Patterns of Open Innovation Between Industry and University: A Fuzzy Cluster Analysis Based on the Antecedents of Their Collaboration

Abstract

Competing in a complex and interconnected environment, firms are increasingly employing open innovation to search for and collaborate with different partners for better performance. While universities are considered an important source of knowledge for industry, there has been limited literature that investigates patterns of their collaboration in an open innovation context. Moreover, the influence of contextual characteristics such as size and industry classes on these patterns has also received little attention. Aiming to address these research gaps, a research framework was developed from the extant literature. Taking into account the main antecedents integrated into this framework, a fuzzy c-means clustering approach was employed to find a typology of open innovative firms in their collaboration with universities. Using the typical value of the fuzzifier factor of this algorithm equal to 2, three distinct clusters were identified with respect to these antecedents as low, insecure, and responsive open innovators. Then, an econometric model using a multinomial logistic regression was constructed to explore the influence of firms’ size and industry type on the identified patterns of such collaboration. Based on the marginal effects analysis, mixed evidence was found regarding the influence of the firm’s size on the identified clusters, while the impact of industry intensity was in line with other prior studies in the extant literature. The results of our study lead to some meaningful implications from both an empirical and managerial point of view that are discussed alongside with future research recommendations.

1. Introduction

Competing in a global and interconnected world, more and more firms are employing an inbound openness to search for and collaborate with different actors for better performing in such an environment [1]. By opening up organizational boundaries to other sources through an outside-in process to complement the internal innovation competencies, firms can and should capture external knowledge and take advantage of their exploitation in their business to deal with the challenges of our times [2]. As external knowledge has been used by firms for a long period, some studies pointed toward the presence of a claim in the literature that the concept of open innovation coined by Chesbrough at the beginning of the 21st century is not something particularly new (e.g., [3]). Nevertheless, open innovation becomes so attractive because it brings together under an umbrella concept a collection of existing developments that integrates a series of activities among different types of partners and their interrelationships, with great perspectives for extension [4]. Thus, open innovation has turned into a multifaceted phenomenon that has become the focus of research across multiple levels of analysis [5].

From the various aspects that have been studied, an important stream of research is related to the organizational actors with whom firms may collaborate within open innovation [6,7]. Regarding the various external sources that firms should integrate throughout their open innovation process, they are heterogeneous and diverse [8], and may be differently categorized. These actors range from market-related sources (e.g., customers, suppliers, competitors) to scientific-related sources (e.g., universities, public/private research institutions) and to other sources (e.g., professional associations, intermediaries) [6,8]. Accordingly, the relationships of the firms with the external actors can be very different [9], and an important question is related to their governance [5].

Among such partners, universities have been considered a major source of scholarly knowledge, which includes both highly codified and tacit knowledge that flow to industry as the two organizational actors collaborate [10]. While universities have become increasingly important in the accelerating innovation of firms based on their frontier discoveries and advanced technologies, the contextualization of university–industry collaboration through open innovation is still not sufficiently developed. According to the extant literature, the collaboration between industry and universities in open innovation is influenced by different types of antecedents [11], which have to be recognized and addressed. As a result, a comprehensive understanding of such factors becomes of great importance as it is expected to better support firms in their open innovation efforts. The motivations, barriers, and knowledge transfer channels have been considered among the main aspects that typically characterize such interaction [12,13], and the adoption of open innovation between industry and university has been pointed out as being influenced by people’s attitudes towards these three main antecedents of their collaboration. Although some of the literature has explored patterns of university–industry relationships related to these three specific dimensions (e.g., [13]), we still know little about such patterns in an open innovation context between the two organizational partners. Thus, further research on this topic would be beneficial. Taking into account its capability to find patterns in data and to classify them into distinct categories, a cluster approach can be employed to identify possible groups of innovators based on their attitudes towards the three main antecedents of their collaboration with universities in an open innovation context. This clustering analysis allows us to categorize people with similar attitudes considering their perceptions of these antecedents, providing a deeper insight into the heterogeneity of industry–university collaboration in such a context. Therefore, with a clustering approach, a better understanding of the different levels of openness and engagement can be achieved by identifying distinct types of open innovators. This can be used to investigate the impact of various policy scenarios as they may respond differently to policy changes and prescribe strategies for more effective collaboration between firms and universities.

