Dyadic Data Analysis

Dyadic Data Analysis

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Outline:

• What is Dyadic Data?

• Examples

• Analysis of Dyadic Data

• Approaches to deal with dyadic data

What is Dyadic Data?

The dyad is arguably the fundamental unit of interpersonal interactionand relations. Many of the phenomena studied by social and behavioralscientists are interpersonal by definition, and as a result, observationsdo not refer to a single person but rather to multiple persons. Theintrinsically dyadic nature of many of the measurements in social andbehavioral science research means that they are often linked to othermeasurements in the study.

Examples

• Two persons are asked to describe a common target person to determinewhether there is agreement in person perception.

• Members of a family describe their attachment relationships with oneanother.

• The amount of self-disclosure made by two people interacting ismeasured to ascertain whether there is reciprocity.

Analysis of Dyadic Data

In each of these cases, the issues of stability, consistency, andcorrelation between related measurements are interesting phenomena.However, none of them can be addressed easily by standard methodsdeveloped for the study of individuals. These cases can be dealt throughinterpersonal processes or dyadic data analysis, that permits theassessment and testing of dependency. The analysis of interdependentdata presents special issues because the covariance across individualsneeds to be addressed in the analyses rather than fixing data forindependence.

In the analysis of dyadic data there are many issues that need to beaddressed in the analysis, such as whether dyad members areexchangeable or distinguishable.

Analysis of Dyadic Data

There are three common types of associations that occur inpsychological data.

• Temporal

• Interpersonal

• Multivariate correlation.

Our focus is on interpersonal association that can be seen in dyadicdesigns. Various models such as repeated measures analyses, multilevelanalyses, and SEM provide similar ways of capturing the associationsthat occur between observations.

Approaches to Deal with Dyadic Data

• Repeated measures

• Multi level modeling

• Structural equation modeling(SEM)

Repeated Measures

This method deals with the temporal association between theobservation.

Suppose we have 20 individuals measured once on a single variable andwe want to estimate the mean across the 20 individuals. We can modelthe data as-

𝑌𝑖=µ+𝑒𝑖with the usual assumption that the error terms are independent andidentically distributed.

Repeated Measures

Now we turn to the case of temporal association by considering twoobservations for the same person, that is, the 20 individuals aremeasured twice, so there are a total of 40 observations. The model forcomparing the difference between the mean at each time becomes-

𝑌𝑖𝑗 = µ + β𝑗 + α𝑖 + 𝑒𝑖𝑗

This results in 40 error terms, which can be

placed in a 40 × 40 covariance matrix, The random effect terms αintroduce a covariance across the 40 observations.

Repeated Measures

This framework can be extended to dyads, Suppose the 40 observationscame from 20 dyads. A covariance is introduce between two membersof the same dyad Similarly, the covariance between individuals fromdifferent dyads is zero.

Interdependence between interval scaled data in the context of linearmodels is captured by the ICC. The basic intuition for the ICC is that itis the percentage of variance associated with between couple variance.

Repeated Measures

The ICC becomes the ratio-

𝞼2α𝞼2α + 𝞼2𝑒

Where α𝑖 is a random effect for dyad, and ‘e’ is the usual error term.

Multi Level Modeling

This model can be represented in multilevel context with the first levelrepresenting data at the individual level and the second levelrepresenting dyads. This model is written in two parts-

𝑌𝑖𝑗=Υ𝑖 + β𝑗 + 𝑒𝑖𝑗Υ𝑖=µ+α𝑖

where β is a fixed effect term that estimates, say, the difference betweenthe two distinguishable dyad members, γ is a random effect dyad term,and the ε is the usual error term.

Multi Level Modeling

If we substitutes 2nd equation into 1st equation, then the result is same asthe result from repeated measures.

Structural Equation Modeling

SEM is also a way to conceptualize the ICC with two indicators onelatent factor, and a specific set of restrictions.

If we set the variance of the latent factor to one, the two indicator pathsto the observed variables equal to each other, and the error variancesequal to each other, then the indicator paths are equal to the square rootof the ICC.


Unique H variane

UniqueW

variane

𝑋𝐻 𝑋𝑊

Shared X variane

1 1

𝑟𝑥𝑥′ 𝑟𝑥𝑥′


Thus, there are several ways to conceptualize the logic of interdependenceas indexed by the ICC, and they all lead to the same result. We can modelthe interclass as a linear mixed model, as a multilevel model, or as anSEM. They all give the same results as long as the same estimationprocedure is used.


To decide which model to use the key point to note is whether dyadmembers are distinguishable or not. Dyad members are distinguishablewhen the individuals can be identified on the basis of a theoreticallymeaningful variable such as gender.

When dyad members are distinguishable, we estimate the path model orCFA model for each of the two members combined in a single model.


The use of SEM with indistinguishable or exchangeable dyad membershas generally been viewed pessimistically, since dyadic SEM model isrestricted to data with nonexchangeable partners.

So, when dyad members are exchangeable multi-level modeling can bea good option to use.

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Dyadic Data Analysis