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Block modeling and equivalencePowerPoint Presentation

Block modeling and equivalence

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Introduction

- Social structures are often not simply the pattern of interaction between nodes that are equal
- There are positions within social structure and roles (expectations) associated with those positions
- Parent-Child
- Manager-Employee
- Advisor-Student

- The idea of block-modeling and equivalence is to discover roles that are emergent (not named)

Blocks

- Procedures to find subsets of a graph that are distinct from other sets
- Bi-component – Identifies parts of a graph that are vulnerable to disconnection using cut-points
- Factions maximize local density
- Think of block-modeling as creating subsets that have similar profiles of connections

Factions

- Because it is easy to use in UCINET
- Factions is a sort of “relaxed” blockmodeling, based on the hypothesis testing that the network is composed by only two types of blocks (null between clusters, and complete within clusters) – structural equivalence
- It is deductive and direct because you can manipulate the raw data, pre-specify the number of factions and interpret it based on goodness of fit.

Concor(CONvergence of iterated CORrelations)

- Create correlation matrix
- Split matrix into two blocks so members of the same block are positively correlated
- Blocks are successively split
- Blocks containing only two nodes are not split any more

CONCOR on class data (standard and interactive)

Graph of Equivalence Classes (Wasserman and Faust, 1994)Structural equivalents (the same relationships): {A}, {B}, {C}, {D}, {E,F}, {G}, {H,I}Automorphic equivalents (the same positions): {A}, {B,D}, {C}, {E,F,H,I}, {G}Regular equivalents (the same kinds of relationships): {A}, {B,C,D}, {E,F,G,H,I}

Some Conclusions

- You should try different partitions of your network based on attributes and relations
- You can try block models as exploratory analysis
- If you have good ideas (based on theory and experience), you can test some hypotheses
- Blockmodeling is less sensitive to large and sparse networks (in this case, you should consider blocking the components or big clusters)
- There’s no right solution, only optimal. Try as many solutions as possible

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