding husbands’ and wives’ T1 somatic symptoms and marital negativity as exogenous variables and marital duration as a covariate. The results from Step 2 indicated that the model had good fit and explained a large proportion of variation in T2 average couple marital negativity (Figure 2). Results for our first research question indicated that husbands’ and wives’ marital negativity were positively associated with couple-level marital negativity five years later. For our second research question, results revealed that wives’ negativity was positively associated, and husbands’ negativity was negatively associated with the overall difference between husbands’ and wives’ negativity five years later. This suggests that prior levels of wives’ negativity predicted increases in the within-couple difference on negativity; prior levels of husbands’ negativity were linked, however, to decreases in the within-couple difference. We found no evidence of links between somatic symptoms and later marital negativity.

Figure 2.

Figure 2.

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Marital negativity results for the difference model (final model estimated).

Note. N = 246 Mexican-origin couples. We present unstandardized coefficients (standard errors). For simplification, the covariance between exogenous variables are not presented. Subscript a refers to person a, in this instance wives. Subscript b refers to person b, in this instance husbands. Model fit: χ2 (1) = .26, p = .61, RMSEA = .00, 90% CI [.00, .14], CFI = 1.00, SRMR = .01. T2 marital negativity intercept R2 = .65 (.12), p < .001.

†p < .10. *p < .05

Discussion

This article illustrated methods of analyzing two-wave data with a dyadic matched-pair design. These approaches are substantively and analytically informative in answering research questions posed about dyads and families, in particular. These approaches offer great potential for enhancing our knowledge on the complex interrelations between (a) individual and family functioning and (b) relationship processes (e.g., romantic, sibling, parent-child). In applying these methods to Latino populations, who have unique strengths and vulnerabilities, we can address significant gaps in the literature. Specifically, the current study yielded insights on associations in Mexican-origin couples’ marital negativity over a five-year span and the predictive validity of somatic symptoms on partners’ marital negativity. The hybrid model suggested that there was not variation in the pattern of actor and partner associations by spouse gender. There was relative stability in actors’ marital negativity over time. Somatic symptoms were related to partners’, but not actors’, increased marital negativity. Relatedly, the results from the difference model did not support a link between prior levels of somatic symptoms on couples’ average marital negativity. The difference model did reveal that prior levels of wives’ marital negatively linked to more discrepancies in marital negativity five years later, whereas husbands’ marital negativity related to fewer discrepancies, pointing to the differential role of husbands and wives on marital quality. This study extends prior research in support of the stress generation (Davila et al., 1997) and spousal discrepancy (Kurdek, 1993) models and yields evidence for couple-level patterns of associations between psychological functioning and changes in future marital quality.

Model Extensions and Limitations

There are several possibilities for moving the field forward in relation to Latino couples/families by using and building on the dyadic models presented here. There have been calls to understand the complex causal pathways linking constructs across macroenvironmental, individual, and family domains (e.g., Helms et al., 2011). For Latinos, this might include questions of sociocultural factors as protective/moderating (e.g., nativity, familism values) or risk (e.g., acculturative stress to depressive symptoms to marital negativity; mediational process) mechanisms for the associations presented here. As with other SEM approaches, moderation can be tested by either including interaction terms or using multiple group approaches; questions of mediation can also be integrated (Kenny et al., 2006). Other questions might include dyadic/family variation over time in cultural orientations/values, individual health, and relationship quality. These questions can be answered using extensions of the techniques presented here by, for example, examining the reciprocal effects between depressive symptoms and marital negativity over time, or by incorporating features such as growth curve analysis. The two-intercept model, but not the traditional parameterization of the APIM, can also be extended to include data from more than two family members by including a latent family-level outcome to understand these associations at the family-system level. The difference approach can also extend to include a measurement model and data involving larger groups (e.g., 2 – 5 members), such as family units (Newsom, 2002). This extension, though, is restricted to distinguishable members because unlike the two-intercept model, the difference model is difficult to implement with indistinguishable (e.g., identical twins) dyad members. Nevertheless, it can be a useful tool for researchers interested in contributing to the literature on dyadic/family differences in relation to individual and relationship processes, such as the parent-child acculturation gap.