Another important aspect that has been covered in the literature is related to the adoption of an open innovation paradigm throughout the industry of application and firm characteristics [7,14]. The existing research has addressed the effectiveness of open innovation considering both the industry’s technological level (e.g., high-tech vs. low-tech industries) and size classes (e.g., large vs. small- and medium-sized enterprises), although its implementation is not always an easy one [9]. The results of the recent studies have pointed out various interpretations of open innovation among firms of different sizes [3] and from different industries [15]. However, the impact of the differences across size and industry classes on the patterns of open innovation between industry and university considering the antecedents of their collaboration is still unexplored in the literature.

Based on the previously mentioned considerations and aiming to fill the identified research gap, this study aims to explore the following research questions:

RQ1. What distinct patterns can be observed within industry by examining the main antecedents of their collaboration with universities in an open innovation context?

RQ2. How are the identified patterns influenced by industry intensity and size classes?

Our work addresses these questions. We begin with the development of the frame of reference, in which the theoretical background of this study is presented. Then, we first describe the proposed research framework and its constructs, followed by the data source and analysis methods. Next, the results of this study are interpreted considering the developed research questions. Finally, discussion and conclusions of the main contributions are provided along with future research suggestions.

2. Frame of Reference

The scientific knowledge generated by universities is one of the main types of external knowledge that firms can absorb, which is more difficult to transfer compared with the practical knowledge that is produced by other entities (e.g., clients, suppliers, or competitors) [16]. The investigation of motives for and barriers to collaboration, and channels of knowledge transfer between industry and universities may be used to capture the complexity of this phenomenon [13]. Thus, an increasing part in the literature on the interaction between industry and universities is dedicated to the analysis of these specific dimensions of their collaboration [7,17]. They have been studied by Vick and Robertson [18] from both a sociopolitical and contextual perspective, aiming to better understand the collaboration environment between the two organizational actors. While the former largely emphasized the social factors that influence the above central measures, the latter addressed different problem-focused factors (e.g., industrial sectors, firm size) [18].

While the motives, barriers, and channels have been found among the main research topics within the university–industry collaboration, most of the existing studies address them rather separately than in an integrative way. Among the exceptions is the work of Gilman and Serbanica [19], which proposed a conceptual framework to investigate the interaction between university and industry that integrates determinants, knowledge transfer patterns, and impacts of their linkage. In their study, the knowledge transfer channels and barriers to interactions were scrutinized as patterns of cooperation. At the same time, they examined the firms’ motivations for collaboration based on the impact on their innovation. Moreover, the sector and size were considered by Gilman and Serbanica [19] among the firm-related factors that significantly influence the interaction. Another notable exception is the study of Ankrah and Al-Tabbaa [20] which developed an integrative approach of collaboration between firms and universities. According to these authors, the relationship between them is started by different motives of each organization, while various barriers can inhibit their interaction. The two organizational actors can employ different knowledge transfer channels to address their relationships. If these factors are correctly managed, they can result in a positive effect on the collaboration outcomes between industry and universities. However, this integrative view has been conceptual in nature, and future replications are required before it can be fully useful in the innovation practice. Based on the framework proposed by Ankrah and Al-Tabbaa [20], Baban et al. [12] developed one of the first hierarchical component models that integrates the main constructs of the collaboration between industry and university in an open innovation context. Their model links together the three main antecedents (i.e., motives, barriers, and channels) and the main outcomes of such collaboration. In this model, the identified antecedents were structured into different categories that included various observable items adapted from the existing literature

