a network-based approach to modeling and predicting...

Research ArticleA Network-Based Approach to Modeling and Predicting ProductCoconsideration Relations

Zhenghui Sha1 Yun Huang 2 Jiawei Sophia Fu3 Mingxian Wang4

Yan Fu4 Noshir Contractor2 and Wei Chen 5

1Department of Mechanical Engineering University of Arkansas Fayetteville AR USA2Department of Industrial Engineering amp Management Sciences and Department of Management amp Organizations andDepartment of Communication Studies Northwestern University Evanston IL USA3Media Technology and Society Northwestern University Evanston IL USA4Global Data Insight amp Analytics Ford Motor Company Dearborn MI USA5Department of Mechanical Engineering Northwestern University Evanston IL USA

Correspondence should be addressed to Wei Chen weichennorthwesternedu

Received 23 September 2017 Accepted 18 December 2017 Published 28 January 2018

Academic Editor Jesus Gomez-Gardenes

Copyright copy 2018 Zhenghui Sha et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Understanding customer preferences in consideration decisions is critical to choice modeling in engineering design Whileexisting literature has shown that the exogenous effects (eg product and customer attributes) are deciding factors in customersrsquoconsideration decisions it is not clear how the endogenous effects (eg the intercompetition among products) would influencesuch decisions This paper presents a network-based approach based on Exponential Random Graph Models to study customersrsquoconsideration behaviors according to engineering design Our proposed approach is capable of modeling the endogenous effectsamong products through various network structures (eg stars and triangles) besides the exogenous effects and predicting whethertwo products would be conisdered together To assess the proposed model we compare it against the dyadic network model thatonly considers exogenous effects Using buyer survey data from the China automarket in 2013 and 2014 we evaluate the goodnessof fit and the predictive power of the two models The results show that our model has a better fit and predictive accuracy thanthe dyadic network model This underscores the importance of the endogenous effects on customersrsquo consideration decisionsThe insights gained from this research help explain how endogenous effects interact with exogeous effects in affecting customersrsquodecision-making

1 Introduction

Complex networkmodeling and simulation have shown theirpower in many engineering applications such as the wirelessnetwork sensor network smart grids supply chain trans-portation systems and many others Recent developmentsin mathematical modeling techniques and computationalalgorithms to study complex networks have also drawn theattention of engineering design field Complex networks havebeen used in engineering design for the study of relationalpatterns effective network visualization of associations ofproducts andmodeling social interactions [1] and cross-levelinteractions between customers and products [2 3] In thedesign of complex products network analysis has been used

to characterize a product as a network of components thatshare technical interfaces or connections Various networkmetrics such as clustering coefficients and path length areused to characterize the product structure and study the cor-relations between design quality and the product structureBased on the network metrics for example the centralitySosa et al [4] defined three measures of modularity as a wayto improve the understanding of product architecture Recentwork by Sosa et al [5] found that proactively managing theuse of network structure (such as hubs) may help improvethe quality of complex product designs Network analysishas also been applied to studying designersrsquo network forunderstanding organizational behavior [6 7] and improvingmultidisciplinary design efficiency [8] In this paper instead

HindawiComplexityVolume 2018 Article ID 2753638 14 pageshttpsdoiorg10115520182753638

2 Complexity

of focusing on the product or the designer we leverage com-plex network modeling and simulation techniques to studyanother key stakeholder in product design the customerWe aim to leverage complex networks to study customerpreference in support of product design and developmentParticularly in this paper we study customersrsquo considerationdecisions by modeling product coconsideration relations twoproducts being concurrently considered in purchase as acomplex network

2 Background and Literature Review

Choice modeling is of great interest in engineering design asit predicts product demand and market share as a functionof engineering design attributes and customer profiles in atarget market [9] Choice models have been integrated intodesign optimization to take account of customer preferencesin supporting engineering design decisions [9ndash12] Previouschoice models mostly assume that customers have boundedrationality and have underlying utilities to rank alternativesin a consideration set ldquoa set of product alternatives availableto an individual who will seriously evaluate through com-parisons before making a final choicerdquo [13] A key step ofconstructing choice models is to determine the considerationset [14] As Hauser et al [15] indicated ldquoif customers do notconsider your product they canrsquot choose itrdquo

From an enterprise perspective understanding customerpreferences in consideration is important for identifyingcrucial product features that customers are willing to payfor Existing studies [16 17] also revealed the considerationset phenomenon that is the size of the consideration settends to be much smaller (roughly 5-6 brands) than thetotal number of choices available in a market As a resultsmall changes in individualsrsquo consideration sets (either sizeor options) may significantly transform the landscape ofthe overall market and reshape the competition relationsin an existing market Therefore understanding customersrsquopreferences in consideration poses new opportunities tooptimize product configurations address customer needsestablish competitive design strategies and make strategicmoves such as branding and positioning

Managerial actions have been taken to influence cus-tomersrsquo consideration decisions directly for example bychanging brand accessibility [18] and by controlling usage andawareness [19] However quantitative studies on customersrsquoconsideration decisions are challenging as consideration is anintermediate construct not the final choice [15]The decisioncontext and a large amount of uncertainty alter decision rulesExisting literature primarily focuses on inferring decision-rule heuristics [20ndash22] such as the cognitive simplicity rule[23] which has been shown to be effective in automobileand web-based purchasing There are three approaches touncover consideration decision-rule heuristics [15] The firstapproach only utilizes final choices and product featuresin the consideration set It adopts a two-stage consider-then-choose decision process and infers model parametersusing the Bayesian or maximum likelihood estimation Typ-ical methods include Bayesian [24] choice-set explosion[25ndash27] and soft constraints [28] The second approach

measures consideration through designed experiments invitro similar to the choice-based conjoint analysis exercise[15] Then the decision rules that best explain the observedconsideration decisions are estimated with Bayesian [29]andmachine-learning pattern-matching algorithms [30]Thethird approach measures decision rules directly through self-explicated questions [31]

Despite the diversity of research on consideration setsfew studies have focused on understanding the underly-ing process of generating customer consideration sets Theconnection between the formation of consideration setsand the driving factors is not well understood Particularlywe know little about how the inherent market structureincluding both the interdependence among existing productsand association among customers affects the considerationdecisions To address this research gap we develop a network-based approach to model customersrsquo consideration behaviorsby modeling product coconsideration relations As shown inFigure 1 the key idea of the proposed network approach is totransform customer consideration sets into a product associ-ation network in which nodes represent products and linksrepresent the coconsideration between two products As aresult the problem of understanding customer considerationcan be addressed by predicting certain network structuresas a function of association networks formed by productattributes and customer demographics It is worth notingthat as the link formation is an aggregation of customersrsquodecisions the links (ie the coconsideration relations) implythe competition among products Therefore our approachenables us to study customer preference andmarket structurein an integrated manner This is different from the studiesin choice modeling (eg the monomial logit choice model[32]) that focus on establishing models for individuals It isalso worth noting that our study is different from the agent-based models which hypothesize certain individual choice-making rules [33] Instead our approach is data-drivenwhich leverages the observed data to drive the establishmentof coconsideration models and prediction analysis using theestimated model parameters

Recently network approaches have been also extensivelyused in recommender systems [34ndash38] Recommender sys-tems are frequently used to recommend products to cus-tomers based on what they searched (considered) Fromthe network representation point of view our approach issimilar to the bipartite projection approach [39] used inthe recommender systems research However the proposednetwork approach is distinct from network-based recom-mender algorithms [37 38] in two aspects first the endgoal is different The recommender algorithms attempt topredict future likes and interests by mining data on past useractivities Common methods include the similarity-basedmethods (eg the collaborative filtering [38] content-basedanalysis [40] and Dirichlet allocation [41]) and the recentlydeveloped hybrid methods [36 42] The approach proposedin this paper relies on the network-based statistical inferencemodel which emphasizes deduction and explanation It aimsto provide an explanatory framework for customersrsquo consid-eration behaviors so that a feedback loop can be created fromcustomer preference to engineering design Therefore the

