STATS 218: Final Project ReportSTATS 218: Final Project Report Introduction The report summarizes the network analysis procedures performed on Bruce Kapferer’s clothing factory data

STATS 218: Final Project Report

Introduction The report summarizes the network analysis procedures performed on Bruce Kapferer’s clothing

factory data [1, 2]. The body of the data is explained in the section below. The dataset is of

instrumental and sociational transactions among workers of tailor factory between two time intervals.

Modern network evaluation techniques (centrality measures, exponential random family graphs, latent

space models) are implemented on the dataset and comparison to the Kapferer observations and

conclusions are made.

The motivation behind choosing this network was the argument made by Kapferer in his text: “the

support by all the factory employees of strike action at the late time period, in contrast to only limited

support to similar industrial action at the close of the time period preceding it, is related to an extension

of interactional relationships cross-cutting and modifying major divisions of interests”.

In this report, Fruchterman Reingold layout algorithm is implemented in all networks using Gephi [3].

Body of Data The data is from Bruce Kapferer’s study of the development of a strike in a clothing factory in Zambia in

1965 [3]. The data were collected by continuous direct observation between June 1965, and February

1966. The data is divided into two transactions: sociational and instrumental.

• Sociational: Convivial interactions among factory members like a general conversation,

drinking together, sharing of gossip. These transactions which mirror the bonding of

actors are inherently symmetric, therefore we constructed an undirected network from

this data.

• Instrumental: Transactions like lending or giving of money, assistance at times of

personal crisis, help at work. These transactions are asymmetric since they lead to a

debt of obligation between actors and hence creates prestige and status among them.

The dataset of both interactions is presented at two times, time 1 and time 2. In the actual data, there

were 43 workers at time 1 and at time 2, 4 of them left the factory, and 15 new workers have joined.

To make the study of social and instrumental transactions consistent, we are analyzing only 39 workers

who were present at both times.

The nodal covariates are:

1. prestige: This covariate indicates the job status in categories according to Kapferer. Lower

number means higher prestige.

2. occupation: This nodal covariate categories the occupation according to Kapferer.

a. head tailor

b. line 1 tailor

c. line 2 tailor

d. line 3 tailor

e. cutter

f. ironer

g. cotton boy

h. button machiner

3. highstatusjob: This nodal covariate indicates workers in high-status jobs.

a. 1: prestige (1, 4)

b. 0: prestige (5, 8)

The data do not have any edge covariates.

Sociational Instrumental

Time 1 G (39, 158) G (39, 109)

Time 2 G (39, 223) G (39, 147)

Instrumental Transactions at Time 1


Sociational Transactions at Time 1


Centrality Measures


Outdegree Centrality Eigen Vector Centrality

Closeness Centrality Betweenness Centrality

Instrumental transactions, in essence, capture the work-related influence of a worker on others. Higher

values of outdegree centrality for head tailor and cutter indicates their higher authority and influence

in work-related matters. Eigenvector centrality gives higher weights to nodes connected to higher

weighed nodes. The higher value of this centrality for line 1 tailor hints at their intent of forming an

alliance and increasing dominance at the workplace. The values of betweenness centrality indicate the

workflow in the tailor shop, higher values for head tailor, cotton boys, and line 1 tailor indicates their

major involvement in the workplace.

Clustering based on occupation is also evident in the centrality networks and is justified by their

increase in centrality networks at time 2.


Outdegree Centrality Eigen Vector Centrality


Between time 1 and time 2 an abortive strike took place at the workplace, and after time 2 a successful

happened which was led by Lyashi (line 1 tailor).

By looking at the graphs of centrality measures, we can infer that out-degree centrality of line 1 tailors

have increased which justifies our assumption of their intent to form an alliance and dominate the

workplace. The biggest centrality values which is indicated in the above figures as biggest node is line 1

tailor (Lyashi) who lead the opposition to the management and a successful strike happened. Eigen

vector centrality and betweenness centrality indicates similar pattern.

The increase in centrality values of Meshak (button machiner) is anomalous in these transactions

which is explained by Kapferer in his text. He wrote “Meshak who had worked at the factory for eleven

years, together with a line 1 tailor Chipata, were treated as ‘supervisors’ by the owner of the factory

when it became clear that the formal supervisors and head tailor had lost credence with the workers”.

Therefore, we observe an increase in centrality values of only one button machiner (Meshak) at time 2.


Degree Centrality Eigen Vector Centrality


Sociational transactions, in essence, capture the conviviality among workers. A clustering based on

occupation is observable in the network and evident from the centrality values. Higher values of

degree, eigenvector, closeness, betweenness centrality of head tailor and cutter indicates their high

social involvement among the factory workers.

By looking at the closeness centrality network, we can say that there is no observable dominance of

any occupation workers in the factory.


