1
Drivers of Consumer Willingness for Co-Creation in
New Product Development in
Online Brand Communities
Master Thesis in Marketing Intelligence
Author: Alexander Manchev
First supervisor: prof. dr. Peter Verhoef
Second supervisor: MSc Arjen Onrust
2 Abstract
This thesis investigates consumer willingness to co-create new products in the context of online brand communities. The methodology is a sequential SEM approach - first based on a measurement model and then on a structural equation model. The structural equation model is adjusted using the Satorra-Bentler test statistic for robustness. The SEM model is also compared to an ordinary least squares regression. Six latent factors are hypothesized to have an effect on consumer willingness for co-creation – desire for knowledge, social motive, psychological factor, the quality of firm employees, non-monetary rewards and firm organization and tools. Consumer knowledge factor and psychological factor, more specifically creative thinking are the intrinsic consumer motivators most important for willingness to co-create. The remaining factors provide inconclusive results, although the employee qualities seem to have a weak statistical significance on willingness to co-create in online brand communities.
3 1. Introduction
The ability to continuously innovate and take advantage of market trends is key to the long-term success of any brand. New product development has been traditionally a firm driven process in which customers are viewed predominantly as buyers (Prahalad & Ramaswamy, 2004). This is an expensive and time consuming approach that brings high degree of uncertainty. Oftentimes, companies develop new products or services without fully understanding consumer needs. Consequently, it comes as no surprise then that the majority of new products fall short of consumer expectations and fail to have any lasting impact on the market (Stevens & Burley, 2003). The pressure to produce successful products has only been increasing in the last decade. The reasons for this have been the intensifying competition and fragmenting of marketing channels. Therefore, brands have been exploring new ways in which to develop their products in order to ensure better fit with consumer demands and improve business performance. One of the most successful new mechanism of product development is consumer co-creation. Market research usually involves consumers passively by means of focus groups, various types of surveys (e.g. conjoint analysis) and interviews. Those techniques are all widely conducted in order to segment the market and gather feedback and opinions from consumers. The drawbacks is that all of them are company driven and predominantly focused on quality and satisfaction and oftentimes ignore innovative customer ideas (Dahlsten, 2003). On the other hand, co-creation actively engages consumers in new product development. Collaboration between consumer and firms means that there is an active and open dialogue not between producer and buyer, but between partners. Co-creation has been greatly facilitated by the wide spread usage of the Internet. Establishing online brand communities is a fast, efficient and cost-effective way to gather engage consumers in new product development.
4
workshop. Community members vote for their favorite designs and the most popular items are introduced into the game. This co-creation approach increases the revenues for Valve, simplifies the process of new content creation and strengthens the community around the core product. Online brand communities are useful not only for digital companies but also for firms manufacturing physical goods as well. The Italian motorbike brand, Ducati, has created its business model based on successful online brand community. Ducati’s ‘Tech-Cafe´’ is a virtual chat room where engaged riders discuss technical aspects, share experiences and propose new products to the company. Ducati records all communications and analyzes them in order to better understand market trends and emerging wishes of their customers, but also to provide customized experiences to engaged fans of the brand (Verona and Prandelli, 2002). Likewise, Audi, started Virtual Labs and engaged over 7000 customers in the design of its new infotainment system which won several innovation rewards and became a distinctive feature of Audi vehicles (Thomas, Kass and Davarzani, 2014). Co-creation is also powerful strategy in the B2B setting: DHL co-creates with their business customers through innovation workshops focused on developing new ideas, processes and innovations (Customer Innovation Workshops).
5
anticipate changes in customer needs and attitudes (Flint, 2002; Matthing, Sandén and Edvardsson, 2004).
Clearly, co-creation is a relevant topic, which can be significant asset if implemented correctly. Nonetheless, if consumers are not willing to co-create, none of the advantages just specified would ever occur. Therefore, understanding the motivating factors behind willingness to co-create is an interesting topic. As a result, the following research question is formulated:
Research question: What are the drivers of customer willingness to co-create in online brand communities?
The ability to judge the willingness for co-creation on the part of the consumer is important for the companies if they want to maximize the positive effects of co-creation (Bijmolt et. al, 2010; Fuchs, Prandelli & Schreier, 2010). This stems from the fact that not all customers are equally willing and able to participate in co-creation (Hoyer et. al 2010). By understanding what drives consumers to co-create, firms could design better co-creation platforms and enhance the benefits of co-creation.
The current master thesis expands previous research in the area of co-creation by combining established latent constructs with new ones and develops new scales for measuring willingness to co-create.
6 2. Literature Review
In order for consumer co-creation to occur, consumers must be willing and open to co-create with the company. The current paper investigates two groups of factors behind consumer willingness for co-creation. The first group is comprised of social, psychological and knowledge motives that are all intrinsic for consumers. The second type of drivers are the firm facilitator of customer co-creation. Those characteristics are the employee qualities, the non-monetary rewards compensation offered to co-creators and the tools and organizational support from the firm. The following section defines and expands on each of the aforementioned constructs.
2.1 Consumer co-creation
Van Doorn et al. (2010) specify that consumer co-creation is part of consumer engagement and represents consumer-firm interactions going beyond the purchase phase. Co-creation is the shared inventiveness and co-design between customers and firms (Lursch and Vargo, 2006). Roser et al. (2009) define co-creation as “active, creative and social process, based on collaboration between producers and users”, with the goal of creating value for the consumers. Co-creation is an “outside-in” approach to innovation focusing on the needs of the consumers (Bilgram, Bartl and Biel, 2011). This “outside-in” involves customers providing insight and suggestions to the company that are then combined with the firm’s expertise and technologies in order to deliver innovative solutions to the users.
New product development (NPD) is a complex process involving multiple stages. Hoyer et al. (2010) distinguish four stages in NPD – initial idea generation, product development, commercialization and post-launch support. Customer co-creation has a significant and positive impact during the initial idea generation, designing of product features, prototype testing and market launch (Gruner and Homburg, 2000).
7 2.2 Online brand communities
One of the most popular ways through which companies attempt to engage customers in co-creations is via online brand communities. Brand community is a social entity consisting of individuals who share similar interests and enjoy interacting with one another. Distinguishing characteristics of a brand community are consciousness of kind, which refers to the sense of belonging to the community, shared history, culture and finally individual’s sense of moral responsibility towards the community (Muniz and O’Guinn, 2001). According to McAlexander, Schouten and Koening (2002), brand communities represent dynamic connections that customers create with other customers, with the firm, with the brand and with the products of the firm.
The brand community complements the experience of the core product and is highly beneficial for the firm. Brand community members are valuable assets who can provide ideas for new products or improvement to existing products, give feedback to the company and change the design of upcoming products (Van Doorn et al, 2010).
8 2.3 Consumer willingness to co-create
Consumer willingness to co-create is the main topic in the current research. Consumers are valuable partners for companies because they could be the source of important insights and new ideas (Lengnick-Hall, 1996). Co-creation is a form of partnership between consumers and companies and proactive information exchange is important between partners (Heide and John, 1992, Lusch and Brown, 1996). However, for this exchange to occur consumers must be willing to co-create with the company. Co-creation involves consumer and firm communicating and exchanging information. This is referred to as dialog and has significant role in the success of NPD (Lundkvist & Yakhlef, 2004; Prahalad and Ramaswamy (2004). Yi and Gong (2013) find that when consumers share information with the company this creates a positive effect on the value co-creation. Another construct that has similar influence to information sharing is feedback (Yi and Gong, 2013). Feedback is “solicited and unsolicited information which customers provide to the employee” (Groth, et. al., 2004, Yi and Gong, 2013). Finally, consumers are expected to behave responsibly in the co-creation process. This means that they will treat the company and its employees with respect and would not deceive or lie in the co-creation process (Yi and Gong, 2013).