Within this framework, it is clear that the adoption of open innovation between industry and university may be influenced by accurately identifying motives, perceiving barriers, and employing preferred channels. Analyzing common patterns across these specific dimensions of their collaboration can provide detailed evidence of the diversified modes of open innovation between the two organizational actors. Clustering is one of the most important methods for discovering such patterns, which has also been used in several innovation studies addressing the above-mentioned antecedents. For example, a cluster analysis was carried out by Verbano et al. [21] to characterize different profiles of openness within manufacturing Italian SMEs. They investigated the differences between and behaviors of resulting clusters based on the motivations and barriers of open innovation strategies, among other factors. Through a cluster analysis, Hertrich and Brenner [22] classified German regions considering the characteristics related to the dominant obstacles of innovation. The results of this study may offer a base for formulating policy measures that can be employed in similar regions. Using a cluster analysis, Fernández-Esquinas et al. [23] proposed a typology of firms based on the channels through which firms interact with universities. These authors discussed the profile of each cluster taking into account the identified determinants for engagement in the analyzed channels of knowledge flow between university and industry. In light of the existing literature, we may conclude that the cluster analysis of these specific dimensions has been applied independently rather than on all the antecedents together. Nevertheless, the clusterization of firms into categories that are homogenous in addressing all motives, barriers, and channels of interaction may provide a more articulate understanding of the open innovation phenomenon between industry and university.

From reviewing the literature, it was also found that their collaboration in an open innovation context can be affected by both internal and external characteristics. Among them, the firm’s size is the most investigated internal one, while industry is the most examined external characteristic [4,24]. The existing studies reveal that both large firms and SMEs are able to open up their innovation process, even if to a different scale [25] and in a different way [24,26]. While earlier studies have mainly described the implementation of open innovation within large companies, the extant literature pointed out that an open innovation approach is also coming forth within SMEs [24]. In light of the challenges they face such as the liability of smallness, SMEs may have to be even more open than the large firms in accessing external knowledge [26]. With regard to the industry characteristics, they have been addressed from different perspectives, with many of the existing studies focusing on the technological levels of the firms. Although open innovation has been commonly adopted in high-tech industries, the literature also investigates its implementation in low-tech firms [6]. However, the open innovation process is not necessarily similar across industries [5], as the scientific knowledge base of universities is very important for innovation advancement of high-tech firms, while that of low-tech industries is more stable and widely spread out [27]. Taking into account these issues, an investigation of the influence of industry intensity and firm’s size on the patterns of open innovation between industry and university based on the motives, barriers, and knowledge transfer channels can offer a more in-depth insight into their collaboration in such context.

3. Methodology

3.1. Proposed Framework and Its Constructs

Consistent with the observations mentioned in the previous section, Figure 1 depicts the resulting framework that will be employed as an investigation base for this study. Our research framework includes three distinct dimensions. The first of them is represented by the generic collaboration between industry and university in an open innovation context that contains linking between these two organizational actors in such context. The next element consists of the identified antecedents that are organized into overarching categories. Finally, is the context dimension, which can be examined considering both internal and external characteristics of firms.

Regarding the three antecedents of the conceptual framework in Figure 1 (i.e., motives, barriers, and channels of knowledge transfer), each of their constructs and corresponding observable items are adapted from the existing literature considering the study conducted by Baban et al. [12]. According to their work, each of the three antecedents was structured using a hierarchical component approach, with the higher-order constructs involving four categories for all motives, barriers, and channels of knowledge transfer. The observable items of each category have also been documented in the previous research of Baban et al. [12] based on an extensive review of the current literature. Contextual factors, i.e., the firm’s size and technological intensity, complete the characteristics of the firms, referring to the features illustrated in the existing literature.

The constructs of the three antecedents are defined following an approach that has also been used in other influential studies on open innovation (e.g., [28,29]). In the proposed framework depicted in Figure 1, each antecedent included four constructs, while the number of items related to these constructs varies from one to five.

