The Structure of Nonprofit Organizational Interactions: Initial

Findings and Implications

Harold D. Green, Jr.University of Illinois Department of

Psychology

Organizational Relations

• Multiplex organizational network setting

• Structure among organizations across multiple relations

Entailment

• To have, impose, or require as a necessary accompaniment or consequence

• A predetermined order of succession• In a logical sense, the idea is one of implication:

A B• Based on a probabilistic or statistical idea of

entailment, rather than a logical or deterministic idea

• Corresponds more readily to empirical data

Key Question

• Are Entailment Structures present in a set of four relations among nonprofit international development organizations working in Washington DC?

Topics to Discuss

• International Development and Food Aid• Background on Development

Organizations• How I arrived at my research question• Explain the method and compare to other

methods• Test method in a constructed situation,

and previously validated empirical data• Apply to my data and discuss implications

Other Research on Multiplex Networks

• Wasserman

• Pattison

• Borgatti

• White

• Contractor

• Hubert

• Etc.

Food Aid

• Begun in 1952 after World War II

• Provide relief and development assistance to Low Income and Food Importing Developing Countries

• Support American Agricultural Industry with subsidies

• Title II of Farm Bill

Food Aid Organizations

• Share Common Operational and Programmatic Problems– Monitoring and Evaluation– Commodity Management– Monetization– Capacity Building/Sustainability

• Generally Work Independently

Food Aid Management

• Began in 1987, ended in 2004

• Sixteen largest development organizations were members

• Funded by USAID Institutional Support Agreement– Develop food aid standards– Exchange relevant information– Organize forums for discussion

Food Aid Management Activities

• Steering Committee

• Food Security Resource Center

• Website

• Working Groups

• Listservs

• Food Forum

Constituency Building Project Goals

• Understand collaborative development activities• Visualize the structure of collaboration• Monitor and evaluate collaborative activities• Provide suggestions for improving collaboration

Analytic Paradigm

• Organizational profiles

• Social Network Analysis– Make organizational relationships visual– Provide quantitative information not

available from qualitative analysis or standard quantitative analyses.

• Provide simple evaluation metrics

Social Network Analysis

• Questionnaire designed in collaboration with network members

• Ten primary interactions investigated

• Four questions intended to be validity checks

• General Interactions• Advice-seeking• Informal Interactions• Formal Interactions

General Interaction Network

Informal Interaction Network

Advice-Seeking Network

Formal Interaction Network

Structure Emerging

• The network diagrams of those four relations began to suggest that there might be some pattern

• MDS of QAP correlations suggested a linear arrangement of these relations

• Network densities and degree of mutuality reiterate the MDS findings

• Ordering seems intuitive• General, Informal, Advice, Formal• Is that intuition statistically sound?

Borgatti and Cross

• Investigate entailment in a for-profit business setting• Extend White’s Structural Entailment Analysis approach

to social relations• Guttman scaling approach

– Dichotomize data– Decompose sociomatrix into a column vector– Each column in new data matrix represents a relation type– Guttman scaling

• Solutions, meta-knowledge, problem reformulation, validation and legitimation formed a Guttman-like scale

• Supports findings from MDS, densities, correlations, reciprocities, etc.

Some Concerns

• White developed this for material entailment (respondent by item matrices)

• Mutual absence is not well defined for most sociomatrices

• Mutual choice against interaction• No opportunity to interact• No possibility for interaction• Error

• Not initially designed for comparing matrices, though extended to social interactions

• Seems like a lot of work

Pattison, Wasserman, Robins and Kanfer

• Relational algebras provide a different perspective for understanding multiplex networks

• Compounds of simple binary relations are binarized products of matrix multiplications

• A nonzero entry in a matrix of compound relations represents the presence of any path between i and j across the relations

• I am only interested in reciprocal paths, from i to j and back to i again

• A compound relation of only reciprocal paths is an item by item matrix multiplication, thus a special, very restricted case of relational algebras

An Entailment Index

• Matrix B is entailed completely in Matrix A if all nonzero values in B exist in A

• If all nonzero values in A also exist in B, then the matrices would be equal

• Create contingency table based on agreement between A and B, disregarding main diagonal

