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Interlock groups, cliques, or interest groups? Comment on Allen
Social Networks North-Holland
INTERLOCK COMMENT
6 (1984)
193-199
GROUPS, CLIQUES, ON ALLEN
Mark S. MIZRUCHI Alberi
Einstem
193
College
OR INTEREST
GROUPS?
*
of Medrcrne
1. During the past decade, Michael Allen has distinguished himself as a creative and original researcher of corporate interlocks. His article, “Convergent Validation using Divergent Techniques” (Allen 1982) builds on his earlier work, especially his 1978 Social Science Quarterly article on economic interest groups (Allen 1978). In the more recent article, he compares direct factor analysis with hierarchical cluster analysis as techniques for detecting cliques of heavily-interlocked corporations. Allen’s main finding is that despite the different assumptions upon which the techniques are based, the findings they yield are surprisingly similar. I will argue, however, that (1) the similarity of results found by Allen is not surprising, that in fact, these and most other clique detection techniques are based on virtually identical principles and assumptions; (2) that furthermore, there has been little attention in the interorganizational literature to the examination of just what a clique is, and whether conventional clique detection techniques are appropriate indicators of our theoretical constructs. Finally, I will illustrate an alternative approach, peak analysis (Bearden et af. 1975; Mariolis 1983), which is based on entirely different assumptions about the structure of network subgroups and their relation to the system as a whole. 2. As Allen points out, numerous techniques exist for identifying network subgroups. Besides factor analysis, graph-theoretic approaches, and *
Scientific
Computing
037%8733/84/$3.00
Center.
Albert
8 1984, Elsevier
Einstein
Science
College
Publishers
of Medicine,
Bronx,
B.V. (North-Holland)
NY
10461,
U.S.A
194
M.S.
Muruchi
/ Inierlock
groups:
Cwnnvznt
on Allen
multidimensional scaling (mentioned by Allen), there is also the wellknown blockmodel approach, as well as McQuitty’s linkage analysis (Lankford 1974; McQuitty 1957). Burt (1978) has distinguished techniques based on cohesion (graph-theoretic approaches) from those based on structural equivalence (such as blockmodeling). Techniques based on cohesion search for groups of actors who are densely tied to one another, as hierarchical cluster analysis does. Those based on structural equivalence search for actors whose relations to all other units are similar, and groups them together, as all types of factor analysis do (MacRae 1960; Lankford 1974). Burt argues that the two approaches are similar, and that the graph-theoretical approaches can in fact be considered a subset of those based on structural equivalence. It should be added that in terms of the kind of subgroups the two approaches attempt to identify, they are virtually identical. To illustrate this, consider the fact that in a graph-theoretic approach such as Alba’s (1973) n-clique technique, units are initially grouped together when they form a maximally complete subgraph, i.e., when each unit is tied to every other unit. In structural equivalence groupings, as mentioned above, units are grouped together not on the basis of ties to one another, but on the basis of identical relations to other units in the system. For example, in a 200 firm network, two companies would be considered structurally equivalent if they interlocked with the same five companies, and did not interlock with the other 195. But if ones are placed in the diagonal of the input matrix, as is usually the case, then two firms must interlock with one another to be structurally equivalent. The only way in which structurally equivalent firms would not be linked with one another (aside from placing zeros in the diagonal) would be if there were absolutely no transitivity operating in the network. But in membership overlap networks, all ties created by a single individual are transitive by definition (i.e., if A interlocks with B and C, then B and C are by definition interlocked), unless these incidental B-C ties are specifically removed, as suggested by Mintz and Schwartz (1981) and others (Mizruchi 1982). If all ties are treated, structurally equivalent actors are likely to interlock with one another, and cliques based on structural equivalence criteria will approach maximally complete subgraphs. In short, techniques based on either cohesion or structural equivalence are likely to yield highly dense subgroups. Thus, the likelihood of the groups being similar in content is high. The main reason for this is
M.S.