Let C_i ($\mathrm{i}=\overline{1,12}$) be one of the antecedent constructs and c_ij ($\mathrm{j}=\overline{1,\mathrm{v}}$) its observable components, where v can take an integer value from 1 to 5 (inclusive). Considering a five-point scale, each c_ij item is coded as follows:

$${\mathrm{c}}_{\mathrm{i}\mathrm{j}}=\left\{\begin{array}{l}0, \mathrm{for} 1-“\mathrm{not} \mathrm{important}”/ 2-“\mathrm{little} \mathrm{important}”/ 3-“\mathrm{somewhat} \mathrm{important}”\\ 1, \mathrm{for} 4 -“\mathrm{important}”/ 5-“\mathrm{very} \mathrm{important}”\end{array}\right.$$

(1)

Then, the c_ij items are summed and divided by their number n_ij, so that a C_i construct is expressed as:

$${\mathrm{C}}_{\mathrm{i}}={\displaystyle \sum _{\mathrm{j}=1}^{\mathrm{v}}\frac{{\mathrm{c}}_{\mathrm{i}\mathrm{j}}}{{\mathrm{n}}_{\mathrm{i}\mathrm{j}}}, \mathrm{i}=\overline{1,12}, \mathrm{v}=1,2,3,4, \mathrm{or} 5}$$

(2)

From relation (2) it can be easily seen that C_i ∈ [0, 1], with the extreme values obtained when all c_ij items are 0 and 1, respectively. In this way, it is assumed that the more important C_i is (i.e., the closer to 1 in this construct), the stronger its influence will be in perceiving universities as a knowledge source for industry in an open innovation context. Completing the description of contextual factors in Figure 1, this study adopts the OECD classification of the firm’s size in two categories based on the number of their employees as an SME (between 10 and 249 employees) and large enterprises (250 or more employees) [30]. Regarding technology intensity, firms are divided according to the Eurostat aggregation as belonging to high-tech, medium high-tech, medium low-tech and low-tech industries [31].

3.2. Data Source and Analysis Methods

Our analysis was based on data collected from a survey concerning the main aspects of open innovation between firms and universities, which was also used in previous studies of the authors [12] and are briefly described next with an emphasis on the analyzed contextual characteristics. Considering the aim of our study, we included several common factors to ensure the survey data are relevant and valid. First, the context of the survey was briefly described at the beginning of the survey. Next, each question was related to only one of the observable items in the logical flow of the three antecedents, starting with those of motives, followed by barriers, and ending with channels. In this way, the survey experience was intended to be more intuitive for participants. Then, the questions were formulated considering the position of the targeted respondents using neutral phrases to avoid their orientation toward a specific answer. After that, only closed-ended questions were included to collect quantitative data on a 5-point Likert scale for each observable item. Finally, questions related to the size and industry sector of the represented firm were included. Because empirical evidence on patterns of their collaboration in open innovation considering all three antecedents depicted in Figure 1 is still missing, an exploratory approach was employed in our investigation. For this purpose, our data included 98 responses from participants in the survey, which is near the limit of the minimum sample size of 100 participants recommended in the literature for explorative studies [32]. They were people with responsibility for the innovation process/owners of firms from two industrial areas, i.e., the Valenza Industrial District and Oradea Industrial Parks. The respondents were heterogeneous in terms of both the size and industry type of the firms where they were employed. Among them, 59.18% were employed by SMEs, while the others 40.82% were from large enterprises. Regarding their distribution on industry type, 11.22% were based in high-tech firms, 39.80% came from medium high-tech firms and 48.98% belonged to low-tech firms. The participants were asked to respond at all c_ij items in Figure 1 using a five-point scale from 1-”not important” to 5-”very important”. Then, their responses were used to compute each C_i construct according to relations (1) and (2).