Therefore, the definition for willingness to co-create is the consumer willingness to engage with the company and its employees by communicating with the company, providing useful and accurate information for the purpose of new product development.
2.4 Antecedents of willingness to co-create
9 2.4.1 Knowledge factor
Knowledge factor refers to the consumer’s motivation to acquire new information which is relevant for them and which allows the consumer to increase their knowledge about the technology used in the product.
Important motivators for consumer co-creation are consumers’ intrinsic curiosity, the desire to learn more about topics that are of interest to them and to acquire fresh knowledge about new technologies and products (Füller, 2006, 2008). Nambisan and Baron (2009) distinguish product related learning benefits as consumer motivator for engaging in co-creation. These benefits enrich customer knowledge about the product, the underlying technologies used to create the product and possible usages of the product. Similarly, Lorenzo-Romero, Constantinides and Brüninkc (2014) find a positive link between consumer learning benefits and positive attitude towards co-creation. Fernandes and Remelhe (2015), who find knowledge acquisition to be the strongest driver of willingness to collaborate, obtain similar results. In the context of open-source software development, contributor’s desire to improve their technical skills and learn more about programming increases willingness to contribute to project development (Hertel et al., 2003; Wu, Gerlach and Young, 2007). This dynamic also applies to paid software. Jeppensen and Molin (2003) investigate the community of a popular paid computer strategy game. They observe that players seek help from other community members when they encounter a technical problem in the design phase of their project and want to learn how to resolve such problem. Yi and Gong (2013) find information seeking to be a significant latent motivator for customer value co-creation in service industries.
H1: Knowledge factor has a positive effect on consumer willingness to co-create
2.4.2 Social factor
The definition of the social factor is adopted from Nambisan and Baron (2009) - the social factor comprises consumer motivators for co-creation that are increased reputation and status in the community, increased sense of belonging to the community and higher self-efficacy.
10
order to increase their own standing and reputation among peers as well as to boost their sense-of-efficacy (Kollock, 1999, McLure and Faraj, 2000). Interaction with other members of the community, sharing knowledge with peers and helping others are all motivators for co-creation and participation in online communities (McLure and Faraj, 2000). According to Lorenzo-Romero et. al (2014) being part of a group which shares similar interest is a significant and positive motivator for customer co-creation. Finding and connecting with people who share similar interests is a major reason for people to be part of an online brand community (Kozinets, 2002).
H2: Social factor has a positive effect on consumer willingness to co-create
2.4.3 Psychological Factor
Consumer willingness for co-creation is also driven by psychological reasons (Hoyer et. al. 2010). The psychological factor is an intrinsic desire by the consumer to express themselves, feel pleasant experiences and assist other people (Nambisan and Baron, 2009).
According to Holbrook (2006), participation in an activity in itself brings personal enjoyment and fun for the person participating. Hertel et. al. (2003) report that one of the reasons contributors to the Linux project are part of the project stems from the pure enjoyment of programming. This is also known as psychological immersion (Mathwick et al., 2001). Evans and Wolf (2005) find that contribution between partners could have strong psychological consequences including satisfaction of participating in a project. Consumers could also take part in the co-creation process because they enjoy stimulation originating from creative experiences. Creative expressions are a natural part of being a human and are important for psychological satisfaction (Csikszentmihalyi, 1996). Burroughs and Mick (2004) report that there is a positive effect on consumer’s attitude towards co-creation when they come up with novel and creative ideas because of feelings of accomplishment, satisfaction and pride. Pursuing creative urges also enhances the sense of uniqueness in consumers (Tian et. al., 2001). Ernst et. al. (2017) find creativity in co-creation on behalf of the consumer to produce better ideas for new products.
11
Faraj (2000) who find one of the drivers of consumer co-creation is the goal to improve one’s own thinking. Consumers actively seeking the benefits of higher mental activity are going to be more willing to collaborate with a company in a new product development.
Furthermore, motivation for co-creation could stem from a consumer’s wish to help others and sense of altruism (Hoyer et. al., 2010). Yi and Gong (2013) find that helping other consumers has a positive influence on customer co-creation behavior. Lorenzo-Romero et al. (2014) find that hedonic benefits include “enjoyment and relaxation, fun and pleasure, entertainment and stimulation, enjoyment due to problem solving and idea generation”. These psychological benefits have a positive impact on consumer attitude towards co-creation. Consumer creativity is an important factor when consumers generate ideas for innovative products, even more so than specific technical skills (Füller, Matzler, Hutter and Hautz, 2012; Faullant et. al, 2012)
H3: Psychological factor has a positive effect on consumer willingness to co-create
2.5 Firm facilitators of willingness to co-create
Virtual brand communities where collaboration with consumers occurs is a strategy which goes to the core of the company and therefore company’s openness for co-creation has to have the right support and tools in place as well as the correct employee attitude (Fournier and Lee, 2009).
2.5.1 Firm organization and tools
In the act of co-creation with the company, consumers essentially become partners of the firm. Füller and Bilgram (2017) find that tool support has a significant and positive effect on the customer’s co-creation experience. Tool support is the “extent to which the virtual environment and tools provided enable the user to accomplish the associated co-creation activity” (Füller and Bilgram, 2017).
12
(2010) identify interaction response capacity as a key factor for customer orientation. Interaction response capacity refers to the manner in which the company records, utilizes and manages customer feedback and whether it incorporates customer suggestions into the business. Von Hippel (2001). One can make the argument that being open to customer co-creation is part of being customer centric. Consumer produce a large number of ideas at different stages of NPD. According to the Avery et al. (2010), companies need to understand this dynamic and have the correct systems that not only capture the signals coming from the consumers, but also to correctly interpret those signals and processes them in an appropriate manner in order to identify viable new product ideas. The systems that support the co-creation experience have to be enjoyable and easy to use for the consumer in order to have engaged co-creating consumers (Bilgram, 2011, Füller and Bilgram, 2017). Appropriate tools and support are needed in order to deal with the high speed and volume of communication channels. Well-constructed toolkits allow co-creators to design new products that are feasible (von Hippel, 2001).
The online interface provided to customers for the purpose of co-creation represents an important touch point between the co-creator and the firm and has direct consequences for both the creator’s enjoyment and the quality of the ideas. Therefore, any tools given to co-creators have to be fast, intuitive and user friendly. This provides enjoyable co-creation experience and produces high-quality ideas (von Hippel, 2001; Nambisan & Nambisan, 2008). Characteristics vital for a good tool kit are to allow consumers to learn by doing, have a library of modules and include the limitations of the manufacturing process (Thonke & von Hippel, 2002).
In order to participate in co-creation, customers need to have access to the right tools in order to obtain the necessary knowledge for co-creation. Additionally, good support from the company ensures that customers are able to clearly express their ideas and enjoy the co-creation experience (Groth et al., 2004).
13
to know the process they are engaging into and to reduce customers’ risk perception (Morgan and Hunt, 1994). Co-creation requires a departure away from the traditional approach of internal development shrouded in secrecy and being transparent with the co-creators (Ogawa & Piller, 2006).