Mixuchi
/
Inierlock
groups:
Conwnent
that at root, all standard subgroup identification on a single underlying principle: that subgroups high density.
on Allen
195
techniques are based are characterized by
3. There is nothing wrong with different techniques leading to similar results. In fact, such a finding increases the reliability of all of them. However, a more fundamental issue is precisely what those techniques are measuring. In Sweezy’s 1939 study (Sweezy 1953), on which Allen’s piece is based, “interest groups” were defined in two ways. On the one hand, they signified corporations linked through “community of interest groups, or more or less loose alliances” (1953:159). On the other hand, they were corporations with “a significant element of control in common” (ibid:161), “the locus of power being normally an investment or commercial bank, or a great family fortune” (Baran and Sweezy 1966:17). If one is interested in groups based on “community of interest”, then standard clique identification techniques are clearly appropriate. But if one is searching for groups in which one central unit dominates other units, with no necessary relations among the subordinate units, then standard clique detection techniques are inappropriate. The groups derived by conventional methods have an egalitarian (non-hierarchical) structure, in which no one unit dominates (Fig. la). Yet the financial and family-based groups described by Sweezy (and Allen 1978) are likely to have more hierarchical structures (Fig. lb), i.e., less dense. Thus, to identify groups in which the units are under the purview of a single central unit, irrespective of relations among themselves, an alternative technique is necessary. The only technique of which I am aware which was designed specifically for this purpose is the “peak analysis” approach designed by Mariolis (1983: see also Mintz and Schwartz (1981), Mizruchi (1982)). Peak analysis is based on the identification of central units (peaks) which designate leadership positions in hierarchically-based interest groups. The first step in a peak analysis is to calculate centrality scores for all units in the system (theoretically, any measure of centrality can be employed). A peak is then defined as a unit which is more central
196
M.S.
peak
Mizruchr
/ Interlock
groups:
Comment
on Allen
peak
peak
(Cl Fig. 1. (a) Hypothetical non-hierarchical cal peak analysis clique structure.
clique.
(b) Hypothetical
hierarchical
clique.
(cj Ideal-typi-
than any other unit with which it directly links. Each peak defines a group. A unit is a member of the group defined by a particular peak if every more central unit with which it directly links is itself a member of that group. No other necessary relations among group members are posited. Units which are tied to more central units which are in two or more different groups are treated as “mixed members”, between but not in either group. Units can be mixed members among any number of groups. A unit which is tied to two peaks is called a “bridge”. The ideal-typical group structure suggested by a peak analysis is similar to, that in Fig. lc.
4.
In his 1978 article, Allen examined the clique structure among 250 large corporations from 1970 as well as 1935. I have analyzed a similar group of 167 corporations from 1969 (for details, see Mizruchi (1982: Ch. 6). I was able to calculate the density of Allen’s 1970 groups by examining data collected by Mariolis for 1969, which contained all firms in Allen’s
M.S.
Mizruchi
/ Inrerlock
groups:
Comment
on Allen
197
set. A slight margin of error occurred due to the one year difference, although, as Mariolis and Jones (1982) point out, this is likely to have little effect on the results. The findings suggest three things: (1) As predicted by the above discussion, factor analysis produces subgroups far more dense than those produced by peak analysis. Among Allen’s ten groups, 126 of 192 possible connections occurred, a density of 0.661. In my five peak analysis groups, only 26 of 65 possible connections occurred, a density of 0.4. Even the groups designated by Allen as financially-based had a combined weighted density of 0.54, and one group classified as possibly financially-based had a density of 0.8. Furthermore, of the 18 nonfinancial members of the five peak analysis groups, only five were members of the corresponding factor analysis groups. This contrasts sharply with the similarity between the hierarchical cluster analysis groups and those of the factor analysis, pointing to the different outcomes possible when theoretically divergent techniques are applied. (2) Allen suggested that two of his groups, Morgan and Citibank, were financially-based groups. According to Sweezy’s definition, the other corporations within those groups should therefore be “controlled” by Morgan Guaranty and Citibank respectively. A study by Kotz (1978) employed bank stockholding data to chart bank control over nonfinancial corporations. Although there is no necessary connection between stock ownership in a firm and interlocking, there is a positive association between the two (Mizruchi 1982: Ch. 2). Yet among the twelve nonfinancial corporations in Allen’s two financially-based groups, only two are classified within those groups by Kotz on the basis of stockholding. (3) To be fair, in the Morgan and Citibank peak analysis groups, only two of the nine nonfinancial corporations are classified into those groups by Kotz. It appears from comparison with the Kotz data that the interest groups found by both approaches may be relatively insignificant. But it is here that the differences between peak analysis and factor analysis most clearly manifest themselves. Factor analysis, and clique detection approaches in general (blockmodel and mds are exceptions here) tend to focus on the subgroups at the expense of looking at the system as a whole. As White et al. (1976) point out, “persons not in the clique are usually disregarded (i.e., treated as outside the effective sociometric system)” (1976:736). In Allen’s factor analysis, only 34
198
M.S.