Since the adoption of open innovation between industry and university is influenced by people’s attitudes towards the three main antecedents of their collaboration presented in Figure 1, we decided to perform a cluster analysis to identify possible groups of respondents that are distinct with respect to such antecedents. Different clustering algorithms can be distinguished and their taxonomy is provided in the literature. Regarding openness, the existing studies have realized that it may not be binary classified as either closed or open, and its adoption has been seen as varying with different degrees of openness, from completely closed to fully open innovators [33]. Considering the subjective and ambiguous thinking of the heterogeneous respondents of our survey, the collected data may face noise due to potential measurement errors caused by the scale used, as the survey participants may have difficulties in making a clear distinction between its levels [29]. An appropriate clustering approach to deal with such data is fuzzy c-means clustering because of its robustness to noise coming from different sources compared with other clustering methods [34]. Considering, for example, the k-means clustering that identifies clusters without taking into account the amount of noise in the data, the fuzzy procedure allows an adaptation of the approach to existing noise by assigning a survey response to all clusters through a fuzzy membership. By having such a membership value, the effect of a response resulting from noise may be decreased, which results in a lower influence of such responses in the computation of the center positions of clusters [34]. In this way, the incorrect identification of clusters produced by random patterns may be also avoided.

Accepting this, we proposed a fuzzy c-means clustering approach to answer the first research question of this study. In such an approach, a response of the participants of the survey is not assigned based on the C_i ($\mathrm{i}=\overline{1,12}$) constructs to exactly one cluster but to all clusters with gradual memberships [35]. Let $\mathrm{r}=\overline{1,\mathrm{n}}$ be the respondents of the survey (n = 98) and $\mathrm{k}=\overline{1,\mathrm{c}}$ the number of clusters to which a respondent might belong. In the fuzzy c-means algorithm, the clustering corresponds to the following objective function ([35], p. 198):

$$\mathrm{Minimaze} {\mathrm{J}}_{\mathrm{c},\mathrm{m}}={\displaystyle \sum _{\mathrm{k}=1}^{\mathrm{c}}{\displaystyle \sum _{\mathrm{r}=1}^{\mathrm{n}}{\mathrm{u}}_{\mathrm{r}\mathrm{k}}^{\mathrm{m}}}}{\mathrm{d}}_{\mathrm{r}\mathrm{k}}^2$$

(3)

where m > 1 is called as “fuzzifier” factor, u_rk represents the membership value of the respondent r to the cluster k (0 ≤ u_rk ≤ 1) relative to all other clusters with ${\displaystyle \sum _{\mathrm{k}=1}^{\mathrm{c}}{\mathrm{u}}_{\mathrm{r}\mathrm{k}}=1}$, while d_rk is the Euclidean distance between the centroids c_k and C_i constructs.

The next step of our analysis aims to investigate the relevance of the size and industry classes in explaining the variation in the adoption of open innovation across previously identified clusters. For this purpose, we employed a multinomial logistic regression to identify differences across the clusters based on these two specific contextual characteristics. In this way, an answer to the second research question of our study is also provided. Let us consider the obtained clusters through the fuzzy c-means method as the dependent variable with k nominal categories ($\mathrm{k}=\overline{1,\mathrm{c}}$) and k^* the reference category. Assuming the firm’s size and industry intensity as the X₁ and X₂ predictors, respectively, the multinomial logistic model may be written as ([36], p. 92):