0 0 1 1

1 0 1 1

1 1 0 1

1 1 0 0

0 0 0 1

1 0 0 0

0 0 0 1

1 0 0 0

A

B

Contingency Table

• Divergence from pure entailment is measured by disagreements between A and B

• We are only interested in those location where nonzero values in B that are not matched with nonzero values in A

• For pure entailment, disagreements are zero

1 0 Total

1 4 6 10

0 0 2 2

Total 4 8 12

Values in Matrix BValues in M

atrix A

Computing Entailment Index

• Based on item by item matrix multiplication

• If you take the complement of A before multiplying, then the product matrix reveals disagreements

• Summing across rows and columns provides the entailment index

An Example

0 0 1 1

1 0 1 1

1 1 0 1

1 1 0 0 X

1 1 0 0

0 1 0 0

0 0 1 0

0 0 1 1 Xc

0 1 0 1

1 0 0 0

0 0 0 1

1 0 1 0 Y

0 1 0 0

0 0 0 0

0 0 0 0

0 0 1 0 YXc

Inferences about Entailment

• Low entailment scores suggest better entailment• How low is low? How do you assess the significance of

the indicator?• Recall that this is a special, very restricted case of a

Relational Algebra Approach, which bases statistical inferences in binomial and multinomial distributions

• P,W,R,K argue that Hubert’s permutation based approaches are the most constrained, controlling for all properties of the relations that are independent of individual identities (graph labels)– Relational density– Degree of mutualism or asymmetry– Level of transitivity

• A permutation approach is the most intuitive– Intuitive, easy to compute, less work than White’s approach

Computing the Distribution

• Empirical Probability Distribution is created by iteratively permuting corresponding rows and columns of one of the target matrix and then re-computing the entailment index

• After all iterations, indices are sorted, those that are greater than the initial index score are counted

• Count is divided by number of iterations to arrive at p-value for your initial index score

Computation at a Glance

• Compute Raw Index• Permute• Compute Distribution Value• Record• Repeat 2-4 for all iterations• Sort the Distribution Values• Count Values > Raw Index• Divide Count by Iterations for p-value

Some Thoughts

• For matrices with size <10, a complete enumeration of permutations can be completed and an exact distribution can be calculated

• For other matrices, the distribution is sampled

• MATLAB does these calculations very easily.

Returning to Our Example

• Recall there were two disagreements between X and Y

• Expected number of disagreements is 1

• Entailment Index is 2• p-value is 0.32• Index does not

suggest a significant entailment

0 1 0 0

0 0 0 0

0 0 0 0

0 0 1 0 YXc

Borgatti and Cross Data• Linear Arrangement of Interactions• Solutions, Meta-Knowledge, Problem

Reformulation, Validation and Legitimation• Entailment procedure recapitulates their findings

Entailment Index

Meta Knowledge

Problem Reformulation

Validation Legitimation

Solutions 4 (49) 4 (49) 1 (23) 1 (23)Meta Knowledge

0 (56) 0 (26) 0 (26)

Problem Reformulation

0 (26) 0 (26)

Validation 0 (35)

FAM Network Data

• Relationship among general interactions, advice seeking, informal collaborations and formal collaborations.

• Six pairs to compare

Entailment Index Informal Ties Advice Seeking Formal Ties

General Interactions

16 (53) 8 (42) 5 (32)

Informal Ties 15 (47) 12 (35)Advice Seeking 9 (41)

Implications

• FAM– Borgatti and Cross argue that the more complex the interaction,

the more likely that trust, knowledge, and experience are associated with the interactions.

– These data support that for the FAM network, where there seems to be some entailment of relations

• Nonprofit Organizational Behavior– Suggest a change in nonprofit culture

• Supported by qualitative research, other reporting, and in other fields (community development)

– Similar to for-profit behavior• Organization Theory

– The two sectors have normally been considered different– May be time to re-evaluate the relevance of organizational

theory

Extensions

• Continue refining indicator and method• Adjust constraints to allow for diagonals or valued

data to be considered• Investigate entailment chains in different ways• Investigate organizational behavior in other

industries• Consider possible sources for changing nonprofit

behaviors• Explore relevance of for-profit organizational

theory for nonprofit applications