Mlrruchr
/ Interlock
groups:
Comment
on Allen
percent of all ties in the system occur within the subgroups. In the peak analysis, the figure is only 20 percent. Part of the reason for this discrepancy is the fact that in factor analysis, the researcher must set an arbitrary cut-off point for both the number of cliques and the level of inclusion for membership within each group. This insures that “groups” will always exist, their size and number subject to the whim of the researcher. In peak analysis, the number of groups is free to vary depending on the structure of the system as a whole, and no arbitrary decisions are necessary. The very existence of groups is problematic and is empirically testable. Thus, the conclusion based on the peak analysis is precisely how little clustering exists, and how widespread is the overlap among the groups. For example, in 1969, only 26 corporations were group members, while 119 were mixed members, 27 between two groups, 46 among three, 28 among four, and 18 among all five groups. What this shows is the striking degree of overlap among the groups, which far overshadows any clustering that exists. This finding is not directly discernable from the factor analysis, and it suggests that peak analysis is superior as a technique for gauging characteristics of the system as a whole.
5. Conclusion Allen has performed the findings of factor needed now is more the rationale for the
a valuable service by showing the similarities in analysis and hierarchical cluster analysis. What is attention to the substantive concepts which form mathematical techniques which are employed.
References Alba, Richard D. 1972 “A graph-theoretic definition of a so&metric clique”. Journal o/ Mathematical Sociology 3: 113-126. Allen, Michael P. 1982 “The identification of interlock groups in large corporate networks: Convergent validation using divergent techniques”. Social Networks 4: 349-366. 1978 “Economic interest groups and the corporate elite structure”. Social Science Quarter!y 58: 591-615. Baran. Paul A. and Paul M. Sweezy 1966 Monopoly Capitol. New
York:
Monthly
Review
Press.
M.S.
Bearden,
Mi-ruchi
/ Inrerlock
groups:
Comment
on Allen
199
James, William Atwood, Peter Freitag, Carol Hendricks, Beth Mintz and Michael Schwartz 1975 “The nature and extent of bank centrality in corporate networks”. Paper presented at the annual meeting of the American Sociological Association, San Francisco. Burt. Ronald S. 1978 “Cohesion versus structural equivalence as a basis for network subgroups”. Sociological Methods and Research 7: 1X9-212. Katz, David M. 1978 Bank Conrrol of Large Corporations rn the United States. Berkeley: University of California Press. Lankford, Philip M. 1974 “Comparative analysis of clique identification methods”. Sociome~ry 37: 287-305. MacRae, Duncan, Jr. 1960 “Direct factor analysis of sociometric data”. Sociometry 23: 360-371. Mariolis, Peter 1983 “Interlocking directorates and financial groups: A peak analysis”. Socrologicol Spectrum in press. Mariolis, Peter and Maria H. Jones “Centrality in corporate interlock networks: Reliability and stability”. Admrnistratrue 1982 Science Quarterly 27: 571-584. McQuitty, Louis L. 1957 “Elementary linkage analysis for isolating orthogonal and oblique types and typal relevancies”. Educational and Psychological Measurement 17: 207-229. Mintz, Beth and Michael Schwartz 1981 “The structure of intercorporate unity in American business”. Socinl Problems: 87-103. Mizruchi, Mark S. The Amerrcan Corporate Network: 1904- 1974. Beverly Hills: Sage. 1982 Sweezy, Paul M. 1953 “Interest groups in the American economy”. In P.M. Sweezy (ed.) The Present As History. New York: Monthly Review Press. Originally published as the appendix to National Resources Committee, The Structure of the American Economy, 1939. White, Harrison C., Scott A. Boorman and Ronald L. Breiger 1976 “Social structure from multiple networks. 1: Blockmodels of roles and positions”. American Journal of Socrologv 81: 730-780.