$$\begin{array}{l}\mathrm{Pr}(\mathrm{Y}=\mathrm{k}\left|{\mathrm{X}}_1,{\mathrm{X}}_2\right.)={\displaystyle \frac{\exp \left({\mathsf{\beta }}_{\mathrm{k}0}+{\mathsf{\beta }}_{\mathrm{k}1}{\mathrm{X}}_1+{\mathsf{\beta }}_{\mathrm{k}2}{\mathrm{X}}_2\right)}{1+{\displaystyle \sum _{\begin{array}{l}\mathrm{k}=1\\ \mathrm{k}\ne {\mathrm{k}}^{*}\end{array}}^{\mathrm{c}}\exp \left({\mathsf{\beta }}_{\mathrm{k}0}+{\mathsf{\beta }}_{\mathrm{k}1}{\mathrm{X}}_1+{\mathsf{\beta }}_{\mathrm{k}2}{\mathrm{X}}_2\right)}}} \mathrm{for} \mathrm{k}\ne {\mathrm{k}}^{*}\\ \mathrm{Pr}(\mathrm{Y}={\mathrm{k}}^{*}\left|{\mathrm{X}}_1,{\mathrm{X}}_2\right.)={\displaystyle \frac{1}{1+{\displaystyle \sum _{\begin{array}{l}\mathrm{k}=1\\ \mathrm{k}\ne {\mathrm{k}}^{*}\end{array}}^{\mathrm{c}}\exp \left({\mathsf{\beta }}_{\mathrm{k}0}+{\mathsf{\beta }}_{\mathrm{k}1}{\mathrm{X}}_1+{\mathsf{\beta }}_{\mathrm{k}2}{\mathrm{X}}_2\right)}}} \mathrm{for} \mathrm{k}={\mathrm{k}}^{*}\end{array}$$

(4)

where β_k0 is the constant for outcome k and ${\mathsf{\beta }}_{\mathrm{k}1} , {\mathsf{\beta }}_{\mathrm{k}2}$ are the regression coefficients.

4. Results

Our dependent variable is a discrete and multinomial-choice response with a logical order. The open-source R software (version 4.3.2) was employed for all computations in this study. Regarding the implementation of the fuzzy c-means algorithm, it was performed with the “fclust” R package [37]. One important aspect of this process is related to choosing the value of the fuzzification factor in relation (3) that was set as m = 2, a typical value for this algorithm [35]. Another important problem is the selection of the number of groups k, which in the field of innovation commonly encountered three [38], four [39], five [40], or six clusters [41]. An outcome that leads to a larger number of clusters has been also pointed out as may be more difficult to interpret [42]. Since our investigation was intended to explore the adoption of open innovation beyond the binary classification of open versus closed innovators, we tested the possible number of clusters between three and six. Different cluster validity indices are described in the literature to determine the optimal number of clusters, and several of them are also available in the R package “fclust”.

Table 1. Values of the preferred number of clusters.

Index *)	Criterion	Number of Clusters
		k = 3	k = 4	k = 5	k = 6
Partition coefficient (PC)	Larger the better	0.448	0.362	0.309	0.272
Modified partition coefficient (MPC)	Larger the better	0.172	0.149	0.137	0.127
Partition entropy (PE)	Smaller the better	0.920	1.176	1.377	1.546
Silhouette (SIL)	Larger the better	0.313	0.279	0.263	0.243
Fuzzy silhouette (SIL.F)	Larger the better	0.505	0.587	0.603	0.648

^*) Available in the “fclust” package [37].

presents the results of the cluster analysis obtained through the prevalent ones in the case of our dataset. As shown in Table 1, the number of three clusters was selected as the best among four of the five indices. Considering the majority rule [43], k = 3 was adopted as the appropriate number of the clusters of our study, and their sizes resulted in 37, 34, and 27. The value of fuzzification factor has been suggested in the existing literature (e.g., [44]) as probably varying between 1.5 and 2.5, while the midpoint of this interval m = 2 has been preferred in many studies. Therefore, we carried out a sensitivity analysis considering 1.5 and 2.5 as the lower and the upper values of m, respectively. For m = 1.5, all criteria of the cluster validity indices shown in Table 1 were similar to those of m = 2, while for m = 2.5, they were different only for the SIL criterion. The same majority rule resulted to a number of clusters equal to 3 for both 1.5 and 2.5 values of the fuzzification factor. In the case of m = 1.5, the sizes of Cluster1, Cluster2, and Cluster3 resulted as 40, 33, and 25, while for m = 2.5 these values were 35, 33, and 30, respectively. They are in a similar range with those of the adopted value of the fuzzification factor in our study (m = 2), which may indicate an adequate cluster stability.