Complexity 3

Customerrsquoconsidered alternatives

Productsrsquococonsiderationnetwork

Network modeling

Model calibration and parameters estimation

Predictedcoconsiderationnetwork

Network construction using survey data Model comparison

and evaluation

Network structures formulation and selection

Figure 1 The research approach and the research focus

end goal of this study is to inform product design for largermarket share In such a context prediction in this study isfor comparison and validation purposes Second the role ofnetwork in the modeling is different In existing network-based recommender algorithms the input takes variousgraph-based node-specific attributes (eg degree) which areessentially the exogenous factors to generate the similaritymetrics In our approach the model input can take intoaccount present network structures (eg triangles and loops)which represents the interdependencies among products sothat the effect of the inherent competition relations can beassessed Such a capability supports better understanding onthe consideration behaviors and could provide additionalinsights into the design research that has been primarilydriven by usersrsquo preferences to engineering attributes

The current work builds upon our previous researchefforts In our recent study Fu et al [43] developed a two-stage bipartite networkmodeling approach to study customerpreferences in making choices by decoupling the choice-making process in two stages the consideration stage andthe choice-making stage Wang et al [44] utilized a dyadicnetwork analysis approach to predict product coconsidera-tion relations based on exogenous factors such as productattributes and customer demographics By mapping specifictechnological advancement (eg turbocharged techniques)to the change of products attributes the authors also demon-strated how the model facilitates the forecast of the impactof technological changes on product coconsideration andmarket competition

In this paper we take a further step to investigatethe power of complex network modeling in understandingproduct coconsideration relations by considering both exoge-nous factors and endogenous factors for example productinterdependence and inherent market competition The coretechnique is based on the Exponential RandomGraphModel(ERGM) [45] While dyadic network models are convenientto predict the associations between products based on exoge-nous factors ERGM incorporates endogenous factors as wellas other network interdependencies [46]

The research objective of this study is therefore twofold (a)to establish the network-modeling framework that supportsthe explanation of customerrsquos consideration behaviors andenables the prediction of future market competitions (b) tocompare the ERGM and dyadic network model to examineif the inclusion of product interdependence through the

endogenous network effects would better capture the dynam-ics underlying the formation of product coconsideration rela-tions The remainder of the paper has five sections Section 3presents the research problem and introduces the methodof constructing a product coconsideration network Wealso briefly provide the technical background of the dyadicnetwork model and ERGM Section 4 describes the vehiclecase study and the data source We present the estimationresults of the dyadic model and ERGM and illustrate howto use the attribute-related network structures to representproduct interdependence that is the endogenous effects Toevaluate the performance of each model Section 5 assessesmodel fit at both the global network level and the local linklevel Section 6 evaluates the performance of each model inpredicting future coconsideration relations Finally Section 7presents practical implications of the findings and directionsfor future research

3 Network Construction and Introduction toNetwork Models

31 Network Construction The product coconsideration net-work is constructed using data from customersrsquo considerationsets The presence of a link (ie coconsideration) betweentwo nodes (ie products) is determined by an associationmetric called lift [47] Equation (1) defines the lift valuebetween products 119894 and 119895 Similar to pointwise mutualinformation [48] lift measures the likelihood of the cocon-sideration of two products given their individual frequenciesof considerations

lif t (119894 119895) = Pr (119894 119895)Pr (119894) sdot Pr (119895) (1)

where Pr(119894 119895) is the probability of a pair of products 119894and 119895 being coconsidered by customers among all pos-sibilities calculated based on the collected considerationdata and Pr(119894) is the probability of individual product 119894being considered The lift value indicates how likely twoproducts are coconsidered by all customers at the aggregatelevel normalized by the product popularity in the entiremarket We use this probability of coconsideration differentfrom market share that is directly determined by the totalpurchases to capture the competition between products

4 Complexity

Product A Product B

Independency assumption

(a)

Product A Product B

Product C

Product D

Interdependency assumption

(b)

Figure 2 Two dependence assumptions underlying the coconsideration network

With the lift value an undirected coconsideration networkcan be constructed using the following binary rule

119864119894119895 =

1 if lif t (119894 119895) ge cutoff

0 otherwise(2)

where cutoff is the threshold to determine the presence of alink 119864119894119895 between two nodes 119894 and 119895 Statistically the lift value1 indicates that two products are completely independent[44] a lift value greater than 1 indicates the two productsare coconsidered more likely than expected by chance Basedon the application context research interest and modelrequirement different lift values greater than 1 can be usedas the cutoff value Equations (1) and (2) suggest that thenetwork adjacency matrix is symmetric and binary In thispaper the research is focused on predicting whether twoproducts would have been coconsidered or notThe extent ofhow often they are coconsidered (reflecting the competitionintensity) is not the research focus of this paper This iswhy we made the decision of using binary network insteadof weighted network Modeling a binary network whilecomputationally simpler is not as rich as the valued networkHence we tested the robustness of our findings by estimatingmultiple models based on varying the cutoff values of lift

32 Research Question in the Network Context Once acoconsideration network is constructed the likelihood ofcustomers considering two products can be formulated as theprobability of a coconsideration link For prediction purposethis leads to the question of what factors (eg productattributes and customer demographics) drive the formationof a link between a pair of nodes and how significantlyeach factor plays a role in the link formation process Theaforementioned research question is recast as how to builda network model to predict whether a coconsideration linkexists given the network structures product attributes andcustomer profiles

We posit that there are two decision-making scenariosunderlying the coconsideration relations The first scenario(Figure 2(a)) assumes that each pair of products is indepen-dently evaluated by customers Even for multiple alternatives

in a consideration set it treats the comparison of eachtwo of these alternatives independent of other pairwisecomparisons The second scenario takes a more generalinterdependence assumption where the formation of onecoconsideration link is not independent of other coconsider-ation links For example in the right diagram of Figure 2 thelikelihood of a coconsideration link between products A andB may be affected by the fact that they are both coconsideredwith product C For the two aforementioned networkmodelsthe dyadic network model takes the simple independenceassumption while the ERGM assumes that all coconsid-eration relations sharing one node are interdependent Inthis paper we will examine whether the ERGM provides amore accurate understanding on the factors driving productcoconsiderations by evaluating the goodness of fit and thepredictability of the two models

33 Introduction to Network Models The dyadic networkmodel is analogous to the standard logistic regressionelement-wise on network matrices where the model is givenby the following

logit [Pr (119884119894119895 = 1)] = 120573X(119899)

= 1205730 + 1205731119883(1)119894119895 + sdot sdot sdot + 120573119899119883(119899)119894119895 (3)

The response 119884119894119895 is the binary links 119864119894119895 between nodes119894 and 119895 defined in (2) The node attributes are convertedto a vector of as dyadic variable X(119899) = (119909(1)119894119895 119909(119899)119894119895 )Each dyadic variable measures the similarity or differencebetween pairs of nodes based on the attributes of nodesand a specific arithmetic function (see Table 1 for variousdyadic variables) The dyadic network models use the dyadicvariables X to predict the complex structures of the observednetwork composed of coconsideration links The coefficients120573 = (1205730 1205731 120573119899) indicate the importance of individualdyadic variable in forming a coconsideration relation Notethat in this model the probability of each link is evaluatedindependently

331 Exponential Random Graph Model Other than thedyadic attribute effects in a network many links connected

Complexity 5

Table 1 Constructing explanatory dyadic attributes

Configuration Statistic Dyadic effects(a) Binary product attributesSum variable 119883119894119895 = 119909119894 + 119909119895 Attribute baseline effectMatching variable 119883119894119895 = 119868 119909119894 = 119909119895 Homophily effect(b) Categorical product attributesMatching variable 119883119894119895 = 119868 119909119894 = 119909119895 Homophily effect(c) Continuous product attributes (standardized)Sum variable 119883119894119895 = 119909119894 + 119909119895 Attribute baseline effectDifference variable 119883119894119895 =

10038161003816100381610038161003816119909119894 minus 11990911989510038161003816100381610038161003816 Homophily effect

(d) Non- product related attributesDistance variable 119883119894119895 =


(i) 119868sdot represents the indicator function (ii) | sdot | represents the absolute-value norm on the 1-dimension space (iii) sdot 2 represents the 1198712-norm on the 119899-dimension Euclidian space

to the same node have endogenous relations That meansthe emergence of a link is often related to other links TheERGM introduced by [49 50] is well known for its capabilityin modeling the interdependence among links in socialnetworks For example two people who have a commonfriend are more likely to be friends with each other tooand therefore the three-person friendship relations form atriangle structure Specific network configurations includingedges stars triangles and cycles can be used to representdifferent types of interdependence The ERGM interpretsthe global network structure as a collective self-organizedemergence of various local network configurationsThe logicunderlying ERGM is that it considers an observed networky as one specific realization from a set of possible randomnetworks Y following the distribution in the followingequation [45]