H4: Firm organization and support have a positive effect on consumer willingness to co-create
2.5.2 Employees
The former CEO of the Xerox Corportaion, Anne M. Mulchacy, said that employees are the company’s greatest asset and a competitive advantage. Employee quality and training is a key part of a successful company. Just as the necessary processes have to be in place in order to support the customer’s co-creation, the employees must believe in co-creation and be properly trained in how to handle incoming suggestions. The interaction between employees and customers could dramatically change the experience the customer has with the company. In the context of service industry, employees are differentiating factor for the entire experience and source of advantage to the company (Harris and De Chernatony, 2001). Employee attitude, training and engagement with the co-creators could have an effect on the willingness to co-create new products. Customer engagement is a connection between the clients and the company based on the experiences the customer has had (Vivek & Morgan, 2012). Therefore, even though there is no explicit research dealing with customer co-creation and employee behavior, extrapolating from the customer engagement literature, one can speculate that the employees do play an important role in co-creation. As a result, it is of interest to include employee co-creation as a construct. Research has shown that employees are a distinctive factor in the communication between the firm and stakeholders. Employees are important for brand building as they execute the brand strategies, including drive for customer co-creation (Harris, 2001). Klaus and Maklan (2012, 2014) identify in their scale development for quality of service experience, the interpersonal skills of the employees as a “moments-of-truth” that deals with whether the employees are perceived as “good people” who listen to consumers and are polite.
14
consumers as valuable partners and source of new ideas. It is important for managers to be receptive to innovative ideas originating from customers. Even if the ideas are too ambitious or unfeasible, they can still pinpoint an underlying customer need. If employees do not believe in the customer’s ideas, those ideas are not going to be used, leading not only to missed business opportunities but also to lower engagement with customers (Matthing, Sandén and Edvardsson, 2004).
Just as is the case with the consumer willingness to co-create, information sharing flowing from employees to customers is an important for high quality partnership (Heide and John, 1992).
H5: Employees have a positive effect on consumer willingness to co-create
2.5.3 Rewards
15
contradicts two important parts of the co-creation process in a brand community, namely the discussion of new ideas between co-creators and the social aspect. Hoyer (2017) finds that financial rewards have no significant impact on willingness to co-create, reinforcing that the intrinsic motivators for knowledge, social recognition and psychological benefits are the main drivers of co-creation. This is also supported by the fact that many co-creators choose to voluntarily reveal their ideas without expecting any monetary payoff (von Hippel et. al, 2006).
Therefore, in the current paper the choice is made to focus on non-monetary rewards, which unlike their counterpart have not been extensively researched. Non-monetary rewards for co-creation include special treatment of valuable co-creators by for example inviting them on factory visits, product launches, special events, the opportunity to discuss new products with company managers, official recognition in the online brand community signalling that a particular individual is a valuable partner, giving them early access to new products. For instance, a successful example of non-monetary rewards is the SAP Community Network (SCN). In SCN, engaged co-creators earn special badges and could reach the status of community moderators and SAP mentors for their contribution to the brand community (SAP Community Reputation). Microsoft rewards its most valuable co-creator with an invitation to the annual Global MVP Summit (Microsoft, 2018).
H6: Firm providing non-monetary incentives increases consumer willingness to co-create
3. Research Methodology
16 3.1 Methodology of Structural Equation Modelling
Structural equation modelling (SEM) is a multivariate statistical technique that estimates relationships between observed and latent variables. SEM consists of two models – the measurement model and the structural model. Variables in SEM could be observed or latent. The latent constructs are also referred to as factors. The variables representing a factor are called indicator variables, measurement variables, manifest variables or instruments. The first step in SEM is review of previous research in order to create the latent constructs. Measurement model specifies the indicators for each latent construct. The structural model resembles a multiple regression and allows for the calculation of causal relationships between latent constructs. An important point for SEM is the necessity to specify the relationships based on previous research and prior to the model estimation. At the core of the SEM method is comparison between the covariances of observed data and covariances as specified by the model estimation. Structural equation allows for modelling of complex relationship of variables that are hard to observe. Moreover, in SEM a variable could be both a dependent and an independent variable depending on the specified relationships. This flexibility has ensured that that SEM is popular technique in psychology, sociology, medicine and management research (MacCallum & Austin, 2000; Shah & Goldstein, 2006).
The ability to represents hard to measure constructs has made SEM popular in many field and consequently there are numerous programs used to calculate SEM such as LISREL and AMOS. The current thesis uses the R package lavaan (Rosseel, 2012) for the analysis. The current chapter explains in detail the process of SEM, the estimation procedure, assessment of model validity and provides illustrative examples of how SEM is applied in the current paper.
3.2 Measurement model
17 Creating Latent constructs
The first of step in the methodology is to define the latent variables that are going to be investigated. This is achieved through review of the relevant literature. After defining each factor the development of the measurement model could proceed. The measurement model, also known as confirmatory factor analysis (CFA) identifies the indicator variables that define each factor. As with the definition of latent factors, the indicator variables must be grounded in theory. It is important to note that CFA model specifies the relationship between indicator variables and factors a-priori. CFA is similar to exploratory factor analysis in the way that both methods collapse a set of indicators to represent latent factors. However, exploratory factor analysis does not assume any connections between indicators and factors and all measures are free to load on all constructs. In confirmatory factor analysis, the loadings of indicator variables on factors are specified by the researcher. Each indicator variable is unidimensional, meaning that it is connected to a single factor and has no cross-loadings. At the stage of measurement model specification, it is important to pay attention to the degrees of freedom, Degrees of freedom depend on the number of parameters that are going to be estimated and the number of items per construct. Degrees of freedom should be positive and each constructs should preferably have at least 3 measurement variables connected to it (also known as the three-item rule). This ensures that each construct is at least just-identified. With more than 4 items per construct, a construct is said to be over-identified.
The CFA compares the covariance matrix for the measured variables observed in the data set and the expected covariance matrix as proposed by the model. Figure 1 illustrates a typical measurement model. In the model represented in figure 1, the traditional notation for SEM is followed: the indicator variables are marked by rectangles while the latent variables are in circles.
18
Example of CFA measurement model Notation:
𝑥𝑖: observed indicator variable i
𝛿𝑖 (𝑑𝑒𝑙𝑡𝑎): unexplained error in indicator variable i 𝜆𝑗𝑖 (𝑙𝑎𝑚𝑏𝑑𝑎): factor loading of indicator i on factor j 𝜉𝑗 (xi): latent factor j
𝜙 (𝑝ℎ𝑖): covariance between two latent constructs
Figure 1: Illustration of a typical measurement model. Source: Nokelainen (1999).