The distribution of the antecedent constructs on the profiles of the identified clusters is depicted in Figure 2.

Table 2. The average cluster scores of the considered antecedents.

Antecedent	Cluster1 (n = 37 Members)		Cluster2 (34 Members)		Cluster3 (27 Members)		Anova Test (F Statistics)
OiM	0.712	a)	0.822	a)	0.219	b)	29.580	***
OiB	0.475	a)	0.826	b)	0.330	a)	22.509	***
OiC	0.554	a)	0.893	b)	0.122	b)	150.596	***
Cluster classification	Insecure open innovators		Responsive open innovators		Low open innovators

Significance levels: *** p < 0.001. ^{a), b)} Indicate statistically significantly different means using Tukey HSD post hoc test following the ANOVA analysis.

summarizes the average cluster scores of the analyzed antecedents for each of the three clusters, which were computed based on the average of their OiMi, OiBi, and OiCi ($\mathrm{i}=\overline{1,4}$) components.

The first cluster (labeled as Cluster1, 37 members of the sample) is characterized by a relatively higher score of the OiM antecedent (0.712 out of 1), and the OiB and OiC antecedents had a score around the middle of the [0, 1] interval. While the respondents in this cluster found motives for open innovation with universities as relatively important, they perceived fewer barriers and used fewer channels in such collaboration. Therefore, the members of this cluster were defined as insecure open innovators. The second cluster (Cluster2, 34 members of the sample) is described by the higher scores of all three antecedents (above 0.8 out of 1 for each of them). Its members not only identified motives most accurately but also had greater awareness of the barriers to and channels for their collaboration with universities in an open innovation context. Thus, they can thoughtfully adapt to this context and were classified as responsive open innovators. Lastly, the third cluster (Cluster3, 27 members of the sample) is specified by lower values of the antecedents (below 1/3 out of 1 for each of them). The members of this cluster identified motives less accurately, perceived fewer barriers, and employed fewer knowledge transfer channels. Accordingly, they were considered to be low open innovators. The impact of the industry intensity and size classes, i.e., the X₁ and X₂ predictors in relation (4), on the probability that an open innovator belongs to one of the three clusters was assessed using the “mlogit” R package [45]. Before performing the multinomial logistic regression, the absence of multicollinearity between these two predictors was assessed by computing the variance inflation factors, and their values were less than 3. Therefore, the absence of multicollinearity was confirmed [46].

Table 3. The results of the multinomial logistic regression.

Cluster	Estimate Coefficients $({\mathsf{\beta }}_{\mathbf{k}0}/{\mathsf{\beta }}_{\mathbf{k}1}/{\mathsf{\beta }}_{\mathbf{k}2}, \mathbf{k}=\overline{1,2})$	Std. Error	z-Value	Pr (>|z|)
Cluster1
Intercept	−1.64211	0.85328	−1.9245	0.05430 .)
Size	−1.16919	1.26896	−0.9214	0.35686
Industry	2.44939	1.08622	2.2550	0.02414
Cluster2
Intercept	−2.93442	0.89982	−3.2611	0.00111 **)
Size	0.23327	1.29904	0.1796	0.85749 *)
Industry	1.93970	1.12509	1.7240	0.08470 .)
Cluster3	(reference category)

Significance levels: **⁾ p < 0.01, *⁾ p < 0.05, ^.) p < 0.1. Log-Likelihood: −95.292. McFadden pseudo-R²: 0.108. Likelihood ratio test: chisq = 23.093 (p < 0.001).

presents the results of applying the multinomial logistic regression considering Cluster3 as the reference category. Two measures, the odds-ratios, and marginal effects, are typically employed to interpret the results.

