2.1 Network analysis in product design and market study

Network analysis has attracted considerable interest in product design and market study. In product design, network analysis has been used to characterize a complex product as a network of components that share technical interfaces or connections. Using the network metrics such as ‘centrality’, Sosa et al. (Reference Sosa, Eppinger and Rowles2007) defined three measures of modularity as a way to improve the understanding of product architecture. Based on Sosa’s work, Fan et al. (Reference Fan, Qi, Hu and Yu2013) developed a bottom-up strategy for modular product platform planning. A recent work by Sosa et al. (Reference Sosa, Mihm and Browning2011) found that proactively managing the use of network structure (such as hubs) may help improve the quality of complex product designs. Network analysis has also been applied to studying designers’ network for understanding organizational behavior (Contractor et al. Reference Contractor, Monge and Leonardi2011) and improving multidisciplinary design efficiency (Cormier et al. Reference Cormier, Devendorf and Lewis2012). In market study, text-mining apparatus has been integrated into a network analysis framework to understand customers’ top-of-mind associative network of products based on a large-scale, customer generated dataset on the Web (Netzer et al. Reference Netzer, Feldman, Goldenberg and Fresko2012). However, all the aforementioned product/feature networks are unidimensional, without including customers and their (preferences) relations to products in the same network. In contrast to the existing unidimensional product network analysis approaches, our multidimensional customer–product network (MCPN) is built with both product and customer nodes, together with product feature associations and customer social network, to understand how customer decision-making interacts with product attributes and how social influence affects individual decisions for new products.

2.2 Modeling the impact of social influence

There is growing recognition that modeling the impact of social influence is important in product design (Aral & Walker Reference Aral and Walker2011). A comprehensive study of how peer influence affects product attribute preference was provided by Narayan et al. (Reference Narayan, Rao and Saunders2011) who modeled three different mechanisms of social influence. By combining traditional conjoint analysis on product features with peer influence, their work showed that peer influence causes people to change perspective on product importance, and that some product attributes are more sensitive to change than others. However, the approach requires a strict format of survey data to evaluate the attitude change before and after exposure to peer influence.

In modeling social influence in customer vehicle choices, a simulation-based approach has been developed in our earlier research to capture the dynamic influence from social networks on the adoption of hybrid electric vehicles (He et al. Reference He, Wang, Chen and Conzelmann2014). The social network impact is captured via introducing ‘social influence attributes’ into the discrete choice utility function. The effects of these attributes are assessed through the social network simulation, where the network was constructed based on the ‘social distances’ measured by the dissimilarities of customers’ social profiles. This approach was demonstrated through a vehicle case study where a customer’s decision in choosing an eco-friendly alternative fuel vehicle could be influenced by neighbors and friends modeled as a small-world network. Similar treatments of using a small-world network for capturing social influence have also been found in Watts & Strogatz (Reference Watts and Strogatz1998) and Delre et al. (Reference Delre, Jager and Janssen2007). In this research, a multidimensional network approach is proposed to measure simultaneously customer–customer social interactions together with customer–product preference relations for assessing social impact on preference decisions. A simulation-based social network construction approach, similar to He et al. (Reference He, Wang, Chen and Conzelmann2014), is applied to convert customer attribute vectors into relational data in constructing the social network as a part of the MCPN which takes into account the interdependence of attributes and the interactions between customers and products.

2.3 Advances in social network analysis

In the past decade, social network scholarship has made a concerted effort to move from describing a network to developing techniques that explain the emergence and dynamics of networks. Development of analytical techniques to explain the emergence of networks is often motivated by the multitheoretical multilevel (MTML) framework (Monge & Contractor Reference Monge and Contractor2003). Social network models are multitheoretical because of the growing recognition among social network researchers that the emergence of a network can rarely be adequately explained by a single theory. Therefore, social network models combine disparate theoretical generative mechanisms, such as self-interest, collective action, social exchange, balance, homophily, proximity, contagion, and co-evolution. Social network models have multilevel interpretations because the emergence of a network can be influenced, for instance, by theories of self-interest that refer to characteristics of actors (at the individual level), theories of social exchange that describe links between pairs of actors (at the dyadic level), theories of balance that explain the configuration of links among three actors (at the triadic level), and theories of collective action that explain configurations among larger aggregates of actors (at the group or network level).