The measurement model from figure 1 is translated in the following mathematical equations: 𝑥1 = 𝜆11𝜉1+ 𝛿1 𝐸𝑞. (1.1) 𝑥2 = 𝜆21𝜉1+ 𝛿2 𝐸𝑞. (1.2) 𝑥3 = 𝜆31𝜉1+ 𝛿3 𝐸𝑞. (1.3) 𝑥4 = 𝜆42𝜉2+ 𝛿4 𝐸𝑞. (1.4) 𝑥5 = 𝜆52𝜉2+ 𝛿5 𝐸𝑞. (1.5) 𝑥6 = 𝜆62𝜉2+ 𝛿6 𝐸𝑞. (1.6) Transforming the above equations in a more matrix-friendly form yields:
𝑥1 = 𝜆11𝜉1+ 0𝜉2+ 𝛿1 𝐸𝑞. (2.1) 𝑥2 = 𝜆11𝜉1+ 0𝜉2+ 𝛿2 𝐸𝑞. (2.2) 𝑥3 = 𝜆11𝜉1+ 0𝜉2+ 𝛿3 𝐸𝑞. (2.3) 𝑥4 = 0𝜉1+ 𝜆42𝜉2+ 𝛿4 𝐸𝑞. (2.4) 𝑥5 = 0𝜉1+ 𝜆52𝜉2+ 𝛿5 𝐸𝑞. (2.5) 𝑥6 = 0𝜉1+ 𝜆62𝜉2+ 𝛿6 𝐸𝑞. (2.6) Which simplifies to:
19
Where 𝑥 is a vector for the indicator variables; 𝛬𝑥 is the matrix containing factor loadings; 𝜉 is a vector with the latent factors and 𝛿 is the vector with errors of the observed variables.
So far, we have represented the connection between the latent constructs and indicator variables but not the covariances between the factors and covariances between error terms of observed variables. This is done with respectively the phi (Φ) and theta (θ) matrices.
𝛷 = [𝜙𝜙11 𝜙12
21 𝜙22] Mat.(1)
The diagonal of Φ represents latent factor variances, while the off-diagonal elements are the between-factor covariances. 𝛩 = [ 𝜃11 ⋯ 0 ⋮ ⋱ ⋮ 0 ⋯ 𝜃66 ] Mat.(2)
The diagonal of 𝛩 contains the variances of the errors (𝛿𝑖 ). The off-diagonal elements are filled with zeroes because the errors of indicators are assumed to be not correlated. Note in figure 1 that the errors of indicators go only to their respective indicator. If some of the errors are specified to be correlated then the appropriate off-diagonal element will no longer be zero. For example, if the researcher knows that 𝑥1 and 𝑥6 are correlated then the error term variance
𝜃
61will not be equal to zero. This is also known as a modification index.
Degrees of freedom and identification
At this stage, the proposed measurement model is clear and this allows for calculation of the degrees of freedom (df). Degrees of freedom are important because they determine whether the model is identified and whether a solution could be found.
𝑑𝑓 = 12(𝑝(𝑝 + 1) − 𝑘 𝐸𝑞. (4)
20
number of indicator errors (6), number of factor loadings after the scales for the latent constructs have been set (4), number of modification indices (0), factor variances (2) and finally factor correlations (2). The result for the example model is 𝑘 = 14. Substituting in the df formula, the df are 7. The df change between the measurement and structural model.
Estimated matrix and maximum likelihood estimator
SEM compares the covariance matrix of the observed data (S) with the expected covariance matrix from the model sigma (∑).
𝛴 = 𝛬𝛷𝛬′+ 𝛩 𝐸𝑞. (5)
In order to investigate whether S and sigma converge an estimator is required. The most widely used estimator in SEM is the maximum likelihood estimator (ML).
𝑀𝐿 = 𝑙𝑜𝑔 ∣ 𝛴 ∣ + 𝑡𝑟𝑎𝑐𝑒 [𝑆𝛴−1] − 𝑙𝑜𝑔 ∣ 𝑆 ∣ − 𝑝 𝐸𝑞. (6) Where p is the number of indicator variables.
3.3 Structural equation estimation
In order to illustrate the second phase in SEM an example from Malo (2016) is used.
21 Notation 𝑥𝑖: 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑣𝑎𝑟𝑎𝑖𝑏𝑙𝑒 𝑤ℎ𝑖𝑐ℎ 𝑙𝑜𝑎𝑑𝑠 𝑜𝑛 𝑎𝑛 𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝑦𝑖: 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑣𝑎𝑟𝑎𝑖𝑏𝑙𝑒 𝑤ℎ𝑖𝑐ℎ 𝑙𝑜𝑎𝑑𝑠 𝑜𝑛 𝑎𝑛 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝜆𝑗𝑖(𝑙𝑎𝑚𝑏𝑑𝑎): 𝑓𝑎𝑐𝑡𝑜𝑟 𝑙𝑜𝑎𝑑𝑖𝑛𝑔 𝜉𝑖(𝑥𝑖): 𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝜂𝑖(𝑒𝑡𝑎): 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝛿𝑖 (𝑑𝑒𝑙𝑡𝑎): 𝑒𝑟𝑟𝑜𝑟 𝑜𝑓 𝑎𝑛 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑣𝑎𝑟𝑎𝑖𝑏𝑙𝑒 𝑡𝑜 𝑎𝑛 𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝜀𝑖 (𝑒𝑝𝑠𝑖𝑙𝑜𝑛): 𝑒𝑟𝑟𝑜𝑟 𝑜𝑓 𝑎𝑛 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑣𝑎𝑟𝑎𝑖𝑏𝑙𝑒 𝑡𝑜 𝑎𝑛 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝜁𝑖(𝑧𝑒𝑡𝑎): 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟 𝛾𝑖𝑗 (𝑠𝑖𝑔𝑚𝑎): 𝑝𝑎𝑟𝑎𝑚𝑒𝑡𝑒𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 𝑎𝑛𝑑 𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑎𝑛𝑑 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑓𝑎𝑐𝑡𝑜𝑟𝑠 𝛽𝑖𝑗 (𝑏𝑒𝑡𝑎): 𝑎𝑛𝑑 𝑒𝑠𝑡𝑖𝑚𝑎𝑡𝑜𝑟 𝑏𝑒𝑡𝑤𝑒𝑒𝑛 2 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝑐𝑜𝑛𝑠𝑡𝑟𝑢𝑐𝑡𝑠
Before moving on with the mathematics of the structural part, there have been several changes compared to the CFA model. The nature of relationships between factors and indicators is the same: changes in a factor explain the change in its observed items. However, the factors in figure 2 are no longer covariates. It is possible to have covariance between factors in the structural part as later you can see in the model used to investigate willingness-to-co-create. There is a clear distinction between endogenous (𝜉𝑖) and exogenous constructs (𝜂𝑖). The model from figure 2 is represented with matrices by the following equations. Measurement of the exogenous factors:
𝑥 = 𝛬𝑥𝜉 + 𝛿 𝐸𝑞. (7)
Measurement of the endogenous factors:
𝑦 = 𝛬𝑦𝜂 + 𝜀 𝐸𝑞. (8)
Structural model:
22
𝐵 is matrix with the regression parameters between endogenous factors. Gamma 𝛤 is the matrix with parameters between exogenous latent variables.
