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Chapter 14
Knowledge Sharing in Organizations:
A Multilevel Network Analysis
Paola Zappa and Alessandro Lomi
Introduction
Social networks and the multiple roles that they play in organizations have received
increasing attention over the last decades (Borgatti and Foster 2003; Brass et al.
2004). The general argument is that social networks represent both conduits
through which material and symbolic resources flow within organizations, as well
as signals of the underlying hard-to-observe qualities of organizational members
connected by social relations (Podolny 2001). The presence and absence of ties
between organizational members has been systematically associated to important
interpersonal differences in outcomes like productivity (Reagans and Zuckerman
2001), resources (Podolny and Baron 1997), reputation (Kilduff and Krackhardt
1994), status (Lomi and Torló 2014), power (Brass and Burkhardt 1993), and
autonomy (Burt 1992).
The extensive literature on organizational social networks builds on the convic-
tion that organizations are meaningful settings for studying social relations. But
considering organizations as settings for studying social networks has far-reaching
implications that have not received sufficient attention until recently (McEvily
et al. 2014). Organizations are first and foremost hierarchical social systems with
multiple and partially nested levels of action (March and Simon 1958;Simon1996).
Perhaps the most obvious implication of adopting organizations as settings for
studying social networks is that hierarchical elements shape the interaction among
organizational members within, but also across structural layers.
Organizations typically consist of individuals nested within a variety of social
aggregates such as, for example, teams, functions, departments or subsidiaries.
P. Zappa ()•A.Lomi
Social Network Analysis Research Center, Faculty of Economics, University of Italian
Switzerland, Via G. Buffi, 13, 6904 Lugano, Switzerland
e-mail: paola.zappa@usi.ch
© Springer International Publishing Switzerland 2016
E. Lazega, T.A.B. Snijders (eds.), Multilevel Network Analysis for the Social
Sciences, Methodos Series 12, DOI 10.1007/978-3-319-24520-1_14
333
emmanuel.lazega@sciences-po.fr
334 P. Zappa and A. Lomi
Organizational members are connected to one another within and across the
boundaries of these aggregates by a variety of mandated (or “formal”) and emergent
(or “informal”) relations. Such relations are rarely independent of one another. For
this reason, it is important to assess the influence that the structure of relations at
one level exerts on the structure of relations at another level (Moliterno and Mahony
2011).
Obvious as this statement may be, virtually no study of intra-organizational
networks is available that takes into account the multilevel formal structures
providing the foci for the development of social relations in organizations (McEvily
et al. 2014). This is surprising because one of the main promises of network
approaches to organizations is to capture connections across multiple structural
levels.
As Contractor, Wasserman, and Faust aptly observe (2006: 684):
[O]ne of the key advantages of a network perspective is the ability to collect, collate, and
study data at various levels of analysis ( :::). However, for the purposes of analyses most
network data are either transformed to a single level of analysis ( :::) which necessarily
loses some of the richness in the data, or are analyzed separately at different levels of
analysis thus precluding direct comparisons of theoretical influences at different levels.
The network perspective that Contractor et al. (2006) advocate involves direct
modeling of tie variables and explicit development of hypotheses about how such
variables may be affected by multilevel network dependences. Contractor et al.
(2006) suggest adoption of the Exponential Random Graph (ERGM) class of models
(a.k.a. p-star – or p* models) as a potential solution to the problem of modeling
multilevel networks. This modeling approach has since been developed into a
comprehensive analytical framework for the analysis of multilevel networks (Wang
et al. 2013). In this paper we show how recently derived ERGMs for multilevel
networks (Multilevel ERGMs or MERGMs) may be adopted for analyzing networks
in organizational settings. We think that the flexibility of this framework provides
the basis for the development of novel insights on social networks in organizations.
The objective of this paper is to illustrate some of the benefits of understanding
formal organizations as multilevel network systems by examining the interdepen-
dence between formal and social interaction in organizations. We show how such an
approach supports a more informative and contextually richer representation of the
interdependences between formal and informal relations in organizations.
We document the existence, complexity, and context-dependence of the rela-
tionships linking informal networks between lower-level actors (individuals in
the case that we will be presenting) to formal networks between higher-level
actors (subsidiary units in our case) in organizations. We argue that ignoring the
formal relations existing between higher-level units may lead to overestimating the
autonomy of social networks from the formal authority structure existing within
organizations. Because authority relations cross-cut organizational levels, this issue
cannot be fully addressed in studies of social networks within organizations
conducted at a single level.
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14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 335
We argue that the unique value of the most recent generation of MERGMs is to
turn this problem into empirically testable hypotheses. Hence, adopting this method-
ological approach allows us to learn more about how both social as well as structural
conditions affect the likelihood that network ties cross-cut formal organizational
boundaries. This is important because research on social networks conducted at a
single level is incapable of establishing the autonomy of network ties with respect
to formal organizational structure. This is a particularly notable weakness in current
organizational research on the role that boundary-spanning ties play in a variety
of important organizational outcomes such as, for example, knowledge transfer
(Hansen 2002), innovation (Hargadon and Sutton 1997), generation of new ideas
(Burt 2004), and organizational performance (Argote and Ingram 2000).
Using field data that we have collected on communication and advice relations
among the 47 members of a top management team within an international multiunit
industrial group we show how this weakness may be addressed. We reconstruct
the complete network of hierarchical reporting relations defined among managers
within and across the subsidiary companies of the corporate group. The resulting
structure defines a multilevel network in which the lower-level units (individual
managers) are linked by interpersonal communication and advice relationships, and
the higher-level units (subsidiary units) are linked by formal reporting relations.