Among the network modeling techniques, the ERGM provides the statistical inference framework for MNA. Technically, we can define matrix Y as a random graph in which rows and columns represent customers and products, respectively. $Y_{ij}=$ 1 refers to a relation, such as the preference (consideration or purchase) decision between customer $i$ and product $j$ , and 0 otherwise. Exponential random graph models have the following form:

where (i) $\mathbf{y}$ is the observed network, a random realization of $\mathbf{Y}$ ; (ii) $z(\mathbf{y})$ is a vector of network statistics corresponding to network characteristics in $\mathbf{y}$ , and the settings of product and consumer attributes; (iii) $\unicode[STIX]{x1D73D}$ is a parameter vector indicating the effects of the network statistics; (iv) $c$ is the normalizing constant that ensures the equation is a proper probability distribution. Eq. (1) suggests that the probability of observing any particular graph (e.g. MCPN) is proportional to the exponent of a weighted combination of network characteristics: one statistic $z(\mathbf{y})$ is more likely to occur if the corresponding $\unicode[STIX]{x1D703}$ is positive. Examples of possible $z(\mathbf{y})$ statistics used in MCPN are detailed in Section 3.3. Our research aims to interpret the meaning of these network effects $z(\mathbf{y})$ in order to understand customer–product relations for product design.

3.1 The multidimensional customer–product network (MCPN) framework

In this paper, we recast the problem of modeling customer preferences as network modeling of customer–product relations. We view engineering products as an inherent part of the expanded social network along with human actors. Figure 3 describes the structure of the MCPN framework, which is characterized by two classes of nodes at two layers (‘product’ and ‘customer’) and multiple types of relations within and between the two layers.

Figure 3. Multidimensional customer–product network.

The product layer contains a collection of engineering products $\mathbf{P}$ (e.g., vehicles, electronics and appliances, software). Products are connected by various links which can be either directed or non-directed. Directed links often involve product hierarchy or preference, while non-directed links imply product similarity or association. Product attributes or features, quantitative (e.g., fuel efficiency, horsepower) or qualitative (e.g., safety, styling), can be taken into account as nodal attributes. Similar attributes/features between products are represented as association links in the product network. Alternatively, product associations can be identified by their co-consideration relations from customers. The customer layer describes a social network consisting of a customer population $\mathbf{C}$ who make decisions or take actions. Each customer has a unique profile (e.g., socioeconomic and anthropometric attributes, purchase history and usage context attributes, etc.) which potentially affects customer preference decisions. Links between two customers represent their social relations, such as friendship or communication. The structural tendencies of these social relations reflect the underlying social processes for creating and maintaining links such as homophily and proximity (Monge & Contractor Reference Monge and Contractor2003). Much of the developed literature in social network analysis can be employed here to construct a customer social network. Customer–product relations are indicated by various human activities such as purchase and consideration decisions. The customer–product links are created between two sets of nodes from two adjacent layers, representing customer preferences. As shown in Figure 3, if a customer purchases a product, there is a solid line linking the customer and product nodes. If a customer considers a product, the link between the two nodes is marked as a dashed line. As noted, a customer can consider several products at the same time while the final purchase is only one or none. These preference links can be flexibly constructed by various sources of data, e.g., survey data, transaction data, and user-generated text data.

As seen, the proposed MCPN framework can capture rich information on dependency in a complex socio-technical system so as to assist product design decision-making. A combined analysis of all relations mentioned above allows designers to evaluate product decisions not in isolation, but with expectation that the market system will react to the planned decisions, and any design change may easily affect other connected entities across the network in ways that were initially unintended.