Covariance matrices for the measurement part:
𝜃𝛿 = 𝐸(𝛿𝛿′) 𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝜃
𝜀 = 𝐸(𝜀𝜀′) 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 Covariance matrices for the structural part:
𝛷 = 𝐸(𝜉𝜉′) 𝑒𝑥𝑜𝑔𝑒𝑛𝑜𝑢𝑠 𝛹 = 𝐸(𝜁𝜁′) 𝑒𝑛𝑑𝑜𝑔𝑒𝑛𝑜𝑢𝑠 Expected covariance matrix in the structural estimation:
𝛴 = [𝛴𝛴𝑥𝑥 𝛴𝑦𝑥
𝑥𝑦 𝛴𝑦𝑦] 𝑀𝑎𝑡. (3)
The covariance matrices are as follow:
𝛴𝑥𝑥 = 𝑐𝑜𝑣(𝑥𝑥) = 𝐸(𝑥𝑥′) = 𝐸((𝛬
𝑥𝜉 + 𝛿)(𝛬𝑥𝜉 + 𝛿)′) = 𝛬𝑥𝛷𝛬𝑥′ + 𝛩𝛿 𝐸𝑞. (10)
𝛴𝑦𝑦 = 𝑐𝑜𝑣(𝑦𝑦) = 𝐸(𝑦𝑦′) = 𝛬
𝑦𝛴𝜂𝜂𝛬𝑦′ + 𝛩𝜀 𝐸𝑞. (11)
Σηη indicates the covaraince between the endogenous factors and is equal to: 𝛴𝜂𝜂 = (𝐼 − 𝛣)−1(𝛤𝛷𝛤′+ 𝛹)(𝐼 − 𝛣)−1
′
𝐸𝑞. (12)
The covariance between endogenous and exogenous factors is given by:
𝛴𝑥𝑦= 𝑐𝑜𝑣(𝑥𝑦) = 𝐸 ((𝛬𝑥𝜉 + 𝛿)(𝛬𝑦𝜂 + 𝜀)′) = 𝛬𝑥𝛴𝜉𝜂𝛬′𝑦 𝐸𝑞. (13)
𝛴𝜉𝜂= ΦΓ′(𝐼 − Β)−1′ 𝐸𝑞. (14)
Once all of the above matrices are calculated, SEM compares the observed covariances with the model expected covariances and tries to find a solution that minimizes the following function:
𝑄 = (𝑠 − 𝜎(𝛩))′𝑊(𝑠 − 𝜎(𝛩)) 𝐸𝑞. (15)
23
Structural equation estimation uses the same estimators as the measurement part and again the most often used estimator is the ML (eq. 6). The explicit differentiation between endogenous and exogenous constructs demonstrates one of the main attractions of SEM – the ability to use latent variable as both an independent and dependent variable. In figure 2, 𝜂1 simultaneously depends on factor 𝜉1 and explains factor 𝜂2.
Reflective versus formative model
As you can see from figure 1 and 2, the arrows connecting the manifest variables and the latent variables originate from the factors and go to the indicator variables (𝜆𝑗𝑖 lambda are factor loadings). This is because the models are specified as a reflective models. In reflective measurement theory, the underlying constructs are the cause for changes in the indicator variables and the error term for a given item is the variance not explained by the factor. Indicators connected to the same construct must be correlated with one another as they are caused by the construct. Most SEM applications use this approach, especially studies dealing with human behavior and attitudes (Bollen & Lennox, R. 1991). On the other hand, formative measurement models specify that the indicators cause the factors. This change in the direction of the relationship means that formative construct are not latent. The current thesis uses reflective constructs.
3.4 Two-step estimation
This paper uses the recommended two-step estimation process. Firstly, the measurement model is estimated and its model fit and validity are evaluated. The second step is the estimation of the measurement model. This approach is consistent with the recommendations of Anderson & Gerbing (1988), Hair et. al. (2006) and Mueller & Hancock (2008).
24
model. The measurement and structural parts of the SEM have different specifications – the former has covariances between all constructs, has no structural parameters while the latter limits factor covariances, and draws directional relationships between factors. This results in a small change in the degrees of freedom as well as a small changes in the estimates, factor loadings and fit indices.
Setting the scale
A crucial part of SEM is setting the scale. Unlike measurement variables, the latent constructs do not have a measurement scale since they are not directly observable. To solve this problem, one indicator loading for each factor has to be set to 1. Usually, the first indicator connected to a factor is used for setting the scale.
3.5 Evaluation of model fit, reliability
After building and estimating both the measurement model and the structural model, they need to be evaluated for fit and reliability. Absolute fit measures evaluate how close are the observed covariance matrix (S) and the estimated covariance matrix (∑). Incremental fit indices draw comparisons between model specifications.
3.5.1 Absolute goodness-of-fit measures
Chi-square test
The chi-sqaure statistically tests whether the observed and expected covariance matrices differ. Therefore, the null hypothesis is formulated as: There is no difference between S and ∑ and the alternative hypothesis is There is a difference between S and ∑. Uncharacteristically, a good fit of the data to the model means that the null hypothesis is not rejected.
Formula Chi-square:
𝜒2 = (𝑛 − 1)(𝑆 − ∑) 𝐸𝑞. (16)
25
of SEM. Larger samples and models using a lot of indicator variables often lead to statistically significant value for the 𝜒2 test and subsequent rejection of similarities between the observed and estimated covariance matrices.
An alternative and widely used absolute fit index is the root mean square of error approximation or RMSEA. RMSEA corrects the shortcomings of 𝜒2 by including sample size and degrees of freedom in the calculations (Rigdon, 1996).
𝑅𝑀𝑆𝐸𝐴 = √(𝜒2−𝑑𝑓𝑘 )
(𝑑𝑓𝑘(𝑛−1)) 𝐸𝑞. (17)
RMSEA ranges between 0 and 1. Values closer to 0 indicate better fitting model. RMSEA of 0.05 or lower indicates very good fit, while the cutoff of 0.08 shows reasonable fit (MacCallum, Browne, & Sugawara, 1996). A bad fitting model would have an RMSEA greater than 0.10 (Browne & Cudeck, 1993). An advantage of RMSEA is the ability to create a confidence interval. On the other hand, RMSEA is susceptible to decreasing as number of variables increases (Kenny & McCoach, 2003).
SRMR is another absolute fit index. SRMR calculates the standardized mean residual that compares standardized scores for the root of the mean square residuals. SRMR uses the correlation matrix of the residuals that is the difference between the observed covariance matrix, S, and the model implied covariance matrix ∑. SRMR values exceeding 0.10 indicate a poor fit of the specified model to the data (Bentler, 2006).
Incremental fit indices
The incremental group of indices compare the specified model to a baseline model without free parameters. The most widely reported incremental index is the comparative fit index (CFI). Comparative fit index ranges between 0 and 1, with values above 0.90 indicating a well-fitting model.
𝐶𝐹𝐼 = 1 −(𝜒𝑝𝑟𝑜𝑝2 − 𝑑𝑓𝑝𝑟𝑜𝑝)
26
Comparison between models in terms of parsimoniousness is done with the parsimony normed fit index (PNFI). The PNFI takes the standard NFI index and adjusts it with the parsimony ratio. In comparison of PNFI, higher values indicate relatively better fitting model.
Reliability and validity of constructs
The reliability and validity of constructs are evaluated using factor loadings, composite reliability (CR) and average variance extracted (AVE). Construct validity evaluates how good the indicator variables represent the latent factors to which they belong. Indicator variables assigned to a specific latent factor must converge and have a common variance. There are three types of construct validity – convergent validity, discriminant validity and face validity. Convergent validity is done by examining factor loadings, average variance extracted and construct reliability.
Factor loadings
All factor loadings should be statistically significant and at least 0.5 (Anderson & Gerbing, 1988). The indicator variables for each factor should be statistically significant and load on their factor by with at least 0.5 and preferably by 0.7 or greater. Higher factor loadings mean that a larger portion of the variance in an indicator item is explained by the underlying latent construct.
Average variance extracted
𝐴𝑉𝐸 = ∑𝑛𝑖=1𝐿𝑖2
𝑛 𝐸𝑞. (19)
Where L is the standardized factor loading of an indicator variable i. For a specific construct, the nominator represents the sum of the squared standardized factor loadings, divided by the number of measurement variables. An AVE exceeding 0.5 means that more than half of the variances in the measurement items are explained by the construct (Hair et. al., 2010).