Pr (Y = y) =exp (120579119879g (y))

120581 (120579) (4)

where 120579 is a vector ofmodel parameters g(y) is a vector of thenetwork statistics and attributes and 120581(120579) is a normalizingquantity to ensure (4) is a proper probability distributionEquation (4) suggests that the probability of observingany particular network is proportional to the exponentof a weighted combination of network characteristics onestatistic 119892(119910) is more likely to occur if the corresponding120579 is positive Note that in ERGM the network itself is arandom variable and the probability is evaluated on theentire network instead of a link as in (3) for dyadic modelsIn brief the advantages of using ERGM in the context ofproduct coconsideration are threefold (1) using networkconfigurations to characterize the endogenous effects amongcoconsideration links (2) providing various dyadic variablesto model different types of exogenous impacts of the productattributes and (3) integrating both exogenous attribute effectsand endogenous network effects in a unified framework

332 Exogenous Dyadic Variables and Endogenous NetworkEffects The exogenous dyadic variables used both in thedyadic model and in ERGM allow the modeling of two types

of effects between a pair of nodes with specific variables thebaseline effects of the attributes and the homophily effectsthat is the similarity or difference between the attributes oftwo nodes [44 51] In the context of the product coconsider-ation network the baseline effects examine whether productswith a specific attribute are more likely to be coconsideredthan products without that attribute for example importedcar models could be more likely to be coconsidered ascompared to domestic car models The homophily effectsexamine whether two products with similar attributes tend tohave a coconsideration link For example customers aremorelikely to consider and compare products with similar pricesThe development of dyadic variables supports the study ofinherent product competition beyond the understanding ofcustomer preferences

Table 1 summarizes the guidelines of creating dyadic vari-ables for different types of attributes such as binary categori-cal and continuous For the product attributes under (a)ndash(c)the strength of link 119883119894119895 is determined by the correspondingattributes 119909119894 and 119909119895 associated with the linked productsBeyond product attributes we also introduce nonproductrelated attributes (d) For example customer demographicscan be included in the model to allow the prediction ofthe impact of customersrsquo associationssimilarities on prod-uct coconsideration relations To create a dyadic variablesrelated to customersrsquo attributes multivariable associationtechniques for example joint correspondence analysis (JCA)[52] have been used to compute the similarity of thecustomer-related attributes as the distance between twoproduct points (119909119894 and 119909119895) in a metric space In this paperwe follow the method presented in [53] to develop twocategories of distance variables the distance of customerperceived characteristics and demographic distance Thecustomer perceived characteristics are user-proposed tags toindicate their perceptions of the products such as youthfulsophisticated and business-oriented Customer demograph-ics include income and family information of the usergroups of each of the car models The inclusion of customerassociations through these distance-based dyadic variables isa unique feature of our network-modeling approach

6 Complexity

Table 2 Representative network characteristics of the generated coconsideration network

Number of nodes Number of links Average degree Average path length Average local cluster coefficient389 2431 125 334 026

Star (degree)

middot middot middot

(a)

Triangle (edgewise shared partner)

(b)

Figure 3 Two network configurations of coconsideration relations

Different from the dyadic models that can only considerexogenous dyadic effects the ERGM supports the modelingof product interdependence with endogenous network effectsIn this paper we are particularly interested in two networkconfigurations the star-type interdependence and triangle-type interdependence [1] The star structures (Figure 3(a))indicate that the probability of one focal product beingcoconsidered with others is conditional on the number ofexisting coconsideration relations of that focal product (egthe node on the top in the figure has three coconsiderationlinks) A positive star effect suggests that a product is morelikely to be coconsidered with another product if it is popularand already being coconsidered with many others Thetriangle structures (Figure 3(b)) indicate that if two productsare coconsidered with the same set of other products theyare more likely to be mutually coconsidered Positive stareffects could include stars with varying number of links (suchas 2 3 4 5 and perhaps many more) Likewise a linkcould have many triangles by linking with varying numberof nodes (1 2 3 4 5 and perhaps many more) Both starand triangular effects imply multiway product competitionTo combine the effects of stars with multiple links andmultiple triangles we use two network configurations thegeometrically weighted degrees and the geometrically weightededgewise shared partner respectively [54]

4 Case Study Modeling VehicleCoconsideration Network

41 Application Context and Data Source When consideringand purchasing a vehicle customers make decisions on carmodels (eg Ford Fusion versus Honda Accord) in partbased on their preferences for vehicle attributes (eg pricepower and make) and their demographics (eg incomeand age) To understand the effects of these factors onvehiclesrsquo coconsideration relations we use data from a buyersurvey in the 2013 China automarket The dataset consistsof about 50000 new car buyersrsquo responses to approximately400 unique vehicle models The survey covered a varietyof questions including respondent demographics vehicleattributes and customersrsquo perceived vehicle characteristicsThe respondents reported the car they purchased as well

as the primary and secondary alternatives they consideredbefore making the final purchase These responses are usedto construct the vehicle coconsideration networkThe vehicleattributes reported in the survey are verified by vehicle catalogdatabases

42 Vehicle Coconsideration Network Following the methoddiscussed in Section 31 we construct a vehicle coconsider-ation network with cutoff = 5 which results in a network of389 nodes and 2431 binary links A smaller cutoff generatesa denser network but has similar analytical results We havetested our models using cutoff at 1 3 5 and 7 respectivelyand no significant changes in the trends of the model resultsare observed Figure 4 shows an example of a partial vehiclecoconsideration network with 11 car models The node sizeis proportional to the degree and colors indicate the clustersin which the vehicles are more likely to be coconsidered witheach otherThenumber on each link is the lift value indicatingthe strength of the coconsideration

Table 2 summarizes some descriptive network charac-teristics For example the average degree suggests that onaverage each vehicle has 125 coconsidered vehicles andindicates the overall intensity of competition in the marketThe clustering coefficient (CC) on the other hand measuresthe cohesion or segmentation of the vehicle market [44]The average local CC at values of 026 indicates the strongcohesion embedded in the network and vehicle models arefrequently involved in multiway competition in the marketThedescriptive network analysis facilitates the understandingof the automarket and provides guidelines on the selection ofnetwork configurations in ERGM

43 Descriptive Statistics of the Independent Dyadic VariablesMany exogenous dyadic variables related to vehicle attributessuch as the difference and sum variables of car pricesengine power fuel consumption and matching variables ofvehiclersquos market segments and make origin could changethe patterns of coconsideration among the vehicle modelsWe use information gain analysis to select 12 most importantdyadic variables among all 22 possible dyadic variables Thelog transformation (base 2) is applied to the price and enginepower variables to offset the effect of large outliers Table 3shows the descriptive statistics of the independent variables

In total six vehicle attributes import price engine powerfuel consumption market segment and vehiclesrsquo make originare considered in the model Import is a binary variabledescribing whether a car is imported (import = 1 373) ordomestically produced (import = 0 627) As suggestedin Table 1 and Section 332 we construct a sum dyadicvariable of import to account for its baseline effect of whethereach of the paired cars is both imported (value 2 for 1390of the pairs) one imported and one domestic (value 1 for4676) or both domestic (value 0 for 3934) If the baseline

Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6

Honda Guangzhou Accord

GM SGM Chevrolet Malibu

Ford Changan Focus Classic

Mazda Changan 3

GM SGM Chevrolet Cruze

New Ford Changan Focus

12

19

76

3862

1311

19

14

22

24

28

1933

24

29

Figure 4 An example of partial vehicle coconsideration network

Table 3 Descriptive statistics of independent variables for 389 car models in 2013

Mean (SD) Min MaxVehicle attributesImport (binary) 145 import amp 244 domesticPrice (log2) 1761 (134) 1450 2084Power (log2) 727 (058) 525 876Fuel consumption (per 100 BHP) 661 (162) 299 1856Market segment (categorical) 17 car segments

Make origin (categorical) 13 American 22 American-Chinese 98 Chinese 90 European 50European-Chinese 31 Japanese 54 Japanese-Chinese 11 Korean 20 Korean-Chinese