The two levels are linked by a bipartite relationship that affiliates individual
managers to subsidiary units. We exploit the natural multilevel structure of social
networks within organizations to specify and estimate MERGMs for different intra-
organizational networks (advice and communication). We show that the effects of
the formal structure on social networks are contingent upon the specific kind of
network that is being considered.
After this general introduction, we organize the chapter as follows. In the
next section we discuss the general background of our work and introduce the
problem of knowledge transfer and sharing in organizations. We state the main
questions that our study addresses. In section “Models for Multilevel Networks”we
briefly summarize our analytical strategy based on MERGMs. Section “Empirical
Illustration” describes data and model specifications. Section “Results” contains the
empirical results. Section “Discussion and Conclusions” concludes the paper by
framing the results in the context of current research on organizational networks.
General Background and Questions
Organizations as Multilevel Network Systems
One of the main motivations for analyzing social networks has been to provide a
theoretical framework for examining relations at various structural levels of action
(White et al. 1976). Among the many substantive contexts for the analysis of social
networks, organizations provide perhaps the clearest illustration of the need to
emmanuel.lazega@sciences-po.fr
336 P. Zappa and A. Lomi
consider how action may – or may not – be connected across structural levels.
Because organizations are multilevel hierarchical objects (Simon 1962), questions
about how social networks link action across levels are central to our understanding
of how organizationsactually work. In organizations, for example,network relations
may link individuals across departments, teams, functions or subsidiaries (Borgatti
and Foster 2003).
Building explicitly on Breiger’s classic insight (1974), Brass et al. (2004:
801) clearly recognize multilevel networks in organizations as an unavoidable
consequence of interpersonal relations cross-cutting the formal boundaries because:
Ties between people in different units [ :::] create ties between organizational units,
illustrating the “duality” of groups and individuals (Breiger 1974). When two individuals
interact, they not only represent an interpersonal tie, but they also represent the groups of
which they are members. Thus, interunit ties are often a function of interpersonal ties.
Less commonly recognized is that “interpersonal ties” may be just as easily
the consequence of interunit ties – thus inducing a multilevel network structure.
Interunit ties may be determined by technology through the workflow (Thompson
1967), or by formal relations that define the organizational hierarchy in terms of
dependence between individuals within and across subunits (Perrow 1970;Pfeffer
1981). Most available studies have analyzed networks observed at different levels
separately, typically ignoring the possible existence of dependences across levels.
The combination between the affiliation of organizational members (lower-level
actors) to departments, teams, functions or subsidiaries (higher-level actors), and the
existence of social relations among organizational members as well as of a formal
structure among aggregate units, implies that organizations are hierarchical systems
of nested relations – i.e., multilevel network systems – almost by construction.
This claim has far-reaching consequences because the autonomy of social networks
between organizational members cannot be established without accounting for the
powerful effects of ties between organizational subunits defined at a higher level
of analysis. Because in organizations lower-level actors are hierarchically nested
within higher-level actors, lower-level (interpersonal) ties may be embedded in
higher-level (interunit) ties. If this is the case, the structure of relations observed
at one level is likely to affect the structure of relations observed at another (typically
lower) level (Moliterno and Mahony 2011). In this perspective, interpersonal ties
derive from the exercise of “discretion with constraints” (Kleinbaum et al. 2013)–
i.e. they are affected by the multiple social foci that organizations offer to their
members (Lomi et al. 2014).
Organizational research has only recently started recognizing the multilevel
network nature of organizations that these considerations imply (Baum and Ingram
2002;Brass2000; Brass et al. 2004;Ohetal.2006). Interest in multilevel
networks arises from the promise of a more realistic representation of important
organizational outcomes, such as, for example, coordination, identity construction,
and learning (Kogut and Zander 1996). Accounting for dependences across levels
would provide a better assessment of the actual autonomy and differential value
of social networks in organizations. It would be possible, in particular, to detect
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14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 337
whether and how interpersonal relations in organizations are shaped by (I) the joint
membership of participants in aggregate units, and (II) the presence of relations
between units.
Until relatively recent times, the implications of dependences across network
levels have not been explicitly articulated. This is partly due to the lack of
suitable methods for dealing with the complex multilevel network structures that
are involved. Most of the available empirical studies have treated organizational
structure as an attribute of individuals rather than as a distinct level of action. As
a consequence, fundamental questions about the relations between network ties
connecting units defined at different levels could not even be asked. As we discuss
in the next section, our relatively primitive understanding of these multilevel issues
severely limits our current understanding of how social networks in organizations
actually work. Equally important is the fact that our limited ability to represent
and analyze multilevel networks in organizations casts doubt on some of the most
influential results produced by decades of organizational research on knowledge-
sharing and knowledge-transfer processes.
Social Networks and Organizational Structure
Understanding multilevel network mechanisms is of direct relevance to the conspic-
uous and influential body of research on learning, knowledgesharing and knowledge
transfer within organizations accumulated during the last quarter of century (Argote
et al. 1990; Argote and Ingram 2000;Hansen2002; Tortoriello et al. 2012).