INTERLOCK COMMENT
6 (1984)
193-199
GROUPS, CLIQUES, ON ALLEN
Mark S. MIZRUCHI Alberi
Einstem
193
College
OR INTEREST
GROUPS?
*
of Medrcrne
1. During the past decade, Michael Allen has distinguished himself as a creative and original researcher of corporate interlocks. His article, “Convergent Validation using Divergent Techniques” (Allen 1982) builds on his earlier work, especially his 1978 Social Science Quarterly article on economic interest groups (Allen 1978). In the more recent article, he compares direct factor analysis with hierarchical cluster analysis as techniques for detecting cliques of heavily-interlocked corporations. Allen’s main finding is that despite the different assumptions upon which the techniques are based, the findings they yield are surprisingly similar. I will argue, however, that (1) the similarity of results found by Allen is not surprising, that in fact, these and most other clique detection techniques are based on virtually identical principles and assumptions; (2) that furthermore, there has been little attention in the interorganizational literature to the examination of just what a clique is, and whether conventional clique detection techniques are appropriate indicators of our theoretical constructs. Finally, I will illustrate an alternative approach, peak analysis (Bearden et af. 1975; Mariolis 1983), which is based on entirely different assumptions about the structure of network subgroups and their relation to the system as a whole. 2. As Allen points out, numerous techniques exist for identifying network subgroups. Besides factor analysis, graph-theoretic approaches, and *
Scientific
Computing
037%8733/84/$3.00
Center.
Albert
8 1984, Elsevier
Einstein
Science
College
Publishers
of Medicine,
Bronx,
B.V. (North-Holland)
NY
10461,
U.S.A
194
M.S.
Muruchi
/ Inierlock
groups:
Cwnnvznt
on Allen
multidimensional scaling (mentioned by Allen), there is also the wellknown blockmodel approach, as well as McQuitty’s linkage analysis (Lankford 1974; McQuitty 1957). Burt (1978) has distinguished techniques based on cohesion (graph-theoretic approaches) from those based on structural equivalence (such as blockmodeling). Techniques based on cohesion search for groups of actors who are densely tied to one another, as hierarchical cluster analysis does. Those based on structural equivalence search for actors whose relations to all other units are similar, and groups them together, as all types of factor analysis do (MacRae 1960; Lankford 1974). Burt argues that the two approaches are similar, and that the graph-theoretical approaches can in fact be considered a subset of those based on structural equivalence. It should be added that in terms of the kind of subgroups the two approaches attempt to identify, they are virtually identical. To illustrate this, consider the fact that in a graph-theoretic approach such as Alba’s (1973) n-clique technique, units are initially grouped together when they form a maximally complete subgraph, i.e., when each unit is tied to every other unit. In structural equivalence groupings, as mentioned above, units are grouped together not on the basis of ties to one another, but on the basis of identical relations to other units in the system. For example, in a 200 firm network, two companies would be considered structurally equivalent if they interlocked with the same five companies, and did not interlock with the other 195. But if ones are placed in the diagonal of the input matrix, as is usually the case, then two firms must interlock with one another to be structurally equivalent. The only way in which structurally equivalent firms would not be linked with one another (aside from placing zeros in the diagonal) would be if there were absolutely no transitivity operating in the network. But in membership overlap networks, all ties created by a single individual are transitive by definition (i.e., if A interlocks with B and C, then B and C are by definition interlocked), unless these incidental B-C ties are specifically removed, as suggested by Mintz and Schwartz (1981) and others (Mizruchi 1982). If all ties are treated, structurally equivalent actors are likely to interlock with one another, and cliques based on structural equivalence criteria will approach maximally complete subgraphs. In short, techniques based on either cohesion or structural equivalence are likely to yield highly dense subgroups. Thus, the likelihood of the groups being similar in content is high. The main reason for this is
M.S.