Vehicle attribute matching and differenceMarket segment matching 101 pairs of cars coconsidered are in the same segmentMake origin matching 165 pairs of cars coonsidered have the same make originPrice (log2) difference 153 (112) 0 634Power (log2) difference 066 (049) 0 351Fuel consumption difference 171 (152) 0 1558Customer associationDistance of customersrsquo perceived characteristics 020 (013) 0 1Distance of customersrsquo demographics 027 (016) 0 1

effect of the import attribute is positive the coefficient ofthe sum variable of import should be positive as well thatis the higher the sum value of the two car models themore likely they are coconsidered together Similarly the sumvariables of price (in RMB and transformed using log2) andpower (in brake horsepower BHP and transformed usinglog2) describe the baseline effects of price and power onproduct coconsideration relations We construct a variable

fuel consumption by dividing liters of gasoline each vehicleconsumed per 100 kilometers over vehicle power (in 100BHP) As such the smaller this value is the more fuel-efficient the car model is The difference variables of pricepower and fuel consumption capture the homophily effectswhich are used to test if the car models with similar attributes(smaller differences) are more likely to be coconsideredtogether

8 Complexity

Table 4 Estimated coefficients and odds ratios of the dyadic model and ERGM

Input variables Dyadic Model ERGMEst coef Odds Est coef Odds

Network configurations of product interdependenceEdgeIntercept minus1436lowastlowast 000 minus1371lowastlowast 000Star effect (inverse measure) 197lowastlowast 720Triangle effect 070lowastlowast 201Baseline effects of vehicle attributesImport 037lowastlowast 145 011lowastlowast 111Price (log2) minus002 098 minus0007 101Power (log2) 068lowastlowast 197 035lowastlowast 142Fuel consumption (per 100 BHP) 019lowastlowast 121 012lowastlowast 113Homophily effects of vehicle attribute matching and differenceMarket segment matching 138lowastlowast 398 066lowastlowast 194Make origin matching 128lowastlowast 360 053lowastlowast 169Price difference (log2) minus175lowastlowast 017 minus080lowastlowast 045Power difference (log2) 008 109 013 114Fuel consumption difference minus008lowast 092 minus007lowastlowast 093Homophily effects of customer associationDistance of customersrsquo perceived characteristics minus042 066 minus031 074Distance of customersrsquo demographics minus057lowastlowast 056 minus037lowast 069Model performanceNull deviance 104618Bayesian Information Criterion (BIC) 16005 14021Note lowast119901-value lt 001 lowastlowast119901-value lt 0001

The autoindustry is very competitive so most car modelshave very clearly targeted customers and compete in aspecific market segment Since vehiclersquos market segment isa categorical variable we use a dyadic matching variable inthe model to investigate whether two cars from the samesegment would affect their coconsideration patterns The top3 in all 17 segments in our sample are the C-Class Sedan(216 of car models) B-Class Sedan (113) and SmallUtility (111) Similarly make origin is also a categoricalvariable and it describes the region where the car brandoriginates Our dataset shows that 90 31 11 and 13 carmodelsare made in Europe Japan South Korea and the UnitedStates respectively 98 car models are produced in Chinawith local brands and other local-foreign joint venture brandscome fromEurope (50) Japan (54) SouthKorea (20) and theUnited States (22)Thematching variables ofmarket segmentsand make origins are used to account for peoplersquos homophilybehavior of comparing cars with the same brand and origin

44 Model Implementation Using ERGM Table 4 shows theestimated coefficients and corresponding odds ratios fromfitting the dyadic and ERGM models Other than the vari-ables described above the ERGM includes three additionalvariables associated with network configurations The edgevariable controls the number of links to ensure the estimatednetworks have the same density as the observed one Con-ceptually if we have no knowledge about the carsrsquo attributesor their coconsideration relations the edge estimates thelikelihood that two cars will be coconsidered randomly like

an intercept term in a regression or a ldquobase raterdquo The stareffect and triangle effect discussed in Section 332 are mea-sured by geometrically weighted degree and the geometricallyweighted edgewise shared partner respectively According tothe results of the ERGM most vehicle attributes except theprice baseline effect and power difference are statisticallysignificant (119901 value lt 0001) and therefore play importantroles in vehicle coconsideration For instance two vehicleswith smaller differences in price and fuel consumption aremore likely to be coconsidered If the price of one car modelis twice the price of another car their odds of coconsiderationare only 45 of the odds of two cars with the same priceSimilarly one liter per 100 km per 100 BHP difference in fuelconsumption leads to 93 of the odds of coconsiderationcompared to the cars with the same fuel consumption Forthe matching of vehicle attributes two vehicles in the samemarket segment are 194 timesmore likely to be coconsideredthan the ones in different segments and two vehicles with thesame make origin are 169 times more likely to be coconsid-ered than the ones with different origins Finally the negativecoefficient for the distance of customersrsquo demographics showsthat customers with different demographics are less likely tococonsider the same vehicle In summary the results showthat customers are more likely to consider cars with similarperceived features such as price fuel consumption marketsegment and make origin

As shown in Table 4 the coefficient of the triangle effectis 070 (119901 value lt 0001) The positive sign indicates thattwo vehicles coconsidered with the same set of vehicles

Complexity 9

are more likely to be coconsidered with each other Itimplies that a form of multiway grouping and comparisonexists in customersrsquo consideration decisions That is productalternatives in a personrsquos consideration set are considered asthe same time On the other hand the positive coefficient ofthe star effect (inversely measured by geometrically weighteddegree) indicates that most of the cars tend to have a similarnumber of coconsideration links and there is an absence of afew cars that are much more likely to be coconsidered thanothers With these endogenous network effects the ERGMsignificantly improves the model fit compared to the dyadicmodel as indicated by the improvement of BIC from 16005to 14021 In the next section we perform a systematic com-parative analysis to evaluate how well the simulated networksmatch the observed vehicle coconsideration network

5 Model Comparison on Goodness of Fit

A goodness of fit (GOF) analysis is performed to comparethe model fit of dyadic and ERGM models Using the dyadicand ERGM models in (3) and (4) respectively and basedon the estimated parameters in Table 4 we compute thepredicted probabilities of coconsideration between all pairs ofvehicle models The links with predicted probabilities higherthan a threshold (eg 05) are considered as links that existOnce the simulated networks are obtained from bothmodelswe compare them against the observed 2013 coconsiderationnetwork at both the network level and the link level Thenetwork-level evaluation uses the spectral goodness of fit(SGOF) metric [55] while the link level evaluation usesvarious accuracy measurements such as precision recall andF scores (see Section 52 for more details)

51 Network-Level Comparison Spectral goodness of fit(SGOF) is computed as follows

SGOF = 1 minus ESDobsfitted

ESDobsnull (5)

where ESDobsfitted is the mean Euclidean spectral distancefor the fitted model while ESDobsnull is the mean Euclideanspectral distance for the null model that is the ErdosndashRenyi(ER) random network in which each link has a fixed prob-ability of being present or absent Hence SGOF measuresthe amount of the observed structures explained by a fittedmodel expressed as a percent improvement over a nullmodel The Euclidean spectral distance computes the 1198712norm (also called Euclidean norm) of the error between theobserved network and all 119896 simulated networks that is 120598119896where error 120598 is the absolute difference between the spectraof the observed network (

obs) and that of the simulated

network (sim

) that is |obs minus sim| Since the calculationof the spectra requires eigenvalues of the entire networkrsquosadjacent matrix this evaluation is performed at the networklevel When the fitted model exactly describes the dataSGOF reaches its maximum value 1 SGOF of zero means noimprovement over the null modelThe SGOFmetric providesan overall comparison of different models It is especially

Table 5 Spectral goodness of fit results of the dyadic model andERGM

Dyadic model ERGMMean SGOF(5th percentile95th percentile)

037 (031 043) 063 (048 076)

useful when a modeler is not clear about which networkstructural statistics are important in explaining the observednetwork For example in our coconsideration network itis hard to tell which network metrics such as the averagepath length or the average CC are more important to theunderstanding of market structure Under this circumstancethe SGOF provides a simple yet comprehensive evaluationTable 5 lists the SGOF scores of both dyadic model and theERGM Based on 1000 predicted networks from each modelthe results of the mean 5th and 95th percentile of SGOFshow that the ERGM significantly outperforms the dyadicmodel