This literature has argued – and repeatedly shown – that networks of informal
interaction represent the main conduits through which knowledge flows within
organizations (Krackhardt and Hanson 1993). Informal relations based on com-
munication and advice seeking can allow organizational members to sample the
experience of distant others, and bring new solutions, practices, and ideas to bear
on local problems. These knowledge transfer relations, embedded in informal social
networks that cross-cut formal organizational boundaries, promote organizational
learning – i.e., processes through which organizations create, disseminate and
exploit knowledge (Kogut and Zander 1996; March and Simon 1958;Simon1991).
More specifically, informal relationships focused on advice and communication
allow organizational participants to access sets of distant others, and hence reach
heterogeneous knowledge resources that are not locally available (Reagan and
McEvily 2003) – and that may be otherwise difficult to mobilize, understand and
integrate across formal boundaries (Nonaka 1994).
The connection that social networks create between different knowledge pools
separated by formal subunits seems to be the main mechanism behind the recurrent
observation that diversity of information sources is systematically linked to organi-
zational innovation (Beckman et al. 2004;Burt2004). To the best of our knowledge,
however, no study is available that has established the autonomy of emergent social
emmanuel.lazega@sciences-po.fr
338 P. Zappa and A. Lomi
ties of interpersonal knowledge exchange from the mandated hierarchical relations
defining a formal organizational structure.
For the reasons that we have identified in the prior section, the multilevel
nature of social networks in organizations suggests that the independence between
emergent social ties and formal structure would be more usefully framed as a
hypothesis to be tested, rather than as an assumption to be maintained. What is
at stake in such a test would be the value, interpretation, and ultimate meaning of
social networks in organizations as they have been studied so far. If informal social
relations connecting individuals across intra-organizational boundaries depend on
the presence of formally mandated relations existing between the subunits in
which individuals are contained, then the knowledge-transfer properties that current
research assigns to organizational networks could turn out to be spurious in
specific settings or contextual conditions. Once formal hierarchical relations among
organizational subunits are accounted for, the extent to which social networks
between individuals across subunits can still be observed becomes an open question
that begs empirical investigation.
Social relations among organizational members may be affected by formal
hierarchical relations existing among organizational subunits in at least two ways.
The first involves a generalization of the transactive memory argument (Ren et al.
2006). By virtue of being in subunits that are more central, prominent or critical,
organizational members may be both more visible, as well as more aware of the
overall distribution of knowledge resources in the organization (Ren and Argote
2011). More generally, members in subunits with differential standing may more
easily attract deference relations across boundaries (such as, for example, requests
for advice), and generate additional opportunities for establishing crosscutting
communication relations. The joint effect of visibility and awareness provided
by “being in the right place” (Brass 1984) is a higher level of “popularity”
and “activity” of organizational participants located in prominent subunits. These
multilevel network effects are likely to be a sort of “basking in the reflected glory”
effect determined by affiliation to prominent subunits or groups within organizations
(Cialdini et al. 1976).
The second way in which formal relations may affect social relations involves
an extensive interpretation of the social foci argument (Feld 1981). Social relations
between individuals are likely to be affected by the presence of formal hierarchical
relations between organizational subunits to the extent that hierarchical relations
provide a social focus for the development of interpersonal network ties where:
“A social focus is defined as a social, psychological, legal or physical entity
around which joint activities are organized” (Feld 1981: 1016). Formal hierarchical
relations existing between subunits possess all the defining features of a social focus
present in Feld’s definition. Because “individuals whose activities are organized
around the same focus will tend to become interpersonally tied and form a cluster”
(Feld 1981: 1016), relations of hierarchical subordination existing among subunits
will tend to generate connection between participants across subunits (Lomi et al.
2014). As in the first case discussed, relations between subunits affect relations
between participants across subunits via clearly identifiable multilevel network
mechanisms.
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14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 339
The argument we have developed so far may be summarized in terms of a
basic multilevel question: How, exactly, does the presence of mandated hierarchical
relations between organizational subunits affect the presence of network ties
connecting organizational members across subunits? To the extent that hierarchical
relations among subunits provide the focus for the development of social relations
among individuals, then a default expectation would be that informal interaction
among individuals aligns to prescribed hierarchical relations among organizational
subunits. If this is the case, we should expect to see cross-cutting network ties
connecting organizational members who belong to subunits that are themselves
connected by relations of hierarchical subordination. Does this expectation hold
independently of the kind of network relation that connects individuals across
subunits? This question is important because the effect of the formal structure
may be contingent on the kind of relation that organizational members develop.
This would suggest that the autonomy of informal social relations from mandated
hierarchical relations varies across network settings.
Motivated by these basic questions, in the next section we outline Multilevel
Exponential Random Graph Models as one possible analytical strategy that may
assist in addressing these questions.
Models for Multilevel Networks
The specific forms of interdependences between levels that we have discussed may
be assessed by directly specifying Multilevel Exponential Random Graph Models
(Wang et al. 2013,2015) (MERGMs henceforth). MERGMs are a new class of
ERGMs specifically designed for modeling multilevel network data. MERGMs are
currently the only method that allows for explicit assessments of specific forms of
network interdependences across levels.
Let MD[A,X,B] denote the network variable for a two-level network, and m
D[a,x,b] the corresponding realizations. Mincludes a network AD[Ahl]of size
urepresenting a relation among a set Uof higher-level actors hD1, :::,l,:::u
nodes in U; a network BD[Bij ]which represents a relation among a set Vof lower
level actors with iD1, :::,j,:::vnodes in V; and a two-mode network XD[Xih]
representing the affiliation of ito h. Let, finally, YD[YA,Y
B]denote the set of
attributes for actors of levels Aand B,andyD[yA,y
B]their realizations.
