Introduction to the special issue: Nonlinear effects and dynamics in close relationships

Theme I: Central relationship theories imply nonlinear effects and dynamics

Several theories involving close relationships allude to underlying processes that are nonlinear by nature, yet have only been tested using linear modelling. Properly modelling nonlinear effects and dynamics, however, can directly test these pivotal processes. Two papers in this special issue utilize nonlinear models to test central tenets of one of the most influential theories in close relationships – attachment theory. According to attachment theory, both high quality and consistent caregiving is required to foster greater attachment security. Although quality caregiving has been studied extensively, most work on attachment has not paid much attention to consistency versus fluctuations in caregivers’ responsiveness (see Girme et al., 2021b; Gunaydin et al., 2021; Eller et al, in press, for exceptions). Eller et al., (2022) show that, beyond mean levels in the quality of maternal sensitivity received across early-to-middle childhood, inconsistent caregiving (i.e., greater within-person standard deviation in maternal sensitivity) has unique, deleterious consequences for the development of attachment security and relationship effectiveness years later in adulthood.

Another core tenet of attachment theory is that attachment working models are hierarchically structured (Overall et al., 2003), with people having both relationship-specific and global working models. Prior research has documented ways in which attachment representations can and do change over time (e.g., Simpson et al., 2003), but it remains unclear exactly how these changes occur. Dugan et al. (2022) employ bivariate growth curve models to examine associations among long-term changes (slope-slope correlations) and short-term fluctuations (correlations among residuals) in different working models or attachment representations. Their results provide important theoretical insights into the dynamic ways in which attachment representations change and how short-term fluctuations in working models can “reverberate through [people’s] network of attachment representations” (pg. 23).

Theme II: Nonlinear applications can reconcile inconsistencies and reveal novel effects

As is true of many fields, relationship science is fraught with inconsistent findings: social support is beneficial, but can also backfire (Girme et al., 2015); conflict is destructive, but it can also be diagnostic and helpful (Overall, 2020); sexual frequency is important for relationship functioning, but life often gets in the way (Muise et al., 2016). Linear models may reveal inconsistent effects because they do not model the association between variables along the full range of values (e.g., curvilinear effects) or because they mask important sources of variation in the data (e.g., fluctuation effects; see Girme, 2020). Nonlinear applications can reconcile inconsistencies in associations that occur at different levels and can sometimes reveal novel effects that may be missed when simply modelling linear effects. In this special issue, Chopik et al. (2022) provide one such example. The literature on the association between age and gratitude is mixed: Different studies have produced contrary evidence that gratitude peaks either in younger age, middle age, or older age, with some studies revealing null associations (see Chopik et al., 2019). Chopik et al. (2022) report a cubic effect of age (age³) that is consistent across cultures, with gratitude levels being low and stable among adolescence, then gradually increasing across middle age, and finally stabilizing in older age. This pattern reflects nonlinear changes in gratitude across the lifespan that has never been captured by previous studies examining linear associations.

Theme III: Relationship interactions involve nonlinear dynamic shifts

Behavioral observation, such as video-recording dyads engaged in discussions, is one of the strongest methods used to measure and witness interpersonal processes that forecast long-term relationship outcomes (Baumeister et al., 2007; Gottman & Notarius, 2000). Observation methods often involve independent coders who rate each partner’s emotions and behaviors across the discussion, which provides very rich data to examine key dyadic processes in diagnostic social interactions (Overall et al., 2016). The resulting quantitative measures and data analytic techniques, however, typically fail to consider the multitude of ways in which conversations unfold. One paper in the special issue introduces a useful tool to examine how dyadic conversations progress. Solomon et al. (2022) use sequence analysis to identify different patterns of sequential behavior based on categorical shifts during couples’ discussions, such as Morgan disclosing a problem, Mateo clarifying it with a question, Morgan elaborating more, Mateo reflecting on what is said, and then ending with Mateo providing advice. Different sequential patterns, or “conversational motifs”, can then be used to predict key outcomes, such as which conversational motifs are associated with discussion success, or whether individual or dyadic characteristics predict certain conversational motifs, such as what types of couples tend to engage in optimal conversational motifs.

Considering nonlinear dynamics also enhances our understanding of processes within dyadic interactions by highlighting that important and consequential changes in emotion, behavior, or communication may not reflect incremental, linear effects across interactions. Indeed, another paper in this special issue shows how nonlinear models can identify abrupt shifts during conversations. Sels et al. (2022) introduce change point detection analysis, which allows researchers to detect sudden shifts in emotions during dyadic discussions. The method Sels et al. illustrate identifies whether abrupt changes are experienced by both dyad members simultaneously, such as Morgan and Mateo both suddenly getting angry, or whether abrupt changes are isolated to one member of the dyad, such as Morgan suddenly gets angry, but Mateo does not. These critical moments may have important implications for the trajectory of dyadic discussions, such as serving as catalysts for couples to become more versus less attuned or synchronized (“on the same page”) following critical change points. These types of abrupt changes may be a critical element of couples’ discussions that remain undetected when researchers rely on global assessments or linear modeling.

Theme IV: Nonlinear dynamics involve temporal and spatial synchrony between partners

One defining feature of close relationships is that dyad members (partners) are highly interdependent—each person’s experiences and outcomes are inherently linked by mutual dependence and influence (Kelley et al., 2003; Kelley & Thibaut, 1978). Relationship science typically accounts for this interdependence by examining contemporaneous and longitudinal partner effects (i.e., how Morgan’s behavior impacts Mateo’s outcomes; Cook & Kenny, 2005). Two papers in this special issue, however, illustrate how nonlinear modelling can identify additional dyadic processes involving patterns of synchrony between relationship partners. Kuelz et al., (2022), for example, use the R statistical package rties (Butler & Barnard, 2019) to model different patterns of physiological synchrony between dyad members using a coupled oscillator model. Using this method, they: (a) identify distinct patterns of physiological synchrony (such as when partners’ physiologies counterbalance, but never achieve homeostasis or stability), and (b) illustrate what partner and couple characteristics might predict distinct patterns of physiological synchrony (such as whether dissatisfied couples have more maladaptive patterns of physiological synchrony).

Although typically conceived as unfolding across time during specific interactions, dyadic interactions also occur at varying levels of proximity. Ogolsky et al., (2021) link continuous measures of individuals’ spatial proximity in their homes with their partner’s heart rates during daily life to determine whether and how proximity is associated with both partner’s physiological responses. Data across three time-series profiles illustrate that not only does lagged-feedback (i.e., cross-correlations across time) emerge between husbands’ heart rate, wives’ heart rate, and each couple’s proximity, but that predicting any of these variables requires critical information about the other two variables. For example, Morgan’s heart rate might increase 3 minutes after Mateo’s heart rate increases and as the proximity between Morgan and Mateo decreases. In sum, nonlinear models not only confirm that close relationships are highly interdependent; they also provide nuanced information about distinct patterns of synchrony in dyads and the novel consequences of these interaction dynamics.