52 Link-Level Comparison In addition to the network-levelcomparison the predicted networks are also evaluated at thelink level We define a pair of vehicles with a coconsiderationrelation as positive whereas the oneswithout links as negativeTherefore the true positive (TP) is the number of links pre-dicted as positive and also positive in the observed networkthe false positive (FP) is the number of links predicted aspositive but actually negative that is wrong predictions ofpositives Similarly the true negative (TN) is the number oflinks predicted as negative and observed as negative the falsenegative (FN) is the number of links predicted as negative butobserved as positive Taking 05 as the threshold of predictedprobability (as it is used in the logistic function) we calculatethe following three metrics to evaluate the performance ofprediction for both dyadic model and ERGM Precision isthe fraction of true positive predictions among all positivepredictions recall is the fraction of true positive predictionsover all positive observations F score is the harmonic meanof precision and recall (see Table 6 for the formulas) Thesemetrics are adopted because each of them reflects the capa-bility of the model from different perspectives It could be thecase where the model predicts many links (eg all links arepredicted in extreme cases andFP is high) so that the precisionis low and the recall is high while another model couldpredict very few links that leads to high FN and therefore highprecision and low recall Therefore using either precision orrecall only practically reveals the model performance HenceF score is often recommended as a fair measure because itconsiders both precision and recall and provides an averagescore In this study we use all three metrics together toprovide a complete picture of the model performance

As shown in Table 6 almost all performance metrics sug-gest that ERGM outperforms the dyadic model In particularthe recall of ERGM is significantly higher than that of thedyadic model The dyadic model is only able to predict about42 of coconsideration whereas the recall of the ERGMreach 311These results imply that the inclusion of product

10 Complexity

Table 6 Results of various metrics for link-level comparison(predicted links based on threshold at 05)

Metrics Dyadic model ERGM

Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311

119865120573 =(1 + 1205732) times Precision times Recall(1205732 times Precision + Recall)

11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall

Figure 5The precision-recall curve of the dyadicmodel and ERGMwith random network benchmarked

interdependence in ERGM indeed improves the model fitand better explains the observed product coconsiderationrelations The only metric for which the dyadic model has abetter value is the precision At the threshold of probabilityequal to 05 the dyadic model only predict 170 links aspositive in total and 101 of them are correct The smalldenominator in the precision formula that is TP + FP = 170produces a larger precision

Since different thresholds of the predicted probabilitycan affect the value of precision and recall we evaluate theprecision-recall curve [56] by altering the threshold from 0to 1 to get a more comprehensive understanding The modelthat has a larger area under the curve (AUC) performs better[57] When evaluating binary classifiers in an imbalanceddataset (withmanymore cases of one value for a variable thanthe other) which is the case we face Saito and Rehmsmeier[57] have demonstrated that the precision-recall curve is moreinformative than other threshold curves such as the receiveroperating characteristic (ROC) curve Figure 5 shows that forany given recall value the precision of ERGM is strictly higherthan that of the dyadic model and the ERGM outperformsthe dyadic model in the full spectrum of the threshold of

Year 2013 Year 20146

7

1 5

4

32

1 5

32

Figure 6 Illustration of the evolution of the coconsiderationnetwork

probability (we studied the ROC curve and drew the sameconclusions)

In summary the comparisons at both the network leveland the link level validate our hypothesis that the productinterdependence that is the endogenous effect plays asignificant role in the formation of product coconsiderationrelations and hence the customersrsquo consideration decisionsIn the next section we examine the predictive power of thetwo models

6 Model Comparison on Predictability

In this section we take a further step to compare the twomodels in terms of the predictability We use the modelsdeveloped with the 2013 dataset (ie the model coefficientsshown in Table 4) to predict the vehicle coconsiderationrelations in the 2014 market From an illustrative examplein Figure 6 we can see that some car models (eg node 4)withdrew from the market in 2014 some new car models(eg node 6 and node 7) were introduced to the market butmost of the car models (eg nodes 1 2 3 and 5) remainedin the 2014 market In this paper we focus on predicting thefuture coconsiderations among the overlapping carmodels intwo consecutive years since the new models may introducecritical features not captured in the previous market suchas electric cars In our study 315 car models were availablein both 2013 and 2014 Therefore the task here is to predictwhether each pair of cars among these 315 car models willbe coconsidered in 2014 given their new vehicle attributesin 2014 the new customer demographics existing marketcompetition structures (The market competition structureis captured by the model coefficients of the three networkconfigurations including the edge star effect and triangleeffect discussed in Section 44) and the model coefficientsestimated based on the 2013 data

Most pairs of cars have the same dyadic status (iecoconsidered or not) in 2013 and 2014 For example iftwo car models were not coconsidered in 2013 customerscontinued to not coconsider these two in 2014 This caseis not of interest because predicting nonexistence is mucheasier due to the imbalance nature of the network datasetand it does not provide new insights Similarly the persistentcoconsideration in both 2013 and 2014 is also expectedTherefore we focus on changes in two prediction scenariosemergence and disappearance of coconsideration links from2013 to 2014 As shown in Table 7 among 47724 pairs ofcars that were not coconsidered in 2013 1202 pairs wereconsidered in 2014 The event of changing from not being

Complexity 11

Table 7 Prediction scenarios of interest

Prediction scenarios Year 2013 Year 2014 Events of interest

Emergence of coconsideration 47724 pairs of cars not coconsidered 1202 pairs of new coconsideration Yes46522 no change No

Disappearance of coconsideration 1731 pairs of cars coconsidered 1087 pairs no longer coconsidered Yes644 no change No

Table 8 The prediction precision and recall at the threshold of 05 in two prediction scenarios

Predictionscenarios Model

Number of eventsof interest (TP +

FN)

Number ofpredictions (TP

+ FP)

Number ofcorrect

predictions (TP)

Predictionprecision Prediction recall Prediction

1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758

coconsidered to being coconsidered indicates the changeof market competition potentially caused by the change ofvehicle attributes such as prices On the other hand 1731pairs of cars were coconsidered in 2013 among the 315 carmodels but 1087 pairs were no longer coconsidered in 2014We indicate the two cases in the last column of Table 7where the predictions of 2014 network using 2013 modelare the events of interest The two ldquoYesrdquo cases predictingemerging coconsideration and disappearing coconsiderationlinks both represent the change of coconsideration statusfrom 2013 to 2014 and are the positive outcomes of modelpredictions Such predictions are more difficult (yet substan-tively more useful) to attain than the other two ldquoNordquo casesof nochange By testing both the dyadic and ERGM modelswe examine which model had better predictive capabilityassuming that the driving factors and customer preferencesof coconsideration characterized by the model coefficients inTable 4 are unchanged from 2013 to 2014

In both prediction scenarios we input the new valuesof vehicle attributes and customer profile attributes from2014 into the model When using ERGM characteristics ofnetwork configurations calculated based on the 2013 data alsoserved as inputs for prediction Once the models predictthe probability of each pair of car models we evaluate theperformance metrics separately in two scenarios (1) theprecision and recall of predicting emerging coconsiderationamong the 47724 pairs of not coconsidered car models and(2) the precision and recall of predicting the disappearanceof coconsideration among 1731 pairs of cars coconsidered in2013 The precision and recall of predictions are calculatedsimilarly to the ones used in Section 52 The precisionscore is the ratio of the number of correctly predicted links(such as corrected prediction of emerging coconsideration ordisappeared coconsideration) over the number of predictionsa model makes The recall score is the ratio of the numberof correctly predicted links over the number of eventsof interest (true emerging coconsideration or disappearedcoconsideration in 2014)

Table 8 shows the results of the prediction precision andrecall calculated based on the predicted probability of 05as the threshold in the two scenarios To predict emergingcoconsideration the ERGM had much better performancethan the dyadicmodel Specifically the dyadicmodel tends tobe overtrained based on vehicle attributes and only predicts asmall set of most likely links that is 9 of the 1202 emergingnew coconsideration relations On the other hand the ERGMpredicted 111 (more than ten times) emerging coconsiderationwith the same precision With the probability threshold of05 the ERGM and dyadic model had similar differencesin performance in predicting disappearing coconsiderationlinks Figure 7(b) shows that ERGM outperforms the dyadicmodel in almost all points of the precision-recall curve Infact the PR curves (Figure 7) show that ERGM at the entirerange of the threshold outperforms the dyadic model in bothprediction scenarios