MERGMs are specified as follows:
Pr .MDmjYDy/D1
expXQ˚aQZT
Q.m/CQZT
Q.m;y/(12.1)
•Mis the set of all possible multilevel networks of size (uv)andmis the
observed network.
•Yis a set of vectors of individual- and subunit-specific characteristics and yis the
observed set.
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340 P. Zappa and A. Lomi
•Qrepresents a potential network configuration. The summation †is over all
different configurations included in the model.
•ZQ.m/DXmYMij2Q
mij are structural network statistics corresponding to
configuration Q. These statistics involve network tie variables only and count,
for each actor in the network, the number of configurations or effects of each
type in which the actor is involved.
•aQis the vector of parameters corresponding to the structural effects ZQ(m).
•ZQ.m;y/DXmYMij2Q
mijyiis the vector of attribute configurations or effects –
i.e., statistics which account for the interaction between network tie variables and
nodal attribute covariates.
•Qis the vector of parameters corresponding to the attribute effects ZQ(m,y).
•is a normalizing constant included to ensure that (12.1) is a proper probability
distribution.
Equation (12.1) describes a general probability distribution of networks and
assumes that the probability of observing the empirical multilevel network structure
depends on a small set of configurations. MERGMs parameterize a number of
configurations. A first class involves the standard ERGM effects that model each
network separately (Robins et al. 2009; Snijders et al. 2006). A second class consists
of the effects that account for the interdependence between two or three networks
(Wang et al. 2013,2015). We introduce these classes of configurations below,
situating them within our empirical exercise.
Empirical Illustration
Data
The data used in the empirical part of the paper contain information on knowledge-
sharing relations among members of the top management team in an international
multiunit industrial group active in the design, manufacturing and sale of leisure
motor yachts (Lomi et al. 2014). The group consists of five subsidiary units and a
small team of consultants. For the sake of clarity, in the remainder of the paper we
refer to subsidiary units and to the team of consultants as “subunits.” The subunits
act as quasi-independent companies. Each subunit has its own product line, target
market segment, customer base, dealer network, management, and organizational
and brand identities. Hence, each occupies an almost completely distinct market
niche. This context makes subunits unlikely to compete with one another and
promotes collaboration and communication among them. In particular, coordination
within the group and collaboration across the boundaries of subsidiaries are crucial.
Boundary-spanning interaction allows organizational members to share information
on technical solutions, and on potential customers or competitors collected through
the global dealers’ network. Likewise, innovative technological and management
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14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 341
solutions developed in one subunit may have implications for others. For these
reasons, organizational members – especially those working in the same functional
areas, but in different subsidiaries – are highly encouraged to cooperate and
coordinate their actions.
We examined interaction in the context of communication and advice relations
among the 47 members of the group’s top management team as identified by the
group CEO. We also included in the list a team of five consultants, because of their
direct and personal relations with the president-founder of the group and because
of their crucial role in boat design. Each member was unambiguously and uniquely
assigned to one subunit.
We administered a questionnaire individually and personally to each member
of the top-management team. The questionnaire was used to collect relational
information as well as individual characteristics of the organizational members. A
member of the research team was always present to offer assistance and to ensure
that the data collected were as accurate and complete as possible. This allowed us
to obtain a 100 % response rate.
We examined relations of task advice and work-related communication because
these contents are directly relevant for intra-organizational knowledge transfer. The
advice relation captures problem-driven interaction. We selected advice relations
because extensive evidence indicates that they support meaningful knowledge
sharing within organizations (Cross et al. 2001; Lazega 2001). Professional and
work-related communication relations better represent routine interaction among the
managers. We included communication relations because we also wanted to capture
channels for intra-organizational knowledge flow that are activated less episodically.
Interpersonal interaction was reconstructed by presenting each manager with
the list containing the names of the other 46 managers in the team. To convert
answers into a multilevel network structure, we assumed for both relationships that
the generic cell bij D1 if manager inominates jas a partner respectively for advice
seeking (network B1) and communication (network B2) on work related matters. B1
and B2are both lower-level networks and are sized (47 47). Table 14.1 reports the
main descriptive statistics for the two interpersonal networks.
Hierarchical relations between subsidiaries were reconstructed by using infor-
mation on the formal reporting relations among members of the top management
Table 14.1 Network descriptive for interpersonal networks
Va r i a b l e Advice network Communication network
Density 0.229 0.076
Average degree 10.553 3.489
Degree standard deviation 7.015 (in); 8.395 (out) 1.852 (in); 2.653 (out)
Degree skewness 1.113 (in); 1.736 (out) 0.195 (in); 0.689 (out)
Reciprocity 0.341 0.505
GCC transitive closure 0.469 0.494
GCC cyclic closure 0.357 0.420
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342 P. Zappa and A. Lomi
team. We interviewed the corporate CEO and asked him to indicate “who reports
to whom.” We provided him with the names of the 47 participants arranged in the
rows and in the columns of a square matrix. We asked him to indicate whenever the
column person reported to the row person. For example,we assumed that the generic
cell aij D1 if the “Chief engineer” (column) jin subsidiary kreported to the “Chief
Corporate Engineer” (row) iin subsidiary l. In this case iwould be hierarchically
superior to i(ij). We used the information on systematic reporting relations between
managers to generate matrix A– the matrix of formal relations between the
subsidiaries. The higher-level (reporting) network between the subsidiaries will be
network A, sized (6 6): the generic cell alk D1 if subsidiary lis hierarchically
superior to subsidiary k, i.e., if there is at least one manager jin kreporting to a
manager iin l.
