This document discusses dyadic data analysis. Dyadic data refers to data that involves two related individuals, such as perceptions between two people or levels of self-disclosure between two interacting people. There are several approaches to analyzing dyadic data, including repeated measures analysis, multi-level modeling, and structural equation modeling. These approaches allow researchers to assess dependencies between individuals and account for the covariance between observations from the same dyad. The key considerations in selecting an analytic approach include whether the dyad members can be distinguished and whether they are exchangeable.

1. Dyadic Data Analysis
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2. Outline:
• What is Dyadic Data?
• Examples
• Analysis of Dyadic Data
• Approaches to deal with dyadic data

3. What is Dyadic Data?
The dyad is arguably the fundamental unit of interpersonal interaction
and relations. Many of the phenomena studied by social and behavioral
scientists are interpersonal by definition, and as a result, observations
do not refer to a single person but rather to multiple persons. The
intrinsically dyadic nature of many of the measurements in social and
behavioral science research means that they are often linked to other
measurements in the study.

4. Examples
• Two persons are asked to describe a common target person to determine
whether there is agreement in person perception.
• Members of a family describe their attachment relationships with one
another.
• The amount of self-disclosure made by two people interacting is
measured to ascertain whether there is reciprocity.

5. Analysis of Dyadic Data
In each of these cases, the issues of stability, consistency, and
correlation between related measurements are interesting phenomena.
However, none of them can be addressed easily by standard methods
developed for the study of individuals. These cases can be dealt through
interpersonal processes or dyadic data analysis, that permits the
assessment and testing of dependency. The analysis of interdependent
data presents special issues because the covariance across individuals
needs to be addressed in the analyses rather than fixing data for
independence.
In the analysis of dyadic data there are many issues that need to be
addressed in the analysis, such as whether dyad members are
exchangeable or distinguishable.

6. Analysis of Dyadic Data
There are three common types of associations that occur in
psychological data.
• Temporal
• Interpersonal
• Multivariate correlation.
Our focus is on interpersonal association that can be seen in dyadic
designs. Various models such as repeated measures analyses, multilevel
analyses, and SEM provide similar ways of capturing the associations
that occur between observations.

7. Approaches to Deal with Dyadic Data
• Repeated measures
• Multi level modeling
• Structural equation modeling(SEM)

8. Repeated Measures
This method deals with the temporal association between the
observation.
Suppose we have 20 individuals measured once on a single variable and
we want to estimate the mean across the 20 individuals. We can model
the data as𝑌𝑖 =µ+𝑒 𝑖
with the usual assumption that the error terms are independent and
identically distributed.

9. Repeated Measures
Now we turn to the case of temporal association by considering two
observations for the same person, that is, the 20 individuals are
measured twice, so there are a total of 40 observations. The model for
comparing the difference between the mean at each time becomes𝑌𝑖𝑗 = µ + β 𝑗 + α 𝑖 + 𝑒 𝑖𝑗
This results in 40 error terms, which can be
placed in a 40 × 40 covariance matrix, The random effect terms α
introduce a covariance across the 40 observations.

10. Repeated Measures
This framework can be extended to dyads, Suppose the 40 observations
came from 20 dyads. A covariance is introduce between two members
of the same dyad Similarly, the covariance between individuals from
different dyads is zero.
Interdependence between interval scaled data in the context of linear
models is captured by the ICC. The basic intuition for the ICC is that it
is the percentage of variance associated with between couple variance.

11. Repeated Measures
The ICC becomes the ratio𝞼2 α
𝞼2 α + 𝞼2 𝑒
Where α 𝑖 is a random effect for dyad, and ‘e’ is the usual error term.

12. Multi Level Modeling
This model can be represented in multilevel context with the first level
representing data at the individual level and the second level
representing dyads. This model is written in two parts𝑌𝑖𝑗 =Υ 𝑖 + β 𝑗 + 𝑒 𝑖𝑗
Υ 𝑖 =µ+α 𝑖
where β is a fixed effect term that estimates, say, the difference between
the two distinguishable dyad members, γ is a random effect dyad term,
and the ε is the usual error term.

13. Multi Level Modeling
If we substitutes 2nd equation into 1st equation, then the result is same as
the result from repeated measures.

14. Structural Equation Modeling
SEM is also a way to conceptualize the ICC with two indicators one
latent factor, and a specific set of restrictions.
If we set the variance of the latent factor to one, the two indicator paths
to the observed variables equal to each other, and the error variances
equal to each other, then the indicator paths are equal to the square root
of the ICC.

15. Structural Equation Modeling
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16. Structural Equation Modeling
Thus, there are several ways to conceptualize the logic of interdependence
as indexed by the ICC, and they all lead to the same result. We can model
the interclass as a linear mixed model, as a multilevel model, or as an
SEM. They all give the same results as long as the same estimation
procedure is used.

17. Structural Equation Modeling
To decide which model to use the key point to note is whether dyad
members are distinguishable or not. Dyad members are distinguishable
when the individuals can be identified on the basis of a theoretically
meaningful variable such as gender.
When dyad members are distinguishable, we estimate the path model or
CFA model for each of the two members combined in a single model.

18. Structural Equation Modeling
The use of SEM with indistinguishable or exchangeable dyad members
has generally been viewed pessimistically, since dyadic SEM model is
restricted to data with nonexchangeable partners.
So, when dyad members are exchangeable multi-level modeling can be
a good option to use.

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