Therefore we conclude that the ERGM has better pre-dictability than the dyadic model In addition to the GOF fit-ness test the prediction test described above further validatesour hypothesis that taking interdependencies in networkmodeling better explains the coconsideration network In thisparticular case study the analyses performed in both GOFand prediction analyses indicate that vehiclesrsquo coconsidera-tion relations are influenced by their existing competitions inthe market

7 Closing Comments

In this paper we propose a network-based approach to studycustomer preferences in consideration decisions Specificallywe apply the lift associationmetric to convert customersrsquo con-siderations into a product coconsideration network in whichnodes present products and links represent coconsiderationrelations between productsWith the created coconsiderationnetworks we adopt two network models the dyadic modeland the ERGM to predict whether two products wouldhave a coconsideration relation or not Using vehicle design

12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on

(a) Predict emerging coconsideration

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision

(b) Predict disappeared coconsideration

Figure 7 Prediction PR curves of dyadic model and ERGM in two prediction scenarios

as a case study we perform systematic studies to identifythe significant factors influencing customersrsquo coconsiderationdecisions These factors include vehicle attributes (pricepower fuel consumption import make origin and marketsegment) the similarity of customer demographics and exist-ing competition structures (ie the interdependence amongcoconsideration choices captured by network configurations)Statistical regressions are performed to obtain the estimatedparameters of both models and comparative analyses areperformed to evaluate the modelsrsquo goodness of fit andpredictive power in the context of vehicle coconsiderationnetworks Our results show that the ERGM outperforms thedyadic model in both GOF tests and the prediction analysesThis paper makes two contributions relevant to engineeringdesign (a) a rigorous network-based analytical frameworkto study product coconsideration relations in support ofengineering design decisions and (b) a systematic evaluationframework for comparing different network-modeling tech-niques using GOF and prediction precision and recall

This study provides three practical insights on coconsid-eration behavior in China automarket First the customersare price-drivenwhen considering potential carmodels Bothmodels suggest significant homophily effects of vehicle pricesand customer demographics in forming coconsiderationlinks that is car models with similar prices and targetingto similar demographics such as income and family size aremore likely to be considered in the same consideration setHowever the ERGM reveals much more influential driverssuch as the homophily effects of car segments and makeorigins These findings confirm the internal clusters in theautomarket Second the ERGMmodel suggests that there are

significantly fewer star structures but much more trianglesin the coconsideration network Beyond the impacts of thevehicle and customer attributes ERGM also illustrates thatcarmodels that received an equal amount of consideration arelikely to get involved in multiway coconsiderationThird themodel comparisons based on the GOF and prediction anal-yses demonstrate that an ERGM approach which capturesthe interdependence of coconsideration helps improve theprediction of product coconsiderations

Finally having an analytical model in this applicationcontext could boost future explorations including the whatif scenario analysis that aims to forecast market responsesunder different settings of existing product attributes asdemonstrated in [44] Since ERGM has a better model fitand predictability it will helpmakemore accurate projectionson the future market trends and aid the prioritization ofproduct features in satisfying customersrsquo needs as well assupport engineering design andproduct development Futureresearch should extend the network approach to a longitudi-nal weighted network-modeling framework which not onlypredicts the existence of a link but also the strength of thecoconsideration between carmodels in subsequent yearsTheweighted network models would help discover the nuance indifferent customersrsquo consideration sets and therefore providemore insights into product design and market forecasting

Disclosure

An early version of part of this workwas presented in the 2017International Conference on Engineering Design [58]

Complexity 13

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper Funding sourcesmentioned in Acknowledgments do not lead to any conflictsof interest regarding the publication of this manuscript

Acknowledgments

The authors gratefully acknowledge the financial supportfrom NSF CMMI-1436658 and Ford-Northwestern AllianceProject

References

[1] G Robins T Snijders P Wang M Handcock and P PattisonldquoRecent developments in exponential random graph (p) mod-els for social networksrdquo Social Networks vol 29 no 2 pp 192ndash215 2007

[2] M Wang W Chen Y Huang N S Contractor and Y Fu ldquoAMultidimensional Network Approach for Modeling Customer-Product Relations in Engineering Designrdquo in Proceedings ofthe ASME 2015 International Design Engineering TechnicalConferences and Computers and Information in EngineeringConference American Society ofMechanical Engineers BostonMassachusetts USA 2015

[3] P Wang G Robins P Pattison and E Lazega ldquoExponentialrandomgraphmodels formultilevel networksrdquo SocialNetworksvol 35 no 1 pp 96ndash115 2013

[4] M E Sosa S D Eppinger and C M Rowles ldquoA networkapproach to define modularity of components in complexproductsrdquo Journal ofMechanical Design vol 129 no 11 pp 1118ndash1129 2007

[5] M Sosa J Mihm and T Browning ldquoDegree distribution andquality in complex engineered systemsrdquo Journal of MechanicalDesign vol 133 no 10 Article ID 101008 2011

[6] E Byler ldquoCultivating the growth of complex systems usingemergent behaviours of engineering processesrdquo in Proceedingsof the in International conference on complex systems control andmodeling Russian Academy of Sciences 2000

[7] N Contractor P RMonge and P Leonardi ldquoMultidimensionalnetworks and the dynamics of sociomateriality Bringing tech-nology inside the networkrdquo International Journal of Communi-cation vol 5 pp 682ndash720 2011

[8] P Cormier E Devendorf and K Lewis ldquoOptimal processarchitectures for distributed design using a social networkmodelrdquo in Proceedings of the ASME 2012 International DesignEngineering Technical Conferences and Computers and Informa-tion in Engineering Conference IDETCCIE 2012 pp 485ndash495USA August 2012

[9] W Chen C Hoyle and H J Wassenaar ldquoDecision-baseddesign Integrating consumer preferences into engineeringdesignrdquo Decision-Based Design Integrating Consumer Prefer-ences into Engineering Design pp 1ndash357 2013

[10] J J Michalek F M Feinberg and P Y Papalambros ldquoLink-ing marketing and engineering product design decisions viaanalytical target cascadingrdquo Journal of Product InnovationManagement vol 22 no 1 pp 42ndash62 2005

[11] Z Sha K Moolchandani J H Panchal and D A DeLaurentisldquoModeling Airlinesrsquo Decisions on City-Pair Route Selection

Using Discrete Choice Modelsrdquo Journal of Air Transportationvol 24 no 3 pp 63ndash73 2016

[12] Z Sha and J H Panchal ldquoEstimating local decision-makingbehavior in complex evolutionary systemsrdquo Journal of Mechan-ical Design vol 136 no 6 Article ID 061003 2014

[13] M Wang and W Chen ldquoA data-driven network analysisapproach to predicting customer choice sets for choice mod-eling in engineering designrdquo Journal of Mechanical Design vol137 no 7 Article ID 71409 2015

[14] Z Sha and J H Panchal ldquoEstimating linking preferencesand behaviors of autonomous systems in the internet usinga discrete choice modelrdquo in Proceedings of the 2014 IEEEInternational Conference on Systems Man and CyberneticsSMC 2014 pp 1591ndash1597 usa October 2014

[15] J Hauser M Ding and S P Gaskin ldquoNon-compensatory(and compensatory) models of consideration-set decisionsrdquoin Proceedings of the in 2009 Sawtooth Software ConferenceProceedings Sequin WA 2009

[16] A D Shocker M Ben-Akiva B Boccara and P NedungadildquoConsideration set influences on consumer decision-makingand choice Issues models and suggestionsrdquoMarketing Lettersvol 2 no 3 pp 181ndash197 1991

[17] J R Hauser and B Wernerfelt ldquoAn Evaluation Cost Model ofConsideration Setsrdquo Journal of Consumer Research vol 16 no4 p 393 1990

[18] P Nedungadi ldquoRecall and Consumer Consideration Sets Influ-encing Choice without Altering Brand Evaluationsrdquo Journal ofConsumer Research vol 17 no 3 p 263 1990

[19] R K Srivastava M I Alpert and A D Shocker ldquoA Customer-Oriented Approach for Determining Market Structuresrdquo Jour-nal of Marketing vol 48 no 2 p 32 1984