Finally, an affiliation network represents top-managers’ affiliation to companies.
The generic cell xil D1 if manager ibelongs to subsidiary l. According to the
notation that we have introduced this is network X, sized (47 6). Figure 14.1
displays symbolically the complete multilevel network structure.
We also collected actor-specific attributes and used them to construct the
control variables incorporated in our empirical model specifications. These variables
account for interpersonal differences that may affect the likelihood of observ-
ing network ties. We collected socio-demographic (nationality) and work-related
(organizational function and job grade) attributes for managers and organizational
characteristics (size) for subunits.
Figure 14.2 displays the empirical multilevel network for communication rela-
tions. The figure clearly points to the coexistence of communication ties between
managers who are affiliated to the same subunits and ties between managers who
Fig. 14.1 Multilevel network. Circles are managers and squares are subunits. Dashed black links
are (hierarchical) subordination ties between pairs of subunits (network A). Grey links are affiliation
ties of managers to subunits (network X). Dotted black links are advice ties (network B1)andblack
links are communication ties (network B2) between managers
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14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 343
Fig. 14.2 Multilevel network for communication relations. Circles are managers and squares
are subunits. Dashed black links are (hierarchical) subordination ties between pairs of subunits
(network A). Grey links are affiliation ties of managers to subunits (network X). Black links are
communication ties (network B2) between managers
are members in different subunits. The average manager degree is 3.02 for within
subunit ties, and 0.47 for between unit ties for the communication relation, and 4.87
and 5.68 for the advice relationships.
In the analysis that follows, we compare the effects of hierarchical relations
between subunits on advice seeking and on communication relations between
managers separately.
Model Specification and Estimation
In formal organizations, neither the affiliations nor the organizational structure
depend on individual or subunit choices, at least in the short-term. Change in
organization structure is likely to occur at a much slower rate than change in
informal interpersonal ties. Consequently, we considered the networks defined by
formal relations (Aand X) as exogenous and kept them fixed during the estimation
process. Our analysis focuses on interpersonal network ties.
To make the two multilevel networks (and the interpersonal relations) com-
parable, we specified the same set of effects for them both. We modeled the
multilevel networks as a combination of two kinds of configurations: (1) ERGM
effects which account for interpersonal interaction (B); (2) MERGM effects which
account for the affiliation of individuals to a subunit (interaction between Band X)
and for interdependences between the interpersonal and interunit networks through
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344 P. Zappa and A. Lomi
Table 14.2 ERGMs lower-level configurations
Effect Configuration Qualitative interpretation
Density Tendency of managers to build ties with colleagues
Reciprocity Tendency of managers to build ties with
reciprocating colleagues
Activity spread Tendency of managers to be active – i.e., to send
ties to many colleagues
Popularity spread Tendency of managers to be popular – i.e., to
receive ties from many colleagues
2-paths Basic tendency of managers to send ties to and to
receive ties from colleagues
Transitive closure Tendency of managers to build ties with colleagues
of colleagues
Cyclic closure Tendency of managers to build ties with colleagues
in small groups without any expectation of being
reciprocated
Multiple
two-paths
Tendency of managers against interaction within
small groups of colleagues
Covariate match Tendency of managers to build ties with colleagues
with same covariate value
Circles are managers and black links are informal (communication or advice) ties between pairs of
individuals. Black is a manager with a relevant attribute
affiliation (interaction among A, B and X). We distinguished between structural and
attribute effects for both kinds of configurations.
We start our discussion commenting on the ERGM effects used to model the
interpersonal network (Table 14.2). We included Density to account for the baseline
tendency of managers toward interacting with others. Since maintaining several
ties is costly, the Density parameter usually carries a negative sign. We specified
Reciprocity to verify the likelihood that interpersonal ties are reciprocated.With
Popularity and Activity spread we modeled the degree distributions and captured
the tendency toward the existence of “hubs”.
Closure configurations verify the propensity toward network clustering. In the
context of intra-organizational relations of knowledge transfer, closure also captures
embeddedness and redundancy of information. We tested closure specifying two
effects, Transitive closure and Cyclic closure, the most common closure configura-
tions. The former models the likelihood that managers interact with one another
if they share several partners. The latter accounts for generalized exchange of
knowledge – i.e., for knowledge exchange without bounds of reciprocity (Breiger
and Ennis 1997; Lazega and Pattison 1999). As a control, we added Multiple two-
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14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 345
paths configuration, accounting for the correlation between in- and out-degree and
suggesting whether the same people are senders and receivers of ties. Multiple two-
paths captures also tendency against closure.
Finally, the Covariate match effect accounts for the likelihood that managers
interact informally with similar others. We controlled for homophily in respect to
nationality, job grade, and organizational function.
The second class of effects consists of MERGM configurations modeling inter-
dependencies between the lower- and higher-level network structures linked through
affiliation (Wang et al. 2013,2015)(seeTable14.3). These configurations account
for progressively more complex effects of the formal organizational structure on
interpersonal interaction. Affiliation based closure arc tests homophily based on a
shared affiliation (Contractor et al. 2006; Monge and Contractor 2001). Showing
that managers are more likely to interact with colleagues who are members of
the same subunit, this effect indicates that knowledge transfer tends to occur
more within subunit boundaries. Also, Affiliation based closure arc suggests that
interaction is shaped by a local hierarchical ordering, with interpersonal ties in one
direction only.