Degree Centrality Eigen Vector Centrality


By looking at the networks, we see that degree centrality of head tailor, button machiner (Meshak) and

line 1 tailors have increased significantly, and their dominance is visible. Meshak’s quasi-supervisory

status can explain the increase in centrality for button machiner.

The high value of eigenvector centrality for all the line 1 tailors as compared to other occupation

workers seems a factor behind their successful strike.

Centralization

Instrumental 1 Instrumental 2 Sociational 1 Sociational 2

Density 0.0735 0.0991 0.213 0.301

Diameter 8 7 4 3

Degree 0.172 0.353 0.441 0.376

Eigen 0.392 0.394 0.334 0.223

Closeness 0 0 0.419 0.358

Betweenness 0.164 0.206 0.198 0.088

The density of network increased for both types of transactions. In instrumental case, it increased from

0.0735 to 0.0991 (35 % increase) and in sociational case, it increased from 0.213 to 0.301 (41%

increase). This increase indicates an increment in instrumental and sociational transactions among

workers between time 1 and time 2.

The reachability of a node from other (called diameter) in a network is also measured for the two

transaction networks. The diameter of the network reduced for both cases but this decrease do not

indicate the increase in reachability since by looking at betweenness centralization, although the

diameter for sociational transactions has decreased from 4 to 3 (which indicate more reachability

among actors) but betweenness centralization decreased from 0.198 to 0.088. This is because at time 2

although the number of connections has increased, there are four workers who are unreachable by 39

others (since they left the job) and are not in the network at time 2.

Degree centralization of instrumental ties increased (more than double) from time 1 to time 2, but for

sociational transactions, its value decreased.

Interesting differences between two-time points

1. Line 1 tailors consistently increased their instrumental and sociational ties.

2. Line 3 tailors, ironers, cotton boys (lower level in occupation pyramid) increased their links but

to a lesser degree than workers in the higher level.

3. The head tailor increased its sociational ties but failed to increase his instrumental ties.

4. The anomalous behavior shown by a button machiner (Meshak) in the events of Tailor shop is

explained by his long work experience and quasi-supervisory status. Adrian who is the other

button machiner does not show any significant increase in instrumental and sociational ties.

Impact of covariates on pattern of ties: Using ergm [4, 5] models, I have tabulated the fit estimates of nodal covariates:

Instrumental 1 Summary

Instrumental 1 Fit Estimate

Instrumental 2 Summary

Instrumental 2 Fit Estimate

edges 109 -3.927 147 -3.661

mutual 33 3.610 52 4.116

highstatusjob 83 0.535 96 0.107

occupation 51 0.779 68 0.894

prestige 51 0.009 68 0.0003

By looking at the summary and fit estimates, we can say that, at both times the propensity of forming a

tie is highly conditioned on mutuality. The positive coefficients of occupation, highstatusjob, and

prestige also affect forming of ties.

From time 1 to time 2, the propensity to form a tie based on mutuality and occupation has increased

which hints the formation of an alliance of Line 1 workers. This similar trend is observed in sociational

transactions from time 1 to time 2.

Sociational 1 Summary

Sociational 1 Fit Estimate

Sociational 2 Summary

Sociational 2 Fit Estimate

edges 158 -1.912 223 -1.311

highstatusjob 106 0.435 139 0.246

occupation 65 1.443 83 1.535

prestige 65 NA 83 NA

By looking at the summary and fit estimates, the positive coefficients of occupation and highstatusjob

indicates their positive effect in formation of social ties.

Triad census on Instrumental Transactions

Time 1

Time 2

Fit model summary

At time 1, the positive coefficients of 030T, 120D, 120U, 300 (transitive triads) and negative

coefficients of 111D, 111U, 021C, 201 (intransitive triads) infer a preference for transitive ties. This

inference is justified by analyzing triad census at time 2 in which for the same actors, the triad census

for 030T, 120D have decreased and 120U and 300 have increased significantly which indicates

transition from intransitive triads to transitive triads.

We have -Inf coefficient for 030C at both time since their count is 0 in the network.

ERGM fit

Instrumental Transactions at time 1

For instrumental transactions at time 1, ergm model with edges term, mutuality term, homophily

terms based on nodal covariates (highstatusjob and occupation) and triples term (cyclic and transitive)

seems the best fit. Analysis of Variance table results supports the best fit model argument.

The model summary demonstrates a high propensity for ties based on mutuality and homophily based

on highstatusjob and occupation. The positive coefficient of transitive triple and a negative coefficient

of cyclic triple suggest an inclination towards transitive ties.

The AIC and BIC values are comparatively smaller as compared to other fit models which suggest that

this model is a good fit for the instrumental transactions at time 1.

Instrumental Transactions at time 2

For instrumental transactions at time 2, ergm model with edges term, mutuality term, homophily

terms based on nodal covariates (highstatusjob and occupation) and triples term (cyclic and transitive)

seems the best fit. Analysis of Variance table results supports the best fit model argument.