[20] S Frederick Automated choice heuristics[21] W Shao Consumer Decision-Making An Empirical Exploration

of Multi-Phased Decision Processes Griffith University Aus-tralia 2006

[22] M Yee E Dahan J R Hauser and J Orlin ldquoGreedoid-basednoncompensatory inferencerdquo Marketing Science vol 26 no 4pp 532ndash549 2007

[23] J RHauser O Toubia T Evgeniou R Befurt andDDzyaburaldquoDisjunctions of conjunctions cognitive simplicity and consid-eration setsrdquo Journal of Marketing Research vol 47 no 3 pp485ndash496 2010

[24] T J Gilbride and G M Allenby ldquoEstimating heterogeneousEBA and economic screening rule choice modelsrdquo MarketingScience vol 25 no 5 pp 494ndash509 2006

[25] R L Andrews and T C Srinivasan ldquoStudying considerationeffects in empirical choice models using scanner panel datardquoJournal of Marketing Research vol 32 no 1 p 30 1995

[26] J Chiang S Chib and C Narasimhan ldquoMarkov chain MonteCarlo and models of consideration set and parameter hetero-geneityrdquo Journal of Econometrics vol 89 no 1-2 pp 223ndash2481998

[27] T Erdem and J Swait ldquoBrand credibility brand considerationand choicerdquo Journal of Consumer Research vol 31 no 1 pp 191ndash198 2004

[28] J Swait ldquoA non-compensatory choice model incorporatingattribute cutoffsrdquo Transportation Research Part B Methodologi-cal vol 35 no 10 pp 903ndash928 2001

[29] T J Gilbride and G M Allenby ldquoA choice model withconjunctive disjunctive and compensatory screening rulesrdquoMarketing Science vol 23 no 3 pp 391ndash406 2004

14 Complexity

[30] E Boros P L Hammer T Ibaraki A Kogan E Mayoraz and IMuchnik ldquoAn implementation of logical analysis of datardquo IEEETransactions on Knowledge and Data Engineering vol 12 no 2pp 292ndash306 2000

[31] M Ding ldquoAn incentive-aligned mechanism for conjoint analy-sisrdquo Journal of Marketing Research vol 44 no 2 pp 214ndash2232007

[32] Z Sha V SaegerMWang Y Fu andW Chen ldquoAnalyzing Cus-tomer Preference to Product Optional Features in SupportingProduct Configurationrdquo SAE International Journal of Materialsand Manufacturing vol 10 no 3 2017

[33] K Eliaz and R Spiegler ldquoConsideration sets and competitivemarketingrdquo Review of Economic Studies vol 78 no 1 pp 235ndash262 2011

[34] P Resnick and H R Varian ldquoRecommender systemsrdquo Commu-nications of the ACM vol 40 no 3 pp 56ndash58 1997

[35] G Adomavicius and A Tuzhilin ldquoToward the next generationof recommender systems A survey of the state-of-the-art andpossible extensionsrdquo IEEE Transactions on Knowledge and DataEngineering vol 17 no 6 pp 734ndash749 2005

[36] T Zhoua Z Kuscsik J Liu M Medo J R Wakeling and YZhang ldquoSolving the apparent diversity-accuracy dilemma ofrecommender systemsrdquo Proceedings of the National Acadamy ofSciences of the United States of America vol 107 no 10 pp 4511ndash4515 2010

[37] F Yu A Zeng S Gillard and M Medo ldquoNetwork-basedrecommendation algorithms a reviewrdquo Physica A StatisticalMechanics and its Applications vol 452 pp 192ndash208 2016

[38] L Lu M Medo C H Yeung Y Zhang Z Zhang and T ZhouldquoRecommender systemsrdquo Physics Reports vol 519 no 1 pp 1ndash49 2012

[39] T Zhou J Ren M Medo and Y Zhang ldquoBipartite networkprojection and personal recommendationrdquo Physical Review EStatistical Nonlinear and Soft Matter Physics vol 76 no 4Article ID 046115 2007

[40] M J Pazzani and D Billsus ldquoContent-based recommendationsystemsrdquo in The Adaptive Web Methods and Strategies of WebPersonalization P Brusilovsky A Kobsa and and W NejdlEds pp 325ndash341 Springer Berlin Germany 2007

[41] D M Blei A Y Ng and M I Jordan ldquoLatent Dirichletallocationrdquo Journal ofMachine Learning Research vol 3 no 4-5pp 993ndash1022 2003

[42] A Fiasconaro M Tumminello V Nicosia V Latora and RN Mantegna ldquoHybrid recommendation methods in complexnetworksrdquo Physical Review E Statistical Nonlinear and SoftMatter Physics vol 92 no 1 Article ID 012811 2015

[43] J S Fu et al ldquoModeling Customer Choice Preferences inEngineering Design Using Bipartite Network Analysisrdquo inProceedings of the in 2017 ASME International Design Engi-neering Technical Conferences amp Computers and Information inEngineering Conference ASME Cleveland OH USA 2017

[44] M Wang Z Sha Y Huang N Contractor Y Fu andW Chen ldquoForecasting technological impacts on customersrsquoco-consideration behaviors A data-driven network analysisapproachrdquo in Proceedings of the ASME 2016 InternationalDesign Engineering Technical Conferences and Computers andInformation in Engineering Conference IDETCCIE 2016 USAAugust 2016

[45] GRobins P Pattison YKalish andD Lusher ldquoAn introductionto exponential random graph (p) models for social networksrdquoSocial Networks vol 29 no 2 pp 173ndash191 2007

[46] M Shumate and E T Palazzolo ldquoExponential random graph(p) models as a method for social network analysis in commu-nication researchrdquo Communication Methods and Measures vol4 no 4 pp 341ndash371 2010

[47] S Tuffery ldquoData Mining and Statistics for Decision MakingrdquoData Mining and Statistics for Decision Making 2011

[48] K W Church and P Hanks ldquoWord association norms mutualinformation and lexicographyrdquo Computational linguistics vol16 no 1 pp 22ndash29 1990

[49] O Frank and D Strauss ldquoMarkov graphsrdquo Journal of theAmerican Statistical Association vol 81 no 395 pp 832ndash8421986

[50] S Wasserman and P Pattison ldquoLogit models and logisticregressions for social networks I An introduction to markovgraphs and prdquo Psychometrika vol 61 no 3 pp 401ndash425 1996

[51] M McPherson L Smith-Lovin and J M Cook ldquoBirds ofa feather homophily in social networksrdquo Annual Review ofSociology vol 27 pp 415ndash444 2001

[52] M Greenacre Correspondence analysis in practice CRC press2017

[53] M Wang et al ldquoA Network Approach for Understanding andAnalyzing Product Co-Consideration Relations in EngineeringDesignrdquo in Proceedings of the DESIGN 2016 14th InternationalDesign Conference 2016

[54] D R Hunter ldquoCurved exponential family models for socialnetworksrdquo Social Networks vol 29 no 2 pp 216ndash230 2007

[55] J Shore and B Lubin ldquoSpectral goodness of fit for networkmodelsrdquo Social Networks vol 43 pp 16ndash27 2015

[56] D M Powers Evaluation from precision recall and F-measureto ROC informedness markedness and correlation 2011

[57] T Saito and M Rehmsmeier ldquoThe precision-recall plot ismore informative than the ROC plot when evaluating binaryclassifiers on imbalanced datasetsrdquo PLoS ONE vol 10 no 3Article ID e0118432 2015

[58] Z Sha et al ldquoModeling Product Co-Consideration Relations AComparative Study of Two Network Modelsrdquo in Proceedings ofthe 21st International Conference onEngineeringDesign ICED172017

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Complexity

of focusing on the product or the designer we leverage com-plex network modeling and simulation techniques to studyanother key stakeholder in product design the customerWe aim to leverage complex networks to study customerpreference in support of product design and developmentParticularly in this paper we study customersrsquo considerationdecisions by modeling product coconsideration relations twoproducts being concurrently considered in purchase as acomplex network