Cross-level in-degree and out-degree assortativity effects test the association
between centrality across levels. These effects represent the tendency for popu-
lar/active people to be affiliated to popular/active subunits and can be interpreted
as the MERGM formalization of the structural linked design (Lazega et al. 2008). A
positive parameter of these effects would suggest that the centrality of managers
in interpersonal interaction is mainly due to the position of their subunit in the
hierarchical interunit structure. Hence, these effects would point to a “sidestepped”
role of the individual.
Cross-level alignment effects account for cross-level mirroring or overlap such
that members of connected groups are themselves connected. In the context of
knowledge sharing, a positive parameter of these effects would indicate that
interpersonal knowledge transfer is sustained by interunit formal ties. We specified
three effects that account for a different kind of dependence of interpersonal ties
on interunit ties. Cross-level alignment entrainment assumes that interunit and
interpersonal ties have the same direction. The qualitative interpretation of such
an effect is that interpersonal interaction is shaped by a hierarchical ordering due
to interunit ties – i.e., managers are likely to seek information from colleagues who
are members in hierarchically subordinate subunits. Cross-level alignment exchange
accounts for the opposite effect. It assumes that interpersonal and interunit ties have
opposite directionality, so that managers seek information from colleagues who
are members in hierarchically superior subunits. Cross-level alignment exchange
reciprocal B, finally, indicates that managers are likely to build reciprocal ties
with colleagues who are members in other subsidiaries, connected to theirs by
hierarchical dependence. Interpersonal interaction, then, enables a reduction in the
hierarchical distance between managers due to the formal interunit structure.
Finally, we included the association between interunit and interpersonal ties
due to control subunit and manager covariates. Similar to the baseline Covariate
match effect specified for the interpersonal network, Cross-level alignment Covari-
emmanuel.lazega@sciences-po.fr
346 P. Zappa and A. Lomi
Table 14.3 MERGMs higher-level configurations
Effect Configuration Qualitative interpretation
Affiliation based
closure
Tendency of managers to build ties with colleagues
based on common membership in subunits
Cross-level
in-degree
assortativity
Tendency of popular managers in interpersonal
network to be affiliated to popular (i.e., hierarchically
subordinate) subunits in interunit network
Cross-level
out-degree
assortativity
Tendency of active managers in the interpersonal
network to be members in active (i.e., hierarchically
superordinate) subunits in interunit network
Cross-level
alignment
entrainment
Tendency of managers to build ties with colleagues
members in subunits hierarchically subordinate to their
subunit
Cross-level
alignment
Exchange
Tendency of managers to build ties with colleagues
members in subunits hierarchically superordinate to
their subunit
Cross-level
alignment
exchange
reciprocal B
Tendency of managers to build ties with reciprocating
colleagues members in hierarchically linked subunits
Cross-level a.entr.
unit covariate
match
Tendency of managers members in subunits with a
given covariate value to build ties with colleagues
members in hierarchically sub-ordinate subunits with
same covariate value
Cross-level a.
exch. unit
covariate match
Tendency of managers members in subunits with a
given covariate value to build ties with colleagues
members in hierarchically super-ordinate subunits with
same covariate value
Cross-level a.entr.
individual
covariate match
Tendency of managers with a given covariate value to
build ties with colleagues with the same covariate value
and members in hierarchically subordinate subunits
Cross-level a.
exch. individual
covariate match
Tendency of managers with a given covariate value to
build ties with colleagues with same covariate value
and members in hierarchically superordinate subunits
Cross-level a.
exch. reciprocal B
individual
covariate match
Tendency of managers with a covariate value to build
ties with reciprocating colleagues with same covariate
value and members in hierarchically linked subunits
Squares are subunits. Dashed black links are (hierarchical) subordination relationship ties
between pairs of subunits. Grey links are affiliation ties of managers to subunits. Black are
managers/subunits with a relevant attribute
ate match tests whether managers’ propensity toward seeking information from
colleagues affiliated to connected subunits increases when managers or subunits
have similar characteristics. Specifying Cross-level alignment entrainment and
exchange Covariate match for subunit size, we assessed manager propensity toward
emmanuel.lazega@sciences-po.fr
14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 347
building ties with colleagues affiliated to hierarchically dependent subunits, when
the subunits employ around the same number of managers – a fairly obvious effect.
Cross-level alignment entrainment,exchange and exchange reciprocal B Covari-
ate match for managers’ job grades and organizational functions verify whether the
same tendency is higher when managers have similar work-related characteristics.
Results
We organize the discussion of our results around Table 14.4, which reports the
estimates of a MERGM for the interdependence between interpersonal (advice,
communication), and interunit relations. The comparison of the configuration
parameters between the two multilevel networks reveals similar tendencies. The Arc
parameter carries a negative sign, as it is typically the case in empirical networks,
thus outlining the existence of a ceiling effect to establishing interpersonal ties.
