Multivariate Analysis of Triadic Relationst

Abstract

To analyze variance in a triadic variable, Bond, Horn, and Kenny (1997) have proposed a Triadic Relations Model. Here we extend this model to analyze the covariances between triadic variables. A bivariate version of the Triadic Relations Model is specified, and estimation methods are presented. These can be used to decompose the covariance between two triadic variables into thirty-three covariance components. Interpretations and an example of this analysis are offered. Applications of this model and alternative techniques are noted.

A Bayesian Approach for The Analysis of Triadic Data In Cognitive Social Structures

“…For a detailed interpretation of the variance components and and the correlation parameters , , and , we refer the reader to Bond et al . () and Card et al . ().…”

“…We assume that the interaction effects .αβ/ ij , .αβ/ ji , .αγ/ ij and .αγ/ ji follow a multivariate normal distribution with mean vector zero and covariance matrix Σ 2 as in equation (6). For a detailed interpretation of the variance components σ 2 αβ and σ 2 αγ and the correlation parameters φ 1 , φ 2 , φ 3 and φ 4 , we refer the reader to Bond et al (2000) and Card et al (2010). Table 4 provides posterior summaries of the variance components and correlation parameters.…”

“…Bond et al . () further extended the model to analyse multivariate triadic relations. Their model incorporated covariances between measurements on different types of relations on the same pair of subjects.…”

“…Bond et al (1997) extended the social relations model of Kenny (1994) to incorporate third-person perceptions. Bond et al (2000) further extended the model to analyse multivariate triadic relations. Their model incorporated covariances between measurements on different types of relations on the same pair of subjects.…”

A Multidimensional Scaling Model for Three-Way Data Analysis

“…Other models have been based on the variances of two objects (e.g., Bond et al, 1997;Bond, Kenny, Broome, Stokes-Zoota, & Richard, 2000). These studies proposed triadic relations models to analyze the variance of a triadic variable.…”