The model summary shows a high propensity for ties based on mutuality and homophily based on

highstatusjob and occupation. The positive coefficient of transitive triple and a negative coefficient of

cyclic triple suggest an inclination towards transitive ties.



Sociational Transactions at time 1

For sociational transactions at time 1, ergm model with edges term, differential homophily based on

nodal covariate (highstatusjob) and homophily based on occupation seem the best fit. Analysis of

Variance table results supports the best fit model argument. The model summary shows a high

propensity for ties based on homophily on occupation.

The nodemixing based on occupation model does reduce the deviance but increase the degree of

freedom by 36.



Sociational Transactions at time 2

For sociational transactions at time 2, ergm model with edges term, differential homophily based on

nodal covariate (highstatusjob) and homophily based on occupation seem the best fit. Analysis of

Variance table results supports the best fit model argument. The model summary shows a high

propensity for ties based on homophily on occupation.

The node mixing based on occupation model does reduce the deviance but increase the degree of

freedom by 36.



Latent Position and Latent Position Cluster Model

Groups|Overall BIC

Instrumental 1 Instrumental 2 Sociational 1 Sociational 2

2 825.494 939.91 803.10 899.75

3 834.11 929.33 794.01 907.40

4 847.90 933.10 801.30 915.18


By looking at the latent space fit for clustering two, three and four groups respectively, the two groups

fit the best. It is indicating the clustering of instrumental transactions in two groups. One explanation

can be given for this grouping based on occupation level (highjobstatus nodal covariate). Instrumental

transactions reflect work-related ties, and we expect grouping in them based on the job status level.

The overall BIC values also suggest that two group model is the best fit.


A similar observation is made for the latent fit models of instrumental transactions at time 2. Two

major clusters are present in the latent fit and can be explained by job status nodal covariate.

Increase in the number of people in a group suggests that people in that group try to increase their

instrumental ties which is justified from the centrality analysis (Line 1 tailors expands their

instrumental ties from time 1 to time 2).

Clustering in the groups of two can be seen as a success factor for the strike which happened after

time 2.


By looking at the latent space fit of sociational transactions at time 1, a grouping of 3 fits the best

(overall BIC is also the least for this model). In the data, we cannot see any variable which indicates the

division of network in three groups, but possible hypothesis might be given based on the spatial

locations of workers in the factory or work tenure or prestige.


Latent space models of sociational transactions at time 2 suggest a grouping of 2 as the best fit in the

network. This can be due to the division of workers into two groups, one who are against the

management and planning for a strike, and other who are not part of that alliance. This latent model is

also showing the transition of three groups at time 1 to two groups (one major group, one minor

group) at time 2.

As from the Kapferer text, we know that a successful strike took place after time 2, it is in accordance

with our latent space models.

Conclusion The general conclusion of this reanalysis of Kapferer data is that the analysis supports Kapferer original

hypothesis. Kapferer’s analysis was based on exchange theory and as would be consonant with an

approach of that sort he made extensive use of ego-centered network characteristics of the members

of the tailor shop as star size, span and zone density [6]. We have used centrality measures and ergm

and latent space models (which Kapferer did not use) between time 1 and time 2 which supported

Kapferer findings.

Structural equivalence and dynamic network analysis procedures should be performed on this data

which might reveal more important pattern. Further testing of the efficacy of the procedures used to

reveal the patterns in the data will turn on a more intensive examination of the finer details of the

analysis against the ethnographic facts [6].

References [1] Kapferer B. (1972). Strategy and transaction in an African factory. Manchester: Manchester

University Press

[2] Christopher L. DuBois, Emma S. Spiro, Zack Almquist, Mark S. Handcock, David Hunter, Carter T.

Butts, Steven M. Goodreau, and Martina Morris. 2003 netdata: A Collection of Network Data

[3] Bastian M., Heymann S., Jacomy M. (2009). Gephi: an open source software for exploring and

manipulating networks. International AAAI Conference on Weblogs and Social Media

[4] Handcock M, Hunter D, Butts C, Goodreau S, Krivitsky P and Morris M (2017). _ergm: Fit, Simulate

and Diagnose Exponential-Family Models for Networks_. The Statnet Project (<URL:

http://www.statnet.org>). R package version 3.8.0, <URL: https://CRAN.R-project.org/package=ergm>.

[5] Hunter D, Handcock M, Butts C, Goodreau S and Morris M (2008). “ergm: A Package to Fit, Simulate

and Diagnose Exponential-Family Models for Networks.” _Journal of Statistical Software_, *24*(3), pp.

1-29.

[6] Mitchell, J. Clyde. "Algorithms and network analysis: A test of some analytical procedures on

Kapferer’s tailor shop material." Research Methods in Social Network Analysis (2017): 365-391.

https://cran.r-project.org/package=ergm

Documents

STATS 218: Final Project ReportSTATS 218: Final Project Report Introduction The report summarizes the network analysis procedures performed on Bruce Kapferer’s clothing factory data