Also, the tendencies toward reciprocating ties (significantly positive Reciprocity
effect) and interacting in small hierarchical groups – as indicated by the combination
of a positive Transitive and a negative Cyclic closure – are the main relational
behaviors that characterize both advice and communication networks. The tendency
toward closure is enforced by the negative Multiple two-paths, suggesting that
triangles are unlikely to remain open. Also, both networks are shaped by a
propensity toward seeking information from managers with the same nationality
(significantly positive Nationality match). By contrast, the degree-related effects
indicate the convergence of ties toward few managers in the advice network only. In
particular, the significantly positive Activity spread (the tendency of the out-degree
distribution to be skewed) points to the presence of a few managers who rely on
many colleagues as sources of advice, thus diversifying their range of available
knowledge.
The parameters of several higher-level configurations are significant, suggesting
an association between information sharing among managers and the formal inter-
unit structure. The Affiliation based closure arc is significantly positive for both
relations, showing that they are affected by a positive tendency toward interacting
with colleagues within the same subunit. This result captures the well-known
tendency of organizational subunits to retain both ties and information within their
boundaries (Reagans and McEvily 2003).
Cross-level in-degree assortativity is significantly positive for the communication
network only. This configuration captures the first class of theoretical mechanisms –
i.e., association between subunit and manager centrality in their own network. The
positive parameter value indicates that managers who are more popular and sought
after by colleagues in day-to-day communications are members of subunits which
are more popular and, have to report to many others in the formal network – i.e.,
hierarchically subordinate subunits. The qualitative implication of this effect is that
information is likely to flow from members of subordinate to members of superior
subunits.
emmanuel.lazega@sciences-po.fr
348 P. Zappa and A. Lomi
Table 14.4 MERGM estimations for interdependences between interpersonal and interunit net-
works
Advice Network
estimate (st.err.)
Communication
Network estimate
(st.err.)
Interpersonal communication
Arc 7.14 (0.64)* 7.08 (1.12)*
Reciprocity 0.90 (0.28)* 2.59 (0.46)*
Popularity spread 0.02 (0.09) 0.49 (0.36)
Activity spread 0.40 (0.09)* 0.35 (0.18)
Transitive closure 1.38 (0.19)* 0.87 (0.21)*
Cyclic closure 0.26 (0.06)* 0.36 (0.16)*
Multiple two-paths 0.08 (0.02)* 0.09 (0.06)*
Grade match 0.04 (0.17)* 0.01 (0.21)
Function match 0.25 (0.22) 0.30 (0.22)
Nationality match 0.58 (0.12)* 0.85 (0.30)*
Cross-level interdependences
Affiliation based closure 1.90 (0.28)* 2.80 (0.65)*
Cross-level in-degree assortativity 0.07 (0.13) 1.08 (0.38)*
Cross-level out-degree assortativity 0.14 (0.05)* 0.15 (0.14)
Cross-level alignment, entrainment 0.68 (0.48) 0.08 (0.78)
Cross-level alignment, exchange 0.59 (0.32) 1.00 (0.95)
Cross-level alignment, reciprocal B 0.08 (0.20) 2.02 (0.84)*
Cross-level alignment, entrainment subunit size
match
0.08 (0.04)* 0.04 (0.06)
Cross-level alignment, exchange subunit size
match
0.06 (0.03)* 0.07 (0.07)
Cross-level alignment, entrainment manager
grade match
0.89 (0.47) 1.14 (1.15)
Cross-level alignment, exchange manager
grade match
0.98 (0.30)* 1.10 (1.23)
Cross-level alignment, reciprocal B manager
grade match
0.37 (0.59) 0.28 (1.92)
Cross-level alignment, entrainment manager
function match
0.08 (0.53) 2.21 (0.86)*
Cross-level alignment, exchange manager
function match
0.49 (0.40) 2.05 (1.30)
Cross-level alignment, reciprocal B manager
function match
1.45 (0.61)* 4.30 (1.92)*
*indicates that the ratio of statistic to standard error is greater than 2 (standard errors in parentheses)
The Cross-level alignment effects refer to the second class of theoretical
mechanisms – i.e., association between interunit and interpersonal ties. The positive
Cross-level alignment reciprocal B for the communication network indicates that
interunit ties are likely to be matched by reciprocal interpersonal ties between
managers affiliated to the connected subunits. That is to say, managers are likely
emmanuel.lazega@sciences-po.fr
14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 349
to establish mutual communication relationships with colleagues who are members
of subunits with which a hierarchical link already exists. Cross-level alignment
reciprocal B emphasizes that interpersonal ties cross-cutting subunit boundaries are
more likely when they are sustained by formal interunit ties. They provide managers
with opportunity to meet and share information (Kleinbaum et al. 2013). Cross-level
alignment reciprocal B, finally, underlines the importance of reciprocity as driver of
boundary spanning.
By contrast, the not significant Cross-level alignment effects for the advice
network suggest that the tendency for advice ties between managers to span subunit
boundaries is not affected by the presence of hierarchical formal ties between the
subunits in which managers are members.
The qualitative implication of the different parameter values of most Cross-
level configurations (i.e., both degree assortativity and alignment) between the two
networks is that the association of interunit and interpersonal ties – and, therefore,
boundary spanning – takes place in different ways for advice and communication
relationships. Advice relationships develop almost independently from the formal
organizational structure, while communication relations align (weakly) with it.
More precisely, in the case of advice relationships the formal organizational
structure seems to operate mostly through a matching process which involves
subunit and manager covariates. In detail, the significantly positive Cross-level
alignment entrainment and exchange subunit size match suggest that managers are
likely to seek advice from colleagues affiliated to connected subunits (thus, crossing
subunit boundaries) which have a size – and, therefore possibly a relevance within
the formal organizational structure – similar to theirs. Managers are likely to build
ties that both maintain (Cross-level alignment entrainment subunit size match)and
reverse (Cross-level alignment exchange subunit size match) the direction of inter-
unit formal ties, seeking advice from colleagues who are members respectively in
hierarchically subordinate or superior subunits.