There are other dyadic analytic approaches not discussed in this paper that measure different forms of dyadic nonindependence. An example is indistinguishable dyads (e.g., same-sex twins or homosexual partners; e.g., Olsen & Kenny, 2006). These data present unique challenges that can be analyzed with the two-intercept approach with slight modifications, but cannot be easily analyzed with the difference approach. Though beyond the scope of this article (but see Table 1), there are other dyadic analytic methods worthy of mention for scholars working with different data sources or related research questions. These include the dyadic feedback or mutual influence model that allows dyad members’ outcomes to influence one another in a feedback loop (e.g., Cook, 1998), the common fate model that uses a reflective approach to distinguish individual from couple effects (e.g., Ledermann, & Kenny, 2011), and dyad classification methods (e.g., Whiteman & Loken, 2006).

As with any analytic method, the models described in this paper are not without their limitations. First, method variance inflation was a possibility because all variables were assessed by self-report. However, many statistical techniques (e.g., such as those that include an indicator of method variance as a covariate) can adjust for this (Podsakoff, MacKenzie, Lee, & Podsakoff, 2003; Van Dulmen & Goncy 2010). Second, power can be a concern in dyadic models because of the nonindependence of data and the need to use the dyad rather than the individual as the unit of analysis. As discussed by Ackerman, Donnellan, and Kashy (2011), who examined power in the context of the APIM, there is low power to detect partner effects. Researchers using matched-pairs data should therefore plan their study with close attention to power considerations. Third, we only presented partial measurement models, but these techniques can be extended to fully model measurement error.

Concluding Comments

The analytic approaches illustrated here may be particularly useful for researchers interested in Latino relationships as these populations have high rates of marriage, face contextual stressors that can strain relationships, and endorse cultural values that highlight the importance of family and interdependence in family relationships (Helms et al., 2011; Monthly Labor Review, 2013; U.S. Census Bureau, 2017). In particular, the two-intercept parameterization is most useful for researchers interested in a general dyadic data method that can be used to examine individual-level exogenous variables operationalized as actor and partner effects similar to APIM, and/or for those seeking a method allowing for the incorporation of observed measures for the dyad, such as family context characteristics (e.g., Are the number of shared cultural activities between spouses associated with husbands’ and wives’ relationship satisfaction?). The difference model is most useful for predicting patterns of difference quantified as an endogenous variable (e.g., Are husbands’ and wives’ perceptions of sexual satisfaction associated with differences in husbands’ and wives’ marital satisfaction?). The integration of multiple analytic approaches is useful as each approach contributes unique information, leading to a more comprehensive understanding of relational dyadic processes among ethnic minority populations.

Public Significance Statement.

This illustration of analytic methods for dyadic matched-pairs data highlights the potential relations between spouses’ psychological functioning and the qualities of their marriages among Mexican-origin couples, an understudied but growing group in the U.S. When spouses are depressed, their partners report increases in marital negativity over time. When wives feel negative about their marital relationship, spouses have larger discrepancies in marital negativity over time (e.g., wives feel more negativity than their husbands). Conversely, when husbands feel negative about their marital relationship, husbands and wives have similar levels of marital negativity over time.

Acknowledgments

We are grateful to the families and youth who participated in this project, and to the following schools and districts who collaborated: Osborn, Mesa, and Gilbert school districts, Willis Junior High School, Supai and Ingleside Middle Schools, St. Catherine of Siena, St. Gregory, St. Francis Xavier, St. Mary-Basha, and St. John Bosco. We thank Ann Crouter, Susan McHale, Mark Roosa, Nancy Gonzales, Roger Millsap, Jennifer Kennedy, Leticia Gelhard, Sarah Killoren, Melissa Delgado, Emily Cansler, Shawna Thayer, Devon Hageman, Ji-Yeon Kim, Lilly Shanahan, Norma Perez-Brena, Sue Annie Rodriguez, Chum Bud Lam, Megan Baril, Anna Solmeyer, and Shawn Whiteman for their assistance in conducting this investigation. We thank Maria Elena Villasante Arce and Kara Brown for help with translating the abstract. Funding was provided by NICHD R01HD39666 (K. Updegraff, PI) and the Cowden Fund to the School of Social and Family Dynamics at ASU. Portions of this manuscript were presented in at the Annual Meeting of the National Council on Family Relations, Phoenix, AZ, October, 2012; and in the first author’s dissertation.

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