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A social network analysis of customer-level revenue distribution

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Abstract

Social network analysis has been a topic of regular interest in the marketing discipline. Previous studies have largely focused on similarities in product/brand choice decisions within the same social network, often in the context of product innovation adoption. Not much is known, however, about the importance of social network effects once customers have been acquired. Using the customer base of a telecommunications company, our study analyzes network autocorrelation in the distribution of customer-level revenue within a social network. Our results indicate a significant and substantial degree of positive network autocorrelation in customer-level revenue. High (low) revenue customers therefore tend to be primarily related to other high (low) revenue clients. Furthermore, we show that approximating communicative proximity by spatial proximity leads to a substantial underestimation of these effects.

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Notes

  1. Autocorrelation refers to the correlation of a variable (e.g., customer-level revenue) with itself. It is a term frequently used in the context of time-series analysis where it describes the correlation between two values of the same variable measured at different points in time (i.e., temporal autocorrelation). It is, however, also used in spatial statistics to represent the correlation between two values of the same variable measured at different locations (i.e., spatial autocorrelation) and social network analysis.

  2. We calculated the distance between all pairs of actors and subsequently normalized those distances by dividing them by the maximum sample distance. Inverse geographical proximity was then defined as 1 − normalized distance.

  3. Specifically, we used the following functions: moran.test and geary.test to calculate Moran’s I and Geary’s C; lm.morantest to calculate Moran’s I for regression residuals and errorsarlm to estimate the spatial simultaneous autoregressive error model in the context of the first robustness check; and joincount.test to calculate join-count statistics in the context of the second robustness check.

  4. While this was possible for virtually all actors within sample B (only 55 out of 19,668 actors showed missing values with respect to the age variable), we were only able to obtain such information for roughly 42% of the 6,681 actors within sample A. The results for the latter case therefore need to be interpreted with caution.

  5. See http://www.appliedgeographic.com/mosaic.html for additional details on the Mosaic typology.

  6. Details on this analysis can be obtained from the author on request.

  7. The three-part tariff structure of the mobile phone operator induces a relationship between customer-level revenue and service plan choice. Mean customer-level revenue for all clients within the same service plan ranges from 0.23 to 1.72 for the 15 service plans analyzed. Nevertheless, due to substantial mobile phone usage outside of the monthly service plan allowance, the standard deviations of the mean are significant (between 0.23 and 0.98). This leads to the fact that although some service plans are associated with strictly larger or smaller customer-level revenue than others, many service plans overlap in terms of customer-level revenue. Service plan choice and customer-level revenue are therefore two distinct measures of post-acquisition customer behavior.

  8. The mobile phone company we collaborated with is based in Europe, where the predominant billing scheme is Calling Party Pays. This implies that the mobile subscriber does not pay for incoming calls but instead the calling party pays for those calls. In order to notify the calling customer that s/he has called a number for which there will be a different tariff, mobile numbers in Europe are usually dedicated to specific blocks. This made it straightforward to generate a set of random numbers which had a reasonably high chance of corresponding with actual mobile phone numbers.

  9. It was necessary to define a cut-off in terms of call duration to eliminate numbers from our analysis that have been called only rarely and that, hence, are unlikely to represent true friends. In line with the well-established 80/20 law, we assumed that friends should account for 80% of total call duration. We subsequently tested a range of potential thresholds between 1% and 5% to identify to what extent they fulfilled this criterion. While a 1% cut-off resulted in friends accounting for 84% of total call duration, a 2% cut-off would have resulted in 73% and a 3% cut-off in 64%. Based on these results, we decided to apply a 1% threshold.

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Authors and Affiliations

  1. ESCP Europe, 79 Avenue de la République, 75011, Paris, France

    Michael Haenlein

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  1. Michael Haenlein
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Correspondence to Michael Haenlein.

Additional information

The author thanks Roger Bivand, Professor of Economics at the Norwegian School of Economics and Business Administration and developer of the spdep package, for his helpful comments during data analysis.

Appendix: Sampling process

Appendix: Sampling process

1.1 Sample A

We started the creation of sample A by taking a random sample from the customer database of the mobile phone provider. Since every customer can be uniquely identified by his/her mobile phone number, we generated a list of 150,000 random numbers and matched it to the customer database.Footnote 8 This resulted in a random sample of 363 customers. For each of these 363 customers, we downloaded information about all outgoing calls made (phone number called and duration of call) over a 3-month time period (March 1 to May 31). We then calculated the total number of minutes any number had been called and expressed it as a percentage of total call duration. Any number which represented at least 1% of total call duration was subsequently considered as a potential friend of the calling customer.Footnote 9 We then matched this list of mobile phone numbers back to the customer database, resulting in 747 customers of the mobile phone provider that could be considered as friends of at least one of the initial 363 customers. Following the same procedure again, we subsequently identified another 2,639 customers (either friends of the initial 363 and/or the 747 customers) and 6,966 customers (either friends of the initial 363 and/or 747 and/or 2,639 customers). In the resulting list of 10,715 customers (363 + 747 + 2,639 + 6,966), 2,710 customers were deleted due to double counting and 292 because they had been acquired after March 1 and, hence, only had incomplete call history information. Out of the remaining 7,713 customers, 7,055 could be matched to a second database containing revenue information and, out of those, 6,681 to a third one containing postcode data. This resulted in a final network consisting of 6,681 actors, who were linked by 19,885 call relationships or ties, with a density of 0.0005628. For our analysis, we transformed all directed relationships into undirected ones (i.e., arcs into edges) to obtain a symmetrical adjacency matrix as the underlying event (mobile phone calls) is by nature a reciprocal relationship.

1.2 Sample B

Similar to the approach taken for sample A, the creation of sample B started by matching a set of random numbers (1.25 million) to the customer database of the mobile phone provider, resulting in a random sample of 4,163 customers. Deleting 424 customers that had been acquired after August 1 led to 3,739 customers, for which we downloaded information about all incoming and outgoing calls made (phone number and duration of call) over a 2-month time period (August 1 to September 30). This resulted in 12,939 customers of the mobile phone provider that called at least one of the initial 3,739 customers and 12,853 that were called by at least one of them. In the resulting list of 29,531 customers (3,739 + 12,939 + 12,853), 9,689 customers were deleted due to double counting. Out of the remaining 19,842 customers, 19,826 could be matched to a second database containing revenue information and, out of those, 19,668 to a third one containing postcode data. This resulted in a final network consisting of 19,668 actors, who were linked by 25,799 call relationships or ties, with a density of 0.0000851. As above, we transformed all directed relationships into undirected ones (i.e., arcs into edges) to obtain a symmetrical adjacency matrix as the underlying event (mobile phone calls) is by nature a reciprocal relationship.

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Haenlein, M. A social network analysis of customer-level revenue distribution. Mark Lett 22, 15–29 (2011). https://doi.org/10.1007/s11002-009-9099-9

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