The significantly positive Cross-level alignment exchange manager job grade
match for advice relations suggests that managers in the same job grade are more
likely to build boundary-spanning ties with colleagues affiliated to superior subunits,
thus reversing the ordering induced by the formal structure. The significantly
positive Cross-level alignment reciprocal B manager function match points to the
likelihood that managersin the same organizational functionbuild mutual boundary-
spanning ties with colleagues affiliated to connected subunits. In doing so, mutual
ties reduce the formal hierarchical ordering.
The communication network is shaped by the opposite tendency. The combi-
nation between the significantly positive Cross-level alignment entrainment and
the significantly negative Cross-level alignment reciprocal B manager function
match indicates that managers in the same organizational function are more likely
to build cross-cutting communication ties that preserve the formal hierarchical
ordering. The (weak) alignment between communication ties and formal inter-unit
ties, suggested by the positive Cross-level alignment reciprocal B is reversed by
managers’ homophily in the organizational function.
emmanuel.lazega@sciences-po.fr
350 P. Zappa and A. Lomi
Discussion and Conclusions
Interest in multilevel theories is not new in the analysis of social networks. The
recent call for multilevel network models, however, has the merit of stimulating
convergence between recent theoretical and methodological developments in the
analysis of multilevel networks. In organizational studies, a multilevel under-
standing of social networks seems to be long overdue, because organizations
are multilevel network systems almost by construction. Organizations are formal
hierarchical systems, where individual action is embedded in aggregate entities
whose interconnections are likely to affect the structure of interpersonal networks
within and across the formal boundaries that are drawn around organizational
subunits. To the best of our knowledge, no empirical study has yet derived the
full consequence of this multilevel view on organizational networks. Surprisingly,
most of the available research on networks within organizations has ignored their
multilevel structure. We have argued that this is precisely what makes organizations
interesting and instructive contexts for studying social networks.
We have offered an integrated analytical framework for assessing multilevel
network dependences explicitly, suggesting that organizations would be better
conceived as a two-level system, consisting in the combination of informal ties
between individuals, formal ties between subunits, and affiliation ties between
individuals and subunits. We have brought new Multilevel Exponential Random
Graph Models (MERGMs) to bear on the problem of understanding cross-cutting
ties within organizations. The empirical value of the analytic strategy proposed
has been documented in the context of intra-organizational knowledge-sharing and
knowledge-transfer networks, examining how knowledge-sharing relations among
individuals may cross formal boundaries defined around organizational subunits.
In particular, the paper has focused on the extent to which boundary spanning is
affected by the presence of interunit ties. Using data that we have collected on
different knowledge-sharing relationships within a multiunit organization where
subunits are linked to each other by hierarchical ties, we have drawn attention to
various multilevel mechanisms that could indicate different types of subordination
of informal interpersonal ties to formal interunit ties.
The main finding concerns the influence of the interunit formal structure
on interpersonal interaction. We have replicated the well-established result that
subunits are generally likely to retain interpersonal ties within their boundaries. In
our sample, information sharing is more likely to take place between participants
who are members of the same subunit. Boundary spanning is a relatively infrequent
event. When it does take place, boundary spanning is likely to be affected by
hierarchical interunit ties, consistent with our assumptions. We have tested and
verified two different ways in which the formal organizational structure can affect
presence and direction of interpersonal boundary spanning ties.
First, in line with transactive memory arguments, managers affiliated to more
central subunits – i.e., subunits which have to report to many others in the formal
network – are more likely to be selected as partners for interpersonal relations. In our
sample, we have found this is a significant tendency for communication relations.
emmanuel.lazega@sciences-po.fr
14 Knowledge Sharing in Organizations: A Multilevel Network Analysis 351
Second, in line with social foci arguments, formal hierarchical ties are likely
to sustain boundary-spanning ties. Hence, managers working in subunits that are
themselves already connected by mandated hierarchical relations display a higher
propensity toward seeking information from each other. Our results indicate that,
within the patterns of interaction offered by interunit ties, managers are also likely to
exert some autonomy. The dependence of interpersonal communication relations on
mandated hierarchical relations is partly weakened by the capability of interpersonal
interaction to reduce the hierarchical ordering.
As an additional finding, boundary spanning between members of connected
subunits can be activated also by homophily between subunits or individuals. In
our sample, we have observed this tendency for advice relations.
Finally, differences in communication and advice-seeking ties highlight the
context-dependent influence of the interunit formal structure on interpersonal
interaction. The effect of formal interunit ties is contingent on the specific rela-
tionship examined – a conclusion that will need to be carefully scrutinized in future
research.
Our general conclusion is that no social network in organizations should be
studied in isolation from the formal structure that shapes social relations between
individuals. The unique contribution of the multilevel perspective that we have
articulated in this paper is a rich contextual assessment of the incremental value
of social networks for our understanding of how formal organizations actually
work. In this sense, this paper may be interpreted as a preliminary step toward the
development of a more general multilevel network theory of organizations.
Acknowledgement We gratefully acknowledge financial support from the Fonds National Suisse
de la Recherche Scientifique (Swiss National Science Foundation. SNSF Grant 615 number
CRSII1_147666/1).
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