3.2 Unidimensional network analysis of product associations

Our development of MCPN started with the unidimensional network analysis to a single layer network with only product nodes and associations. The unidimensional network can be viewed as a compressed but simplified version of the more complicated bipartite (customer–product) networks by projecting it to a single layer (Wasserman & Faust Reference Wasserman and Faust1994). The unidimensional network enables designers to explore the use of descriptive metrics in identifying aggregated product associations that can reveal the implied product similarity and diversity, product market competence, product market segmentation, and other opportunities for design improvements.

The links in a product association network can be constructed in many ways. For example, using the customer preference data, a customer-driven product association network can be established, where the links between products reflect the proximity or similarity of two products in customers’ perceptual space. Standard measures of association rules, such as the ‘lift’, can be used to quantify the strength of the connection (Tan et al. Reference Tan, Kumar and Srivastava2004) between two products based on how often they are in the same consideration set. Alternatively, a feature-driven product association network can be established with the help of product specification data, where the association between products can be determined by measuring the similarity of product attributes/features from designers’ point of view. Distance measures commonly used in content-based recommender systems, such as Jaccard index (Real & Vargas Reference Real and Vargas1996), Cosine similarity (Chowdhury Reference Chowdhury2010), Gower similarity (Gower Reference Gower1971) etc., can be applied to assess the strength of connections.

The descriptive network analysis involves the computation of topological measures to assess the position of nodes and the implication of structural advantages. Examples for analyzing customer-driven product associations are provided in Table 1. Centrality (Freeman Reference Freeman1979; Wasserman & Faust Reference Wasserman and Faust1994) measures a product’s competitiveness, indicated by its level of connectivity to other products. As an example in Figure 4(a), a vehicle network is constructed based on co-consideration data, indicating if two vehicles are co-considered by the majority of customers. As seen, Toyota Camry is more ‘central’ to other vehicles, implying it has the potential to satisfy a broader range of customers. Honda Civic SDN and Lincoln MKX are the next widely considered cars in customers’ minds. Network community (Clauset et al. Reference Clauset, Newman and Moore2004; Newman & Girvan Reference Newman and Girvan2004) analysis identifies products in the same community based on the link strengths and connections. In Figure 4(b), two distinct communities (‘compact vehicles’ in green dots and ‘high-performance midsize vehicles’ in orange dots) are found in the vehicle co-consideration network. The emergent product communities can be used to detect consumer choice set and potential product competitions (Wang & Chen Reference Wang and Chen2015). ‘Crossover’ vehicles that belong to multiple (overlapping) communities can also be identified through this analysis (Palla et al. Reference Palla, Derényi, Farkas and Vicsek2005; Gregory Reference Gregory2007). Network hierarchy (De Vries Reference De Vries1998; Gupte et al. Reference Gupte, Shankar, Li, Muthukrishnan and Iftode2011; Corominas-Murtra et al. Reference Corominas-Murtra, Goñi, Solé and Rodríguez-Caso2013) is illustrated by the directional network links in Figure 4(c) which encode preference ranking based on both consideration and purchase data. Products with high preference ranks (e.g., Camry with many incoming edges) are shown in darker colors. Note that in analyzing feature-driven product association networks where products are linked based on shared features, centrality, community, and hierarchy have different implications. For example, community implies product families where common features are shared among products.

Figure 4. (a) Vehicle centrality in network, constructed based on co-consideration data, (b) vehicle community in network, constructed based on co-consideration data, (c) vehicle hierarchy in network, constructed based on co-consideration and purchase data.

Figure 5. Multidimensional network considering product associations.

Although the unidimensional network approach can describe interdependencies in relational data, the method cannot provide quantitative assessment of the impact of product attributes for a particular group of customers of interest. Further, the unidimensional network analysis studies customers’ averaged (aggregated) preference across the population. Advanced network modeling approaches that capture disaggregated preference behaviors of individual customers are needed as examined next.

3.3 Analyzing multidimensional network considering product associations

To model heterogeneous customer preferences in products with close associations, we integrate the product association links with customer–product preference relations as a multidimensional network (see Figure 5), including two classes of nodes (customers and products), multiple types of customer preference relations, and association relations among products. By introducing the information from the second mode (i.e., customers), we aim to develop a network model capable of capturing customer preference heterogeneity and multiple dependent decisions, while considering product feature associations.