Construct reliability
𝐶𝑅 = (∑𝑛𝑖=1𝐿𝑖)2
(∑𝑛𝑖=1𝐿𝑖)2+ (∑𝑛𝑖=1𝑒𝑖)
27
Another measure of convergent validity is the composite reliability of a factor. High composite reliability, above 0.7, mean that the indicator variables represent well the latent factor.
Discriminant validity investigates how different are the separate latent factors. Discriminant validity is tested by comparing the AVE scores for two factors with the square of the correlation between those two factors (Fornell & Larcker, 1981). A factor has to give better explanation to items that are assigned to it compared to items of a different construct. Therefore, if the AVE score is greater than the squared correlation this is proof of discriminant validity (Hair, et. al. 2010).
Face validity in SEM is defined prior to estimation in the specification stage. Factors included in SEM have to be well-defined, distinct and to logical given the topic of the research. Another method for assessing the fit of the model is through the standardized residuals of measurement variables. It is desirable for all error estimates to fall between -2.5 and + 2.5. Variances greater than I4I indicate problems with the model.
Maximum Likelihood Estimation – reporting
The advantages of provided by SEM have resulted in more publications in the fields of social sciences including marketing using structural equation models. In order to follow proper scientific process the reporting in academic literature has to be thorough and transparent. With regards to SEM, the following topics have to be explicitly discussed: model specified a-priori, sample size, data descriptive statistics, type of matrix analyzed, estimation method, software used for the analysis, method for latent variable scale fixing, fit indices, any modifications in the model, factor loadings and factor correlations (Jackson & Gillaspy, 2009).
Despite the popularity of SEM and numerous guides on SEM reporting (Breckler, 1990; Boomsma, 2000), the discussion on SEM assumptions, methodology and data quality remain unsatisfactory and oftentimes do not follow the recommended reporting practices. This is especially troubling given that in many case the raw data from the indicator variables follows a non-normal distribution (Micceri, 1989). Given how SEM relies on normally distributed data, ignoring descriptive statistics of raw data puts in question the conclusions of a lot of research.
28
assumptions (Breckler, 1990). MacCallum and Austin (2000) discover that in half of all SEM cases in psychology the estimated parameters were not fully reported and some articles were even lacking the basic model specification (10%). Similar results are obtained from McDonald and Ho (2002) who review 41 articles from which only 5 deal with data normality. This is consistent with other research showing that in 85% of cases – there is no discussion on data normality, estimation procedure was omitted in 50% of publications, 42% did not report the type of matrix analyzed (covariance or correlation matrix) and 64 % did not explicitly decided on the fit measures that are going to be used (Jackson & Gillaspy, 2009).
In order to follow proper scientific methods the next paragraphs are dedicated to outlining the assumptions of structural equation models, the ramifications of possible violations.
Maximum likelihood estimation – assumptions and violations
Following West, Finch & Curran (1995), structural equation models using the maximum likelihood estimator have four main assumptions. Firstly, the estimates for the parameters are unbiased. Secondly, parameter estimates should represent the population parameters. Thirdly, as sample size increases, parameter estimates have to converge closer and closer to the true population parameters. Moreover, the parameters estimates are assumed to be efficient, meaning that the estimates are the best possible and with the least amount of variance. For the raw data, SEM assumes that the variables are continuous and normally distributed, that the model is correctly specified and sufficiently large sample size is used for the estimation. Measurement variables with Likert scales could be used for SEM but each variable should have at least 5 categories in order to be considered continuous. Finally, the distribution of the maximum likelihood function follows a chi-square distribution. As already mentioned, one or multiple of these assumptions are usually not met in practice.
29
from their true population values under non-normal condition and should be used together with the chi-square test. If the indicator variables are ordered and with fewer than five categories (e.g. Likert scale with Dislike – Neutral-Like), and the data is skewed in opposite directions, the results from SEM estimation process are biased.
Dealing with non-normality in the maximum likelihood estimation
The chi-square fit statistic under ML is resistant to skewness in the range of -1 to + 1 (Mutben & Kaplan, 1992). Similar results have been obtained by Harlow (1985) who finds that for skewness (-2 +2) and for kurtosis (-1 +8), the ML estimator exhibits good results.
The maximum likelihood estimation assumes normal data distribution. Even though ML estimation is resistant to some degree of non-normality in more severe cases of normality violations, appropriate steps need to be taken. As seen later in the non-normality tests for our sample, the data generally is not extremely non-normal: the maximum skewness is - 1.69 and the maximum kurtosis is 3.42. Therefore, following the recommendation of Finney & DiStefano (2006), the Satorra-Bentler scaled test statistic and robust standard errors are going to be used.
The Satorra-Bentler (SB) statistics corrects the chi-square for non-normality in order to approximate true chi-square distribution (Satorra & Bentler, 1994). The formula for the SB statistics is:
χSB2 = χML2
k 𝐸𝑞. (20)
30 Regression and individual factor scores
The final part of the analysis uses ordinary least squares regression in order to compare how well the factors describe the relationship to willingness for co-creation in online brand communities. Individual factor scores for each latent construct and for each respondent were calculated after the SEM part was concluded (DiStefano & Mindrila, 2009).
Multiple regression cannot use latent variables and factor scores had to be computed for using the equation:
𝐹𝑎𝑐𝑡𝑜𝑟 𝑠𝑐𝑜𝑟𝑒𝑖𝑗 = ∑ 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 𝑣𝑎𝑟𝑎𝑖𝑏𝑙𝑒
𝑗 𝑖=1
𝑛𝑗 𝐸𝑞. (21)
Where i denotes the observation, j is the latent factor, the nominator is the sum of the observed indicators for factor j and the denominator is the number of measurement variable.
Table 1 provides a very simple example of how the factor scores were obtained.
Respondent Indicators KNW 1 KNW 2 KNW 3 KNW 4 KNW 5
6 Observed data 7 5 5 4 5
Table 1 – Example of subject 6, with the items for knowledge factor
𝐹𝑎𝑐𝑡𝑜𝑟 𝑠𝑐𝑜𝑟𝑒6,𝐾𝑁𝑊 =
7 + 5 + 5 + 4 + 5
31 3.6 Measures
The SEM model uses in total 7 latent factors, all of which were defined in chapter 2. Literature review was used to find the pertinent measures for the factors. In creating the measurement items, the rules specified by Hair et. al (2010) were followed. Namely, each concept has at least four measures, ensuring that factors are overidentified. Overidentification ensures the model has positive degrees of freedom and has a solution. All measures use a 7 point Likert scale, ranging from strongly agree to strongly disagree (Gruner and Homburg, 2000; Hoyer 2017). All measures have positive wording. Most of the measures were derived from previous published articles. Several measures did not exist and were created using the literature review. Items were adjusted in order to better represent the constructs relating to willingness to co-create in online brand communities.
The items included as a representation of the knowledge construct are based on the literature and reflect consumer’s desire to know more about the company with which they are going to co-create as well as the new technologies used in new product development (Hertel et al., 2003, Jeppensen and Molin, 2003; Fernandes and Remelhe , 2005; Füller, 2008; Baron, 2009). The knowledge item for skill improvement was adopted from Wu, Gerlach and Young (2007) and Füller (2008). A single measure for the social construct was based on the item To meet other users who share similar interests used by Fernandes and Remelhe (2015).