Mixuchi
/
Inierlock
groups:
Conwnent
that at root, all standard subgroup identification on a single underlying principle: that subgroups high density.
on Allen
195
techniques are based are characterized by
3. There is nothing wrong with different techniques leading to similar results. In fact, such a finding increases the reliability of all of them. However, a more fundamental issue is precisely what those techniques are measuring. In Sweezy’s 1939 study (Sweezy 1953), on which Allen’s piece is based, “interest groups” were defined in two ways. On the one hand, they signified corporations linked through “community of interest groups, or more or less loose alliances” (1953:159). On the other hand, they were corporations with “a significant element of control in common” (ibid:161), “the locus of power being normally an investment or commercial bank, or a great family fortune” (Baran and Sweezy 1966:17). If one is interested in groups based on “community of interest”, then standard clique identification techniques are clearly appropriate. But if one is searching for groups in which one central unit dominates other units, with no necessary relations among the subordinate units, then standard clique detection techniques are inappropriate. The groups derived by conventional methods have an egalitarian (non-hierarchical) structure, in which no one unit dominates (Fig. la). Yet the financial and family-based groups described by Sweezy (and Allen 1978) are likely to have more hierarchical structures (Fig. lb), i.e., less dense. Thus, to identify groups in which the units are under the purview of a single central unit, irrespective of relations among themselves, an alternative technique is necessary. The only technique of which I am aware which was designed specifically for this purpose is the “peak analysis” approach designed by Mariolis (1983: see also Mintz and Schwartz (1981), Mizruchi (1982)). Peak analysis is based on the identification of central units (peaks) which designate leadership positions in hierarchically-based interest groups. The first step in a peak analysis is to calculate centrality scores for all units in the system (theoretically, any measure of centrality can be employed). A peak is then defined as a unit which is more central
196
M.S.
peak
Mizruchr
/ Interlock
groups:
Comment
on Allen
peak
peak
(Cl Fig. 1. (a) Hypothetical non-hierarchical cal peak analysis clique structure.
clique.
(b) Hypothetical
hierarchical
clique.
(cj Ideal-typi-
than any other unit with which it directly links. Each peak defines a group. A unit is a member of the group defined by a particular peak if every more central unit with which it directly links is itself a member of that group. No other necessary relations among group members are posited. Units which are tied to more central units which are in two or more different groups are treated as “mixed members”, between but not in either group. Units can be mixed members among any number of groups. A unit which is tied to two peaks is called a “bridge”. The ideal-typical group structure suggested by a peak analysis is similar to, that in Fig. lc.
4.
In his 1978 article, Allen examined the clique structure among 250 large corporations from 1970 as well as 1935. I have analyzed a similar group of 167 corporations from 1969 (for details, see Mizruchi (1982: Ch. 6). I was able to calculate the density of Allen’s 1970 groups by examining data collected by Mariolis for 1969, which contained all firms in Allen’s
M.S.
Mizruchi
/ Inrerlock
groups:
Comment
on Allen
197
set. A slight margin of error occurred due to the one year difference, although, as Mariolis and Jones (1982) point out, this is likely to have little effect on the results. The findings suggest three things: (1) As predicted by the above discussion, factor analysis produces subgroups far more dense than those produced by peak analysis. Among Allen’s ten groups, 126 of 192 possible connections occurred, a density of 0.661. In my five peak analysis groups, only 26 of 65 possible connections occurred, a density of 0.4. Even the groups designated by Allen as financially-based had a combined weighted density of 0.54, and one group classified as possibly financially-based had a density of 0.8. Furthermore, of the 18 nonfinancial members of the five peak analysis groups, only five were members of the corresponding factor analysis groups. This contrasts sharply with the similarity between the hierarchical cluster analysis groups and those of the factor analysis, pointing to the different outcomes possible when theoretically divergent techniques are applied. (2) Allen suggested that two of his groups, Morgan and Citibank, were financially-based groups. According to Sweezy’s definition, the other corporations within those groups should therefore be “controlled” by Morgan Guaranty and Citibank respectively. A study by Kotz (1978) employed bank stockholding data to chart bank control over nonfinancial corporations. Although there is no necessary connection between stock ownership in a firm and interlocking, there is a positive association between the two (Mizruchi 1982: Ch. 2). Yet among the twelve nonfinancial corporations in Allen’s two financially-based groups, only two are classified within those groups by Kotz on the basis of stockholding. (3) To be fair, in the Morgan and Citibank peak analysis groups, only two of the nine nonfinancial corporations are classified into those groups by Kotz. It appears from comparison with the Kotz data that the interest groups found by both approaches may be relatively insignificant. But it is here that the differences between peak analysis and factor analysis most clearly manifest themselves. Factor analysis, and clique detection approaches in general (blockmodel and mds are exceptions here) tend to focus on the subgroups at the expense of looking at the system as a whole. As White et al. (1976) point out, “persons not in the clique are usually disregarded (i.e., treated as outside the effective sociometric system)” (1976:736). In Allen’s factor analysis, only 34
198
M.S.