Beyond existing network approaches that are mostly descriptive in nature, we use ERGM as a unified statistical framework to analyze the MCPN. In ERGMs, the observed network is considered one realization of an underlying probabilistic distribution, without assuming the independence of nodes or links. A local topological configuration in the network, i.e., a set of connected nodes and links, is regarded as an exploratory variable representing the structural features of potential interest. Networks in the distribution are assumed to be ‘built up’ from the localized patterns represented by the structural features. Exponential random graph model literature has established more than 20 different types of effects (Lusher et al. Reference Lusher, Koskinen and Robins2012) for describing the various forms of dependence that exist in the relational data within social networks. Examples of effects, their configurations, and interpretations are provided in Table 2. Our focus is to interpret the meaning of these effects to understand customer–product relations for product design.

The network effects fall into three categories: pure structural effects, attribute-relation effects involving product/customer attributes, and cross-level effects involving both between-level and within-level relations. Pure structural effects are related to the well-known structural regularities in the network literature (e.g., effects [A] to [C] in Table 2); attribute-relation effects assume the attributes of products/customers can also influence possible tie formations in a given structure. At the two-node level (effects [A], [D], [E]), interpretation resembles the attribute effect in a logistic regression [121, 122]. The main effect (effect [D]) can be used to test how attractive a product attribute is. The interaction effect (effect [E]) captures whether certain features are favored by a particular group of customers or not. Beyond conventional logistic models, the network approach also evaluates higher-order effects such as at the levels of three-node (effect [F]) and four-node (effect [G]). The product association relations can be captured by the cross-level effects (effect [H]) that integrate customer preferences with product similarities. In this way, the analysis can explain whether certain types of customers tend to consider product alternatives associated with a specific set of attributes.

Once the network effects of interest are identified, their significance can be determined by estimating the model parameters of an ERGM via likelihood maximization, given the observed network data. As the exact maximization of the likelihood function requires a summation over all possible configurations of the network and is computationally demanding, approximation techniques, e.g., maximum pseudolikelihood (Frank & Strauss Reference Frank and Strauss1986) or Markov Chain Monte Carlo maximum likelihood (Geyer & Thompson Reference Geyer and Thompson1992) can be employed to determine the estimates of effects.

Compared to a unidimensional network (Section 3.2), a multidimensional network provides a more natural way to model relations between two different classes of nodes (customers and products) and the non-hierarchical association relations between products. Moreover, its capacity to preserve two types of nodes allows designers to parse out the unique contribution of different types of nodes to the overall network structure. Its ability to integrate product networks and customer–product relations allows designers to model interdependent product relations and correlated preference decisions explicitly, without specifying complicated error structures as often done in DCA.

3.4 Analyzing multidimensional network incorporating social influence

To account for the effect of social influence on customer preference decisions, we further expand the multidimensional network structure to simultaneously measure within-layer social relations, within-layer product associations, and between-layer customer–product relations (Figure 6).

Figure 6. Multidimensional network considering social interactions.

The proposed multidimensional network allows the evaluation of both the ‘peer effect’ and the more general ‘crowd effect’ (Urberg Reference Urberg1992), depending on how product associations and social relations are defined. Relations between customers are used to model ‘peer effect’ on customer attitudes and preferences. The term ‘peer’ has a broad meaning which may include ‘friends’, ‘neighbors’, ‘experts’, ‘relatives’ or even ‘online reviewers’ with whom customers may exchange information about new products. The preference hierarchies among products, as defined in Section 3.2, can be used to capture the effect of ‘social crowd’. The evaluation of social influence is done by assessing the structural tendencies of networks informed by social influence theories (Table 3). Using ERGMs, one can quantify the effects of social influence by statistically estimating the extent to which structural tendencies implied by social theories influence the probabilities of the observed network. Similar to the network effects in Table 2, customer and product attributes can be incorporated into the social influence structures for investigating how social influence varies across customers and products.