Two items reflecting creativity were developed from Füller, Matzler, Hutter & Hautz (2012). A single item for curiosity was created using Füller (2008) and Fernandes and Remelhe (2015). Two items for the employee construct were sourced from Klaus and Macklan (2012, 2013). Research by Matthing, Sandén & Edvardsson (2004) was the base for two more measures for the employee factor. Items EMP5 and EMP6 were based off Heide and John (1992).
32 Factor Item Question
Knowledge
KNW 1 I like to acquire new knowledge
KNW 2 I want to improve my skills through co-creation
KNW 3 I want to know more about the company
KNW 4 I want to know more about the process of new product development in the company
KNW 5 I like to better understand the technologies which go into new product creation
KNW 6 I like to explore alternative usages of products
Social
SOC 1 I want to be part of the online brand community of the company
SOC 2 I care how others view me
SOC 3 I want to connect with others who share similar interests to mine
SOC 4 I care about my reputation in the online brand community
SOC 5 I care about my status in the online brand community
SOC 6 I want to share my ideas about new product development with others in the online brand community
Psychological
PSY 1 I like working towards a greater goal
PSY 2 I generally consider myself to be creative
PSY 3 I generally consider myself to be original in my thinking
PSY 4 I seek experiences that intellectually stimulate my mind
PSY 5 I am generally curious
PSY 6 I generally help others
Employee
EMP 1 Firm employees support my co-creation efforts
EMP 2 Firm employees are polite
EMP 3 Firm employees have an open-attitude towards my co-creation efforts
EMP 4 Firm employees clearly communicate with me
EMP 5 Firm employees see me as a partner of the company
EMP 6 Firm employees share information that might help my co-creation efforts
Firm
Organization and Tools
FOT 1 The firm supports my co-creation efforts
FOT 2 The firm has the necessary systems to assist in my co-creation
FOT 3 The firm provides me with user friendly tools for co-creation
FOT 4 The firm takes my co-creation ideas seriously
FOT 5 There are clear guidelines about my interaction with the company
FOT 6 The company is transparent with me about co-creation
Non-monetary Reward
NR 1 I expect to be rewarded by the company for my co-creation
NR 2 I expect non-monetary rewards from the company
NR 3 I expect special recognition from the company about my co-creation in new product development
NR 4 Non-monetary rewards increase my willingness to co-create in NPD
Willingness to co-create
WTCC 1 I am willing to co-create new products with the company
WTCC 2 I am open to sharing my ideas with the company about new product development
WTCC 3 I am willing to actively communicate with the company about new product development
WTCC 4 I am open to communicating with firm employees about new product development
WTCC 5 I am willing to spend time and effort co-creating new products with the company
WTCC 6 I will respect the rules set by the company about NPD co-creation
33 3.7 Empirical study
The empirical study was created with the online service qualtrics, access to which was provided by University of Groningen. Prior to data collection, the questions were pre-tested with graduate students and were also evaluated by a marketer with experience in survey creation. Based on the feedback, several questions were shortened and clarified. The questionnaire was distributed online using social media and snowball sampling. The total sample size is 108 respondents. Validity of the data was increased by including a manipulation check in order to distinguish participants who are not paying attention during the survey (Oppenheimer, Meyvis & Davidenko, 2009). Following the check, 3 responses were not admissible. Force responses ensured that there was no missing data among the remaining 105 observations. Gender distribution was 53.3% male (n = 56) and 46.7% female (n = 49). Most respondents were younger than 35 years-old (73.3%; n = 77) and the mean age in the sample was 30.6 years-old. The majority of participants (n = 81) had not co-created with a company at the time of the survey. Bachelor’s and master’s education levels were the most common, accounting for 81.9% of all respondents. The subjects were presented with a scenario where they had to evaluate their willingness to co-create in new product development for a fictional company.
Normality of the sample was assessed first by visual inspection of the histograms and then by calculating descriptive statistics for each variable (table 3). All indicator variables show similar left-skewed distributions. Two examples are provided in graph 1:
34
Indicator Mean SD Min Max Skewness Kurtosis
Shapiro- Wilk p-value Jarque- Bera p-value Missing (in %) KNW1 6.06 1.17 2 7 -1.69 2.97 0.000*** 0.000*** 0 KNW2 5.54 1.28 1 7 -1.30 1.72 0.000*** 0. 000*** 0 KNW3 5.69 1.21 2 7 -0.87 0.34 0.000*** 0.007*** 0 KNW4 5.69 1.17 2 7 -1.09 1.28 0.000*** 0.001*** 0 KNW5 5.79 1.20 2 7 -1.29 1.56 0.000*** 0.001*** 0 KNW6 5.67 1.13 2 7 -1.10 1.10 0.000*** 0.002** 0 SOC1 5.05 1.48 1 7 -0.73 -0.31 0.000*** 0.017** 0 SOC2 5.27 1.35 1 7 -0.83 0.74 0.000*** 0.007*** 0 SOC3 5.91 0.96 2 7 -1.37 3.42 0.000*** 0.000*** 0 SOC4 5.01 1.64 1 7 -0.83 -0.05 0.000*** 0.011** 0 SOC5 4.90 1.61 1 7 -0.70 -0.24 0.000*** 0.025** 0 SOC6 5.23 1.36 1 7 -0.78 0.24 0.000*** 0.016** 0 PSY1 5.95 0.96 3 7 -0.80 0.27 0.000*** 0.011** 0 PSY2 5.69 1.23 2 7 -1.00 0.82 0.000*** 0.005*** 0 PSY3 5.50 1.19 1 7 -0.93 1.17 0.000*** 0.002*** 0 PSY4 6.10 1.07 2 7 -1.36 1.87 0.000*** 0.002*** 0 PSY5 6.12 0.97 3 7 -1.13 1.16 0.000*** 0.001*** 0 PSY6 5.88 1.12 2 7 -1.21 1.49 0.000*** 0.000*** 0 EMP1 5.30 1.21 2 7 -0.56 -0.12 0.000*** 0.048** 0 EMP2 5.74 1.11 3 7 -0.57 -0.59 0.000*** 0.043** 0 EMP3 5.68 1.11 3 7 -0.55 -0.53 0.000*** 0.044** 0 EMP4 5.94 1.13 1 7 -1.45 3.25 0.000*** 0.000*** 0 EMP5 5.19 1.41 1 7 -0.78 0.33 0.000*** 0.014** 0 EMP6 5.69 1.27 1 7 -1.18 1.34 0.000*** 0.001*** 0 FOT1 5.80 1.06 2 7 -1.23 2.03 0.000*** 0.000*** 0 FOT2 5.62 1.17 2 7 -1.19 1.25 0.000*** 0.001*** 0 FOT3 5.66 1.28 1 7 -1.32 1.89 0.000*** 0.000*** 0 FOT4 5.80 1.19 2 7 -1.18 1.23 0.000*** 0.000*** 0 FOT5 5.69 1.20 2 7 -0.89 0.09 0.000*** 0.007*** 0 FOT6 5.88 1.24 2 7 -1.24 1.13 0.000*** 0.000*** 0 R1 5.48 1.39 1 7 -0.94 0.42 0.000*** 0.006*** 0 R2 4.43 1.51 1 7 -0.39 -0.77 0.000*** 0.066* 0 R3 5.34 1.34 1 7 -1.07 1.09 0.000*** 0.000*** 0 R4 4.55 1.38 1 7 -0.54 -0.33 0.000*** 0.06* 0 WTCC1 5.34 1.09 2 7 -0.97 0.80 0.000*** 0.003*** 0 WTCC2 5.43 1.16 2 7 -0.87 0.45 0.000*** 0.008*** 0 WTCC3 5.55 1.16 2 7 -1.06 0.73 0.000*** 0.004*** 0 WTCC4 5.59 1.16 2 7 -1.23 1.44 0.000*** 0.000*** 0 WTCC5 5.30 1.19 2 7 -0.73 0.19 0.000*** 0.019** 0 WTCC6 5.91 0.98 3 7 -0.92 0.38 0.000*** 0.007*** 0
35
36
Initial Measurement model
Figure 3 – Initial measurement model including all latent and observed variables. Created using R package semPlot (Sacha Epskamp, 2018)
4. Initial measurement model – specification, results and validity
37
indicator depicts variance of an indicator. The lines to the indicators KNW1, PSY1, SOC1, EMP1, FOT1, R1 and WTCC1 are dashed because these items are used to set the scale for the constructs. The double-headed arrows between constructs represent the factor covariances. There are no single-headed arrows between the factors since this is the measurement model and there are no dependent factors. This changes later in the structural model.