Mlrruchr
/ Interlock
groups:
Comment
on Allen
percent of all ties in the system occur within the subgroups. In the peak analysis, the figure is only 20 percent. Part of the reason for this discrepancy is the fact that in factor analysis, the researcher must set an arbitrary cut-off point for both the number of cliques and the level of inclusion for membership within each group. This insures that “groups” will always exist, their size and number subject to the whim of the researcher. In peak analysis, the number of groups is free to vary depending on the structure of the system as a whole, and no arbitrary decisions are necessary. The very existence of groups is problematic and is empirically testable. Thus, the conclusion based on the peak analysis is precisely how little clustering exists, and how widespread is the overlap among the groups. For example, in 1969, only 26 corporations were group members, while 119 were mixed members, 27 between two groups, 46 among three, 28 among four, and 18 among all five groups. What this shows is the striking degree of overlap among the groups, which far overshadows any clustering that exists. This finding is not directly discernable from the factor analysis, and it suggests that peak analysis is superior as a technique for gauging characteristics of the system as a whole.
5. Conclusion Allen has performed the findings of factor needed now is more the rationale for the
a valuable service by showing the similarities in analysis and hierarchical cluster analysis. What is attention to the substantive concepts which form mathematical techniques which are employed.
References Alba, Richard D. 1972 “A graph-theoretic definition of a so&metric clique”. Journal o/ Mathematical Sociology 3: 113-126. Allen, Michael P. 1982 “The identification of interlock groups in large corporate networks: Convergent validation using divergent techniques”. Social Networks 4: 349-366. 1978 “Economic interest groups and the corporate elite structure”. Social Science Quarter!y 58: 591-615. Baran. Paul A. and Paul M. Sweezy 1966 Monopoly Capitol. New
York:
Monthly
Review
Press.
M.S.
Bearden,
Mi-ruchi
/ Inrerlock
groups:
Comment
on Allen
199
James, William Atwood, Peter Freitag, Carol Hendricks, Beth Mintz and Michael Schwartz 1975 “The nature and extent of bank centrality in corporate networks”. Paper presented at the annual meeting of the American Sociological Association, San Francisco. Burt. Ronald S. 1978 “Cohesion versus structural equivalence as a basis for network subgroups”. Sociological Methods and Research 7: 1X9-212. Katz, David M. 1978 Bank Conrrol of Large Corporations rn the United States. Berkeley: University of California Press. Lankford, Philip M. 1974 “Comparative analysis of clique identification methods”. Sociome~ry 37: 287-305. MacRae, Duncan, Jr. 1960 “Direct factor analysis of sociometric data”. Sociometry 23: 360-371. Mariolis, Peter 1983 “Interlocking directorates and financial groups: A peak analysis”. Socrologicol Spectrum in press. Mariolis, Peter and Maria H. Jones “Centrality in corporate interlock networks: Reliability and stability”. Admrnistratrue 1982 Science Quarterly 27: 571-584. McQuitty, Louis L. 1957 “Elementary linkage analysis for isolating orthogonal and oblique types and typal relevancies”. Educational and Psychological Measurement 17: 207-229. Mintz, Beth and Michael Schwartz 1981 “The structure of intercorporate unity in American business”. Socinl Problems: 87-103. Mizruchi, Mark S. The Amerrcan Corporate Network: 1904- 1974. Beverly Hills: Sage. 1982 Sweezy, Paul M. 1953 “Interest groups in the American economy”. In P.M. Sweezy (ed.) The Present As History. New York: Monthly Review Press. Originally published as the appendix to National Resources Committee, The Structure of the American Economy, 1939. White, Harrison C., Scott A. Boorman and Ronald L. Breiger 1976 “Social structure from multiple networks. 1: Blockmodels of roles and positions”. American Journal of Socrologv 81: 730-780.