Due to the complexity of data collection, customer social network data is often not collected in consumer surveys. An alternative is to construct social relations through network simulations (He et al. Reference He, Wang, Chen and Conzelmann2014), based on certain hypotheses of network structure and ‘social distance’ measured by the collected customer profiles. For example, based on the theory of homophily (Mcpherson et al. Reference Mcpherson, Smith-Lovin and Cook2001), we can assume that two nodes with shorter social distance (similar customer attributes) are more likely to be connected. Unlike the prior research that incorporates social influence as customer attributes, this research employs the ERGM to assess the social influence effects. In theory, compared to the use of DCA, one should draw more reliable conclusions based on the results from the network approach, because of its capability of handling correlated node attributes and interdependent link relations, which avoids faulty inferences on covariates (Cranmer & Desmarais Reference Cranmer and Desmarais2011).

4.1 Using unidimensional network for modeling vehicle associations and hierarchies

In the first implementation, we demonstrate the unidimensional network analysis (Section 3.2) for identifying aggregated product associations and hierarchical preference relations. Beyond existing literature, our work utilizes both consideration and purchase data in market surveys to derive relationships among vehicle products for understanding customer preferences and product competitions. We develop two types of product association networks – a vehicle association network with undirected links showing the similarity of products, and a vehicle hierarchal network with directed links indicating preference hierarchies.

The two vehicle association networks are constructed using the 2013 New Car Buyers Survey (NCBS) data provided by an independent research institute in China. The dataset contains 49,921 new car buyers who considered and purchased from a pool of 389 vehicle models in 2013. Both the set of considered vehicles and the final purchase are recorded for each customer. Customer demographics and product information are also reported by respondents.

The vehicle association network is created to aid the analysis of customer consideration decisions by linking any pair of vehicles if both vehicles are considered by most consumers in his (her) consideration set. The association link is viewed as a form of similarity or closeness between any two vehicles in customers’ minds. The link strength is quantified by lift to reflect how often the two products are compared by a population of customers. The lift between product $i$ and product $j$ is defined as the probability of co-consideration over the probability that they are being considered individually, see Eq. (2). The probability value is approximated by the percentage of product (co)occurrence recorded in the NCBS data.

To prune the network links, a thinning threshold at 1 is chosen for the lift value; a lift greater than 1 has a precise statistical meaning showing a positive association between the two products (Tan et al. Reference Tan, Kumar and Srivastava2004). For example, Honda Guangzhou Odyssey and Mazda FAW 8 are positively associated, as shown in Figure 7(a). The association link implies that the two products have a high chance of being co-considered. From the customer’s perspective, it means that a customer considers Odyssey is also very likely to consider Mazda 8 at the same time.

Figure 7. Unimodal vehicle networks constructed from NCBS 2013. Nodes are sized by network degrees (or in-degrees) and colored by network communities. Network layout is computed by the Fruchterman–Reingold force-directed algorithm based on aesthetic criteria (Fruchterman & Reingold Reference Fruchterman and Reingold1991). Link strength is not specified and has no relation to the distance of nodes. (a) Centrality and community in vehicle association network. (b) In-degree hierarchy in hierarchical preference network.

As a measure of network centrality, the node degree calculates the number of links attached to a node. In the vehicle association network, products with a higher-degree centrality are those frequently co-considered with many other vehicles by customers. Examples of high-degree centrality vehicles include GM SGM Chevrolet Sail, Audi FAW Q5, and Kia Dongfeng Yueda K2. One interesting observation is that most of the high-centrality vehicles are also among the most popular vehicles considered by customers, though the two quantities are not equivalent in definition. Another observation is that the node degrees are not uniformly distributed such that some vehicles are considered more frequently than others.

