The networked role of intermediaries in education governance and public-private partnership

Figures & data

Figure 1. Directing and representing intermediaries.

Note: In both figures, B is the intermediary actor. A is the macro-level actor and C are the micro-level actors.

Figure 2. Blank network showing actor groups by level and sector.

Notes: Figure shows the actors and potential relations in the network to clarify actors groups’ level and sector. The three vertical levels show the macro level (federal government), intermediary level (regional governments and employers’ associations), and micro level (schools and firms). Horizontally, the left-side actor groups belong to the public sector (federal and regional governments, schools) and the right-side actor groups belong to the private sector (employers’ associations and firms). Dotted lines show where we expect to find relations in the network, including within-group relations shown as outlines around each actor group.

Table 1. Respondents by actor group.

Actor	Respondents
Federal Government	55
Regional Government	33
Employers’ Associations	267
Firms	1,593
Schools	138
Total	2,086

Table 2. Data and method for each research question and hypothesis.

Question	1: How do we evaluate education governance networks?		2: How do intermediaries operate in education governance networks, especially those that connect the public and private sectors?
Hypothesis	1A: Balance	1B: Fairness	2A: Public sector directing intermediaries	2B: Private sector representing intermediaries
Data	Satisfaction scores	Lindahl outcomes	Relation intensity, share of given actor group reporting relation	Relation intensity, share of given actor group reporting relation
Method	Blocked adjacency matrix	Regression of eigenvalues on relation load	Relation loads	Relation loads

Table 3. Adjacency matrix showing the percent of adjacency among pairs.

		Originator					Receiving Mean
		FedGov	RegGov	EmpAssn	Firm	School
Receiver	FedGov	67%*	57%	50%	17%	48%	48%
	RegGov	56%	64%	46%	40%	56%	52%
	EmpAssn	47%	82%	71%	57%	72%	66%
	Firm	24%	46%	42%	35%	52%	40%
	School	47%	57%	64%	84%	75%	65%
Originating Mean		48%	61%	55%	47%	61%
Overall Mean**		46%	56%	59%	44%	62%

*Percentages match the Incidence numbers from Table 1A.

**Overall mean is equal to degree centrality, and does not double-count loops.

Figure 3. Actor-level network with relation strength and satisfaction.

Notes: Line thickness represents relation load, and color is satisfaction according to the scale shown in the top-right corner. Relations flow in the direction that arrows indicate. Within-group relations are shown as outlines around each actor group. On the vertical axis, we show actor levels, with the federal government at the macro level, our intermediaries at the middle level, and schools and firms occupying the micro level. The horizontal axis differentiates the public (left) and private (right) sectors.

Table 4. Blocked matrix of satisfaction and relation load by sector.

		Originating Actor
		Public	Private
Receiving Actor	Public	Satisfaction = 3.94	Satisfaction = 3.77*
	Private	Satisfaction = 4.00	Satisfaction = 3.92

Notes: Public-sector actors include the federal and regional governments, plus schools. Private-sector actors include employers’ associations and firms. Satisfaction is reported on a 1-to-5-point Likert scale. Relation load is reported relation intensity multiplied by the percentage of originating actors reporting the relationship and is on a 0-to-5 scale. * Stands for statistical significance at p<0.05..

Table 5. Table of actors’ eigenvalues, investment in the network, and residuals.

	FedGov	RegGov	EmpAsn	Firm	School
Eigenvalues	0.26	0.62	0.43	0.25	0.55
Investment*	1.49	2.33	1.87	1.40	2.10
Residuals (OLS)**	0.033	0.026	0.004	−0.027	−0.036

*Investment is mean of each actor’s relation load in out-directed relations.

**Residual standard error is 0.036 on 3 degrees of freedom, so no residual is significant. R² = 0.9938..

Figure 4. Hypothesized (above) vs. observed (below) intermediary behavior.

Notes: Figure shows hypothesized intermediary roles in the upper half and observed roles in the lower half. A is the macro-level actor, B is the intermediary, and C are micro-level actors.

Table A1. Network summary.

Pair	From	To	Intensity^4	Satisfaction^5	Incidence^6	Relation Load^7
1&1	FedGov^1	FedGov	2.78	3.76	66.67%	1.85
1&2	FedGov	RegGov	2.60	3.44	55.56%	1.44
1&3	FedGov	EmpAssn	3.21	3.67	46.67%	1.50
1&4	FedGov	Firm	3.82	4.36	24.44%	0.93
1&5	FedGov	School	3.67	4.14	46.67%	1.71
2&1	RegGov^2	FedGov	2.79	3.68	57.14%	1.59
2&2	RegGov	RegGov	3.61	4.15	64.29%	2.32
2&3	RegGov	EmpAssn	3.80	3.91	82.14%	3.12
2&4	RegGov	Firm	4.54	4.00	46.43%	2.10
2&5	RegGov	School	4.38	4.56	57.14%	2.50
3&1	EmpAssn^3	FedGov	2.87	3.58	50.00%	1.43
3&2	EmpAssn	RegGov	2.61	3.46	46.40%	1.20
3&3	EmpAssn	EmpAssn	3.49	3.93	70.72%	2.46
3&4	EmpAssn	Firm	4.21	4.21	42.34%	1.78
3&5	EmpAssn	School	3.82	3.98	64.41%	2.46
4&1	Firm	FedGov	1.98	3.45	16.97%	0.33
4&2	Firm	RegGov	2.42	3.55	40.05%	0.97
4&3	Firm	EmpAssn	3.03	3.82	57.34%	1.73
4&4	Firm	Firm	3.45	4.03	35.47%	1.22
4&5	Firm	School	3.25	3.95	84.17%	2.73
5&1	School	FedGov	2.24	3.51	47.62%	1.06
5&2	School	RegGov	2.75	3.64	56.35%	1.54
5&3	School	EmpAssn	3.55	3.88	72.22%	2.56
5&4	School	Firm	4.08	4.23	52.38%	2.13
5&5	School	School	4.26	4.47	74.60%	3.17

^aFedGov is Federal Government.

^bRegGov is Regional Government, or Cantonal governments in the Swiss context.

^cEmpAssn is Employer Association.

^dIntensity is how much actors work together as reported by the ‘from’ partner on a 1-to-5-point Likert scale.

^eSatisfaction is average satisfaction reported by the ‘from’ partner on a 1-to-5-point Likert scale.

^fIncidence is the percentage of all unique ‘from’ actors reporting a relation with the ‘to’ actor.

^gRelation load is the product of intensity and incidence on a 0-to-5 scale.