4.1 Fit of the initial measurement model
In evaluating the measurement model validity, the steps described in Hair et. al. (2010) were followed. The measurement model uses maximum likelihood estimation. The Chi-square χ2 has a significant p-value (p = 0.000), suggesting differences between the observed and estimated correlation matrices. However, given the large number of indicator variables and the rather small sample size additional fit measurements are required (table 4). The CFA model has positive degrees of freedom (df = 719), but rather low goodness-of-fit statistics. The root mean square error of approximation (RMSEA) is high at 0.093 with the upper confidence interval exceeding 0.1. The standardized root mean residual (SRMR) is above the guideline of 0.05. The comparative fit index (CFI) is below 0.9 and indicates poor fit. Overall, the validity statistics of the measurement model indicate that the model does not fit the sample very well.
Validity of Initial Measurement Model
Chi-square χ2 1375.90
df 719
p-value χ2 0.000
Comparative Fit Index (CFI) 0.743
Tucker-Lewis Index (TLI) 0.721
RMSEA 0.093
90 Percent Confidence Interval RMSEA 0.086 0.101
SRMR 0.098
PNFI 0.541
38
Standardized factor loadings of initial measurement model
KNW SOC EMP FOT PSY R WTCC
Standardized Residual KNW1 0.645 0.584 KNW2 0.864 0.253 KNW3 0.695 0.518 KNW4 0.702 0.507 KNW5 0.692 0.522 KNW6 0.533 0.716 SOC1 0.668 0.554 SOC2 0.618 0.618 SOC3 0.635 0.597 SOC4 0.918 0.158 SOC5 0.900 0.191 SOC6 0.586 0.656 EMP1 0.557 0.690 EMP2 0.588 0.654 EMP3 0.823 0.322 EMP4 0.689 0.526 EMP5 0.591 0.651 EMP6 0.824 0.320 FOT1 0.824 0.321 FOT2 0.819 0.329 FOT3 0.801 0.359 FOT4 0.826 0.317 FOT5 0.496 0.754 FOT6 0.655 0.571 PSY1 0.371 0.862 PSY2 0.778 0.395 PSY3 0.771 0.405 PSY4 0.528 0.721 PSY5 0.573 0.672 PSY6 0.449 0.799 R1 0.825 0.320 R2 0.320 0.898 R3 0.696 0.516 R4 - 0.010 1.000 WTCC1 0.855 0.268 WTCC2 0.892 0.204 WTCC3 0.877 0.230 WTCC4 0.789 0.377 WTCC5 0.798 0.363 WTCC6 0.521 0.729 AVE 48.35% 53.79% 47.27% 55.80% 35.76% 31.68% 63.77% Construct 0.84 0.87 0.83 0.87 0.75 0.56 0.91 Reliability
39
4.2 Construct validity in the initial measurement model
The first evaluation of construct validity is done by analyzing the factor loadings. All factor loadings should be statistically significant and at least 0.5 (Anderson & Gerbing, 1988). One item, R4Non-monetary rewards increase my willingness to co-create in NPD, is not significant (p = 0.928). Four more item have a factor loading below 0.5. Those items are FOT 5, PSY 1, PSY 6 and R2. None of the standardized factor loadings violate the feasible range of -1 to +1. No standardized error variance exceeds the value of I4.0I and no errors are negative.
The next measure for construct validity is the average variance extracted (AVE), calculated as the aggregated squared loadings of all indicator constructs and then divided by the number of indicators (Hair et.al, 2010). AVE must be at least 0.5, otherwise more than half of the variance in a factor is due to the error term. In the initial CFA model, the factors for social recognition, firm organization and tools and willingness to co-create exceed the threshold of 50%. The psychological and reward constructs both exhibit very low AVE scores of respectively 35.7% and 31.68%. In terms of construct reliability, only the non-monetary reward factor exhibits reliability below 0.7 (Fornell & Larcker, 1981). Table 5 shows reliability statistics for the remaining constructs.
Construct Correlations and Validity Measures Initial CFA Model
Construct KNW SOC PSY EMP FOT R WTCC
KNW 1.00 0.501 0.322 0.187 0.149 0.046 0.496 SOC 0.708*** 1.00 0.207 0.109 0.172 0.045 0.284 PSY 0.568*** 0.456*** 1.00 0.013 0.013 0.039 0.391 EMP 0.433*** 0.331*** 0.166 1.00 0.739 0.052 0.134 FOT 0.386*** 0.415*** 0.116 0.860*** 1.00 0.052 0.072 R 0.215* 0.213* 0.199 0.229* 0.230* 1.00 0.000 WTCC 0.704*** 0.533*** 0.626* 0.367*** 0.269** - 0.011 1.00 AVE 0.483 0.537 0.357 0.472 0.558 0.316 0.637 Construct 0.84 0.87 0.75 0.83 0.87 0.56 0.90 Reliability
Table 6 - Below the diagonal are the construct correlations; the diagonal represents construct variances; above the diagonal are the squared correlation coefficients. Significance levels: * = 10%,
40
Discriminant validation is done through comparison of the averaged extracted variance for each construct with the squared correlation coefficients for that particular construct (table 6). Three of the factors exhibit problems – knowledge, rewards and finally firm organization and tools. The AVE for these constructs is smaller than several squared correlations. This suggests that those three constructs are not completely separate in the initial CFA.
Based on the test statistics, it is concluded that initial proposed measurement model represents a poor model fit. This makes proceeding to full structural equation model estimation unwise. The main reasons for these results are the complex nature of the proposed measurement model and large number of indicators, both of which necessitate large sample. Another possible explanation, related to the first reason is that there is skewedness and kurtosis present in the data (table 3). The next section refines the measurement model and repeats the tests in order to continue with the structural equation model.
5. Refinement of the measurement model
The large number of indicator variables provides flexibility when it comes to adjustments in the measurement model and ensures that the degrees of freedom remain positive for estimation of the structural model. The first step in adjusting the measurement model is to remove indicator variables with low factor loadings.
41
Revised Measurement Model
Figure 4 – Revised specification of the CFA model. Indicator items have been reduced and modification indices have been included. The dashed lines represent the variable that sets the scale for a given construct; the outside arrows pointing towards the items are error variances
