Definition and Introduction
A dyad is composed of two people who relate to each other (e.g., romantic partners, two friends, parent-child, or patient-therapist dyads). Interactions between the dyad’s members and/or their characteristics (e.g., personality traits) are called dyadic. Dyadic interactions follow Koffka’s gestalt principle “the whole is other than the sum of its parts,” since a dyad is not only characterized by its members’ attributes but also possesses unique characteristics on the basis of how they interact. Dyad members relate to each other; they show interdependence based on mechanisms such as assortative mating or sharing a common social environment (e.g., Weidmann et al. 2016). However, there are differences between dyads (e.g., in members’ agreement or similarity) and the study of dyadic effects analyses whether such differences contribute to explaining external outcomes. For example, the most frequently studied dyadic effect addresses the question of whether similarity (e.g., in romantic partners or friends) relates to criteria such as relationship quality or the longevity of relationships.
Researchers can choose from numerous methodological approaches to analyze dyadic data (e.g., Kenny et al. 2005). This entry gives an overview on the measurement of dyadic effects, popular frameworks for dyadic data analysis, and describes the major merits and caveats of each method. Throughout the entry, the dyadic effect of similarity will be used for illustrations.
Unit of Analysis
While statistical approaches and interpretations differ between the methods used to analyze dyadic data, they share an important methodological quality: the unit of analysis. The members of a dyad are nested within “their” couple to account for their interdependence. Thus, the sample size must be determined on the level of the dyads (k[dyad] = N/2), which should be considered for power analyses and significance testing. For illustration, a study using data of N = 300 romantic partners should be analyzed on basis of k = 150 couples. Ignoring the nested nature of the data will lead to distorted findings, as (1) the shared variance between dyad members is not considered and (2) incorrect degrees of freedom will underestimate p-values and increase type-I error rates; for example, a correlation of r = 0.17 goes along with different estimates of statistical significance depending on the unit of analysis (individuals: t[N = 300] = 2.98, p = 0.003; couples: t[k = 150] = 2.10, p = 0.038; Δp = 0.035).
The description of dyadic interdependence across the sample (i.e., all studied dyads) is operationalized as the correlation between members’ expressions (e.g., the similarity between male and female partners in the study of romantic couples). However, analyzing dyadic effects requires the computation of an index on the dyad level in the way that every dyad is assigned a numerical value reflecting members’ interaction/relationship. Such scores are utilized as independent variables when testing whether dyadic interactions affect a criterion (e.g., “is similarity associated with relationship quality?”).
Different options for mathematically characterizing the relation of dyad members exist. Most commonly, the (absolute) difference between dyad members’ scores is used as a measure of their overlap (dyadic similarity). Such difference scores assume that zero indicates perfect overlap (i.e., high agreement/similarity), but dissimilarity is interpreted differently across approaches. Absolute differences only describe the magnitude of dyadic dissimilarity independently of which member reaches higher scores than the other. Contrarily, raw score differences indicate the ratio of dissimilarity between members by the sign of the difference; for example, a negative sign might indicate that women show higher expressions than men in a given variable, whereas positive values might indicate that men score higher than women. When correlating difference indexes with a dependent variable (e.g., relationship quality), the interpretation of a dyadic effect depends on which difference approach is utilized. Difference scores have been subject to criticism (e.g., Edwards 2002; Kenny et al. 2005), as their usage is prone to confound dyadic effects with main effects (cf. section “Separating Dyadic Effects’”), reduced reliability, and the simplification of multidimensional associations into a single score. Thus, difference scores should be utilized cautiously when studying dyadic effects. Further, a statistical interaction term computed by multiplying the dyad members’ scores has been proposed in the literature. In line with the reasoning in ANOVA-designs, an interaction informs whether certain combinations of members’ expressions affect an outcome (see Cook and Kenny 2005; Kenny et al. 2005).
These indexes describe dyad members’ interactions regarding a single variable but researchers might be interested in dyadic effects concerning a set of variables (profiles); for example, one might be interested to analyze romantic partners’ similarity with respect to their complete set of the Big Five traits. While there are several approaches to compute profile indexes for dyadic research, Furr (2008) has proposed a method that overcomes problems of other methods (e.g., stereotype effects; normativeness) and allows the distinction between several types of profiles. Most importantly, raw and stereotype-adjusted indexes of profile similarity are computed for every dyad, enabling their use as dyadic index for testing dyadic effects that are expressed in a correlation coefficient (coefficients close to 1.00 = high overlap; close to 0.00 = independence; close to −1.00 = dissimilarity; for details see Borkenau and Leising 2016). This approach has been frequently used, for example, to study how similarity in romantic partners’ personality profiles contributes to relationship quality or how similarity affects attraction and impression formation when two strangers meet for the first time.
