Dyadic Data Analysis


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This is a small presentation of commonly used statistical techniques for analyzing dyadic data.

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Dyadic Data Analysis

  1. 1. Dyadic Data Analysis -PIE TUTORS Your Statistical Partner www.pietutors.com …committed to deliver 24/7…
  2. 2. Outline: • What is Dyadic Data? • Examples • Analysis of Dyadic Data • Approaches to deal with dyadic data
  3. 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. 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. 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. 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. 7. Approaches to Deal with Dyadic Data • Repeated measures • Multi level modeling • Structural equation modeling(SEM)
  8. 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. 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. 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. 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. 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. 13. Multi Level Modeling If we substitutes 2nd equation into 1st equation, then the result is same as the result from repeated measures.
  14. 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. 15. Structural Equation Modeling Unique W variane Unique H variane 1 1 𝑋𝐻 𝑋 𝑟 𝑥𝑥 ′ 𝑊 𝑟 𝑥𝑥 ′ Shared X variane
  16. 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. 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. 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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