For the constructed vehicle network, the product community analysis is employed following Newman’s modularity method to determine groups of interconnected vehicles. In Figure 7(a), the seven identified communities are marked in different colors. The product communities inform designer the marketing coverage of a brand family and marketing competence across several brands. For example, the yellow community includes most domestic entry-level sedans (e.g., BYD F6, Chery QQ, etc.), while the green community is featured by premium SUVs by foreign manufacturers (e.g., Jeep Grand Cherokee, Land Rover Discovery, etc.). It is also observed that a product line’s marketing success is highly influenced by its product positioning strategy. The successful product lines in the market generally cover more network communities. For example, as two marketing leaders in China, Volkswagen and GM have covered 6 out of the 7 network communities, implying a great diversity of their vehicle products across multiple segments.

As a refinement to the above undirected network, a directed network is constructed where a link direction is determined through both consideration and purchase data in NCBS. If for any pair of vehicles, a customer considers both vehicles but chooses one over the other, the link direction will point towards the purchased vehicle. The lift metric shown in Eq. (3) is slightly modified to accommodate the evaluation of directed link strength.

Again, the links are trimmed to highlight positive associations, where the link direction captures the preference hierarchy between the two linked products. For example, a bi-directional (mutual) link between Toyota Alphard and Mercedes Fujian Viano can be interpreted as the intense competition between the two products (Figure 7(b)), because both vehicle models attract significant percentages of customers in considerations. Nevertheless, Viano gains a slight upper hand in market competition, because the strength of the link in that direction is stronger.

With a directed network, graph metrics indicating node hierarchy, such as node in-degree, can be computed to reflect customers’ aggregated preferences across the population. The in-degree of a node computes the number of incoming links pointed to that node. A node with a high in-degree value implies the corresponding vehicle is very likely to be considered with other vehicles and is also more preferred in customer choice (purchase) decisions. For example, Audi FAW Q5 and Ford Kuga are popular vehicles in choice, which are ranked high in both degree centrality and in-degree hierarchy. In contrast, Volvo V40 and Ford Edge have been frequently considered (high-degree centrality in undirected network), but fall behind in customers’ final choices (low in-degree hierarchy).

Our illustrative example shows that descriptive network analysis may serve as a useful tool for designers to determine product positioning and product priorities in the phase of design planning. Centrality, community, and hierarchy allow designers to uncover the root causes of the differences in vehicle sales under a specific market. These efforts may reveal issues that a design team could work on, e.g., product recognition (low centrality rank), coverage and diversity of product lines (products not appearing in certain communities), product competence (several vehicles in the same community), and product configuration (low hierarchy rank).

While analyzing the structural information of a unidimensional network can be useful in describing product associations, there is a need for an approach to quantitatively evaluate customer heterogeneous preferences while addressing issues such as dependent alternatives, multiple decisions, social influence, and correlated observations. To demonstrate such capabilities of a network model, our next example employs ERGM in the MCPN framework with various nodes, relations and attributes included.

4.2 Using MCPN for modeling luxury vehicle preferences in Central China

Our second implementation demonstrates the use of inferential network technique (ERGM) for analyzing the vehicle MCPN framework (Sections 3.3 and 3.4). This network implementation also draws from the 2013 NCBS data to understand customer preference trends in China. With a focus on the luxury vehicle market, we examine respondents who live in the central provinces of China and consider only luxury imported vehicle models in their decision journey. This focused interest results in a subset data of 378 customers and 65 luxury vehicle models for modeling and evaluation. As reported by McKinsey, the top reasons for Chinese customers to choose a luxury vehicle are: ‘reflection of social status’, ‘self-indulgence’ and ‘business credibility’. Therefore, we expect that socially influenced decisions are more common in luxury vehicle buyers in China. In addition, the Chinese auto market is renowned for its complexity and volatility. Strong regional differences exist as a result for brand accessibility and lifestyle needs. Because of these hidden reasons beyond the functionality and design of a vehicle itself, quantifying the attractiveness of a vehicle attribute in such conditions becomes even more difficult.

The proposed MCPN integrates a feature-driven product association network, a customer–product network, and a customer social network as a unified entity for analysis. The implementation of the proposed approach goes beyond the descriptive analysis and consists of three major steps: network construction, ERGM specification, and ERGM interpretation; each of these steps is explained in the remainder of this section.