Separating Dyadic Effects
As mentioned previously, dyadic indexes rely on dyad members’ characteristics. For illustration, readers might imagine testing the hypothesis “partner similarity in extraversion positively predicts happiness.” One might compute a difference score and test the dyadic effect by correlating the dyadic index with the happiness scores of both partners. However, this intuitive approach confounds the dyadic effect with main effects and thus over estimates the dyadic effect of similarity. Main effects describe how the independent variable (each members’ extraversion) explains variance in the dependent variable (happiness). Since the dyadic index is composed of the members’ extraversion scores, the index contains main effects of each dyad member (i.e., individual level: how does a members’ extraversion contribute to his/her happiness) and the unique dyadic feature (i.e., dyadic level: similarity of partners’ extraversion) − the “pure” dyadic effect cannot be estimated. This problem is addressed by controlling the main effects of independent variables in order to isolate the unique contribution of the dyadic effect (similarity) on a dependent variable (happiness; cf. Kenny et al. 2005). It has been argued that early research on romantic relationships robustly over estimated the contribution of partner similarity to relationship satisfaction by not controlling for main effects. Thus, cautious interpretation of dyadic effects is warranted when main effects are not controlled.
Statistical Frameworks for Testing Dyadic Effects
The Actor-Partner Interdependence Model (APIM; Cook and Kenny 2005) is among the most popular methods for studying dyadic data. The APIM estimates the association between both members’ predictor (e.g., personality trait) and outcome variables (e.g., relationship satisfaction) while controlling for members’ interdependence. Further, two main effects are estimated, namely, the actor effect, which describes the within-person association between a predictor and outcome variable (e.g., how Partner A’s extraversion is associated with Partner A’s happiness), and the partner effect, describing the between-person association (e.g., how Partner A’s extraversion is associated with Partner B’s happiness). Although partner effects are typically smaller in size than actor effects, they contribute to our understanding of dyadic mechanisms (see Weidmann et al. 2016). Further, the influence of dyad characteristics can be tested by adding a dyadic index (e.g., interaction term, difference score, or profile correlation) to the model. A merit of this model is that main effects of actors and partners can be controlled through the actor and partner effects. Thus, the APIM allows the disentanglement of how the dyad members as well as their dyadic characteristics (similarity) are differentially associated with members’ outcomes. The computation of APIMs is based on structural equation modelling (SEM) or multilevel modelling (MLM) and is available in R and Mplus (see Kenny et al. 2005 for an introduction).
The Social Relations Model (SRM; Kenny 1994) enables the estimation of dyadic effects within groups that comprise four or more members. The standard research design follows the round-robin principle (i.e., each participant interacts with multiple others and members provide ratings reciprocally). The SRM partitions the variance of a criterion variable and accounts it to the group (constant), actors, partners, errors, and the relationship effect, which reflects the interaction between two group members − the dyadic effect. Thus, the SRM allows the testing of how much variance of a criterion, such as the desire to maintain a relationship in a clique of friends, can be explained by dyadic interaction between two group members. For further information, see the entry “Social Relations Model” by Locke (this book).
Further, Response Surface Analysis (RSA, e.g., Edwards 2002) provides a statistical framework for analyzing the relationship between combinations of two predictor variables and an independent variable in three-dimensional space, where the X- and Y-axis describe dyad members’ scores (e.g., extraversion) and the criterion variable is displayed on the Z-axis (e.g., relationship quality). Using polynomial regression analysis allows to generate a response surface that describes the relationship between the three dimensions. This approach has the merit that the complete dyadic information is utilized and no condensed dyadic index is required. RSA describes four characteristics of dyadic combinations: namely, how the criterion variable is affected by (a) members matching at low vs high expressions; (b) the ratio of incongruence between members (i.e., does X > Y or Y > X matter?; cf. section “Dyadic Indexes”); (c) congruence at extreme versus midpoint values (i.e., are similar couples happier when matching at extreme vs average values?); and (d) the degree of matching (i.e., magnitude of similarity). Thus, RSA describes which patterns of dyadic combinations matter in the prediction of a criterion beyond testing the mere existence of dyadic effects.
However, researchers are often interested in dyadic effects on both members’ outcomes. Using RSA, each members’ outcome must be computed in a separate model, adding complexity to the analysis and interpretation. To address this shortcoming, Dyadic Response Surface Analysis (DRSA; Schönbrodt et al. 2018) was introduced, which allows the testing of the equality of both members’ RSA coefficients by combining the APIM and RSA. Illustrations and R/Mplus syntaxes are provided in the literature (RSA: Barranti et al. 2017; DRSA: Schönbrodt et al. 2018).
Finally, the association between two dyadic effects (e.g., how does dyadic coping affect relationship conflict?) might be of interest. Both the dependent and independent variable exist on the dyad level as they are composed of dyad members’ ratings according to how they judge their relationship. The Common Fate Model (CFM; Ledermann and Kenny 2011) analyzes the dependent and independent dyad-level variables on the latent level, based on the manifest indicators of members’ ratings using SEM or MLM. An extension combining the APIM and CFM exists, which allows the influence of actor and partner effects (i.e., individual-level) on the association between dyadic effects (dyad-level) to be tested. Illustrations and examples are described in Ledermann and Kenny (2011).
Describing the relationship or interaction between two people (e.g., romantic partners, teacher and student) as well as testing their consequences on individual (e.g., satisfaction) and/or dyadic (e.g., couple’s coping) outcomes enables conclusions to be drawn about the role of personality in social life. The complexity of this line of research is reflected in the diversity of methodological approaches to describe dyadic effects. Moreover, researchers are challenged to adjust their interpretations upon a number of factors, such as the chosen approach for analysis and its underlying philosophy, considered covariates, and research designs.
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