2 Background and Literature Review

Choice modeling is of great interest in engineering design asit predicts product demand and market share as a functionof engineering design attributes and customer profiles in atarget market [9] Choice models have been integrated intodesign optimization to take account of customer preferencesin supporting engineering design decisions [9ndash12] Previouschoice models mostly assume that customers have boundedrationality and have underlying utilities to rank alternativesin a consideration set ldquoa set of product alternatives availableto an individual who will seriously evaluate through com-parisons before making a final choicerdquo [13] A key step ofconstructing choice models is to determine the considerationset [14] As Hauser et al [15] indicated ldquoif customers do notconsider your product they canrsquot choose itrdquo

From an enterprise perspective understanding customerpreferences in consideration is important for identifyingcrucial product features that customers are willing to payfor Existing studies [16 17] also revealed the considerationset phenomenon that is the size of the consideration settends to be much smaller (roughly 5-6 brands) than thetotal number of choices available in a market As a resultsmall changes in individualsrsquo consideration sets (either sizeor options) may significantly transform the landscape ofthe overall market and reshape the competition relationsin an existing market Therefore understanding customersrsquopreferences in consideration poses new opportunities tooptimize product configurations address customer needsestablish competitive design strategies and make strategicmoves such as branding and positioning

Managerial actions have been taken to influence cus-tomersrsquo consideration decisions directly for example bychanging brand accessibility [18] and by controlling usage andawareness [19] However quantitative studies on customersrsquoconsideration decisions are challenging as consideration is anintermediate construct not the final choice [15]The decisioncontext and a large amount of uncertainty alter decision rulesExisting literature primarily focuses on inferring decision-rule heuristics [20ndash22] such as the cognitive simplicity rule[23] which has been shown to be effective in automobileand web-based purchasing There are three approaches touncover consideration decision-rule heuristics [15] The firstapproach only utilizes final choices and product featuresin the consideration set It adopts a two-stage consider-then-choose decision process and infers model parametersusing the Bayesian or maximum likelihood estimation Typ-ical methods include Bayesian [24] choice-set explosion[25ndash27] and soft constraints [28] The second approach

measures consideration through designed experiments invitro similar to the choice-based conjoint analysis exercise[15] Then the decision rules that best explain the observedconsideration decisions are estimated with Bayesian [29]andmachine-learning pattern-matching algorithms [30]Thethird approach measures decision rules directly through self-explicated questions [31]

Despite the diversity of research on consideration setsfew studies have focused on understanding the underly-ing process of generating customer consideration sets Theconnection between the formation of consideration setsand the driving factors is not well understood Particularlywe know little about how the inherent market structureincluding both the interdependence among existing productsand association among customers affects the considerationdecisions To address this research gap we develop a network-based approach to model customersrsquo consideration behaviorsby modeling product coconsideration relations As shown inFigure 1 the key idea of the proposed network approach is totransform customer consideration sets into a product associ-ation network in which nodes represent products and linksrepresent the coconsideration between two products As aresult the problem of understanding customer considerationcan be addressed by predicting certain network structuresas a function of association networks formed by productattributes and customer demographics It is worth notingthat as the link formation is an aggregation of customersrsquodecisions the links (ie the coconsideration relations) implythe competition among products Therefore our approachenables us to study customer preference andmarket structurein an integrated manner This is different from the studiesin choice modeling (eg the monomial logit choice model[32]) that focus on establishing models for individuals It isalso worth noting that our study is different from the agent-based models which hypothesize certain individual choice-making rules [33] Instead our approach is data-drivenwhich leverages the observed data to drive the establishmentof coconsideration models and prediction analysis using theestimated model parameters

Recently network approaches have been also extensivelyused in recommender systems [34ndash38] Recommender sys-tems are frequently used to recommend products to cus-tomers based on what they searched (considered) Fromthe network representation point of view our approach issimilar to the bipartite projection approach [39] used inthe recommender systems research However the proposednetwork approach is distinct from network-based recom-mender algorithms [37 38] in two aspects first the endgoal is different The recommender algorithms attempt topredict future likes and interests by mining data on past useractivities Common methods include the similarity-basedmethods (eg the collaborative filtering [38] content-basedanalysis [40] and Dirichlet allocation [41]) and the recentlydeveloped hybrid methods [36 42] The approach proposedin this paper relies on the network-based statistical inferencemodel which emphasizes deduction and explanation It aimsto provide an explanatory framework for customersrsquo consid-eration behaviors so that a feedback loop can be created fromcustomer preference to engineering design Therefore the

Complexity 3



Network modeling




and evaluation










lif t (119894 119895) = Pr (119894 119895)Pr (119894) sdot Pr (119895) (1)


4 Complexity

Product A Product B


(a)

Product A Product B

Product C

Product D


(b)



119864119894119895 =

1 if lif t (119894 119895) ge cutoff

0 otherwise(2)






logit [Pr (119884119894119895 = 1)] = 120573X(119899)

= 1205730 + 1205731119883(1)119894119895 + sdot sdot sdot + 120573119899119883(119899)119894119895 (3)



Complexity 5








Pr (Y = y) =exp (120579119879g (y))

120581 (120579) (4)





6 Complexity



Star (degree)


(a)


(b)










Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6




Mazda Changan 3



12

19

76

3862

1311

19

14

22

24

28

1933

24

29








8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 3



Network modeling




and evaluation










lif t (119894 119895) = Pr (119894 119895)Pr (119894) sdot Pr (119895) (1)


4 Complexity

Product A Product B


(a)

Product A Product B

Product C

Product D


(b)



119864119894119895 =

1 if lif t (119894 119895) ge cutoff

0 otherwise(2)






logit [Pr (119884119894119895 = 1)] = 120573X(119899)

= 1205730 + 1205731119883(1)119894119895 + sdot sdot sdot + 120573119899119883(119899)119894119895 (3)



Complexity 5








Pr (Y = y) =exp (120579119879g (y))

120581 (120579) (4)





6 Complexity



Star (degree)


(a)


(b)










Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6




Mazda Changan 3



12

19

76

3862

1311

19

14

22

24

28

1933

24

29








8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




4 Complexity

Product A Product B


(a)

Product A Product B

Product C

Product D


(b)



119864119894119895 =

1 if lif t (119894 119895) ge cutoff

0 otherwise(2)






logit [Pr (119884119894119895 = 1)] = 120573X(119899)

= 1205730 + 1205731119883(1)119894119895 + sdot sdot sdot + 120573119899119883(119899)119894119895 (3)



Complexity 5








Pr (Y = y) =exp (120579119879g (y))

120581 (120579) (4)





6 Complexity



Star (degree)


(a)


(b)










Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6




Mazda Changan 3



12

19

76

3862

1311

19

14

22

24

28

1933

24

29








8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 5








Pr (Y = y) =exp (120579119879g (y))

120581 (120579) (4)





6 Complexity



Star (degree)


(a)


(b)










Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6




Mazda Changan 3



12

19

76

3862

1311

19

14

22

24

28

1933

24

29








8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




6 Complexity



Star (degree)


(a)


(b)










Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6




Mazda Changan 3



12

19

76

3862

1311

19

14

22

24

28

1933

24

29








8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 7

Ford Changan Kuga

Ford Edge

Honda Dongfeng CR-V

Ford Changan Mondeo

Mazda FAW 6




Mazda Changan 3



12

19

76

3862

1311

19

14

22

24

28

1933

24

29








8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




8 Complexity








Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 9






ESDobsnull (5)



network (sim




037 (031 043) 063 (048 076)




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




10 Complexity



Precision = 119879119875(119879119875 + 119865119875) 0594 0543

Recall = 119879119875(119879119875 + 119865119873) 0042 0311


11986505 = 01621198651 = 00781198652 = 0051

11986505 = 04731198651 = 03961198652 = 0340

DyadicERGM

0010203040506070809

1

Prec

ision

02 04 06 08 10Recall





7

1 5

4

32

1 5

32







Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 11








FN)


+ FP)

Number ofcorrect

predictions (TP)


1198651

(1) Dyadic 1202 36 9 0250 00075 0015ERGM 442 111 0251 0092 0135

(2) Dyadic 1087 1654 1076 0651 0990 0785ERGM 1183 860 0727 0791 0758





7 Closing Comments


12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




12 Complexity

DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1Pr

ecisi

on


DyadicERGM

02 04 06 08 10Recall

0

01

02

03

04

05

06

07

08

09

1

Prec

ision







Disclosure


Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




Complexity 13



Acknowledgments


References































14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




14 Complexity





































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of











Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




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