The odds-ratios are computed as the exponential function of the estimated regression coefficients, ${\mathrm{e}}^{{\mathsf{\beta }}_{\mathrm{k}\mathrm{i}}}, \mathrm{k}=\overline{1,2},\mathrm{i}=\overline{1,2}$, in Table 3. A positive value of such coefficient implies an odds-ratio greater than 1, which means that increasing this coefficient also raises the odds-ratio. A negative value of a regression coefficient results in an odds-ratio of less than 1 and indicates that an increase in the coefficient decreases the odds-ratio. Therefore, the odds-ratios can be used to express the relative change in the probability of belonging to Cluster1 or Cluster2 compared with Cluster3 when the corresponding X_i predictor ($\mathrm{i}=\overline{1,2}$) is increased by one unit [47]. For example, in the case of the X₁ predictor, increasing the size predictor by one unit (i.e., from 1 = SME to 2 = large firm) decreases the odds of belonging to Cluster1 as opposed to Cluster3 by a factor of e^−1.169 = 0.310. At the same time, being a large firm versus an SME one increases the odds of belonging to Cluster2 versus Cluster3 by a factor of e^0.233 = 1.262. A similar interpretation can be carried out for the X₂ predictor. However, the magnitude of the odds-ratios can be more difficult to interpret as the relative changes depend on the occurring probability of the reference category.

The marginal effects of the X1 and X2 predictors explain how the identified clusters change in relation to the predictors’ change with one unit [47], and may be more useful and easier to interpret. The marginal effects depend on all the estimated coefficients in relation (4) and different approaches can be employed in their computing. The average value of each predictor is commonly used [47], and the marginal effects were derived in this way in our study.

Table 4. The marginal effects of the size and industry class predictors.

Predictor	Contrast	Estimate	Std. Error	z	Pr (>|z|)	Conf. Low	Conf. High
						2.5%	97.5%
Size
Cluster1	mean(dY/dX)	−0.2918	0.164	−1.780	0.0751.)	−0.6131	0.0295
Cluster2	mean(dY/dX)	0.2012	0.152	1.324	0.1854	−0.0966	0.4990
Cluster3	mean(dY/dX)	0.0906	0.199	0.455	0.6490	−0.2996	0.4808
Industry
Cluster1	mean(dY/dX)	0.2924	0.119	2.449	0.0143 *)	0.0584	0.5265
Cluster2	mean(dY/dX)	0.0746	0.119	0.627	0.5307	−0.1586	0.3079
Cluster3	mean(dY/dX)	−0.3670	0.165	−2.222	0.0263 *)	−0.6907	−0.0433

Significance levels: *⁾ p < 0.05, ^.) p < 0.1.

shows their values that were computed using the “marginaleffects” R package [48]. Because the marginal effects are relatively low in magnitude, only their signs were considered in interpreting the results in Table 4 as follows. As the value of the size predictor increases by one unit (i.e., from 1 = SME to 2 = large firm), the probability of being a member of Cluster1 decreases (negative value of the marginal effect estimation in Table 4). At the same time, the probability of being included in Cluster2 and Cluster3 increases (positive values of the marginal effects estimation in Table 4). Therefore, both indifferent and responsive open innovators show a tendency to be involved with large firms, while insecure open innovators with SMEs. If the industry type predictor is increased by one unit (i.e., from 1 = low-tech to 2 = medium high-tech firm, and from 2 = medium high-tech to 3 = high-tech firm), the probability of belonging to Cluster1 and Cluster2 increases (positive values of the marginal effects estimation in Table 4). In this case, the probability of being included in Cluster3 decreases (negative value of the marginal effect estimation in Table 4). Accordingly, medium high-tech firms are more likely to be included in Cluster1 and Cluster2 than low-tech firms, while the latter are more likely to belong to Cluster3 than the former. In a similar way, the high-tech firms are more likely to be in Cluster1 and Cluster2 than medium high-tech firms, and vice versa for belonging to Cluster3.

5. Discussion and Conclusions

5.1. Discussion

Our work contributes to the study of the open innovation profiles between industry and universities, a research area that has been little explored so far. The analysis of such profiles using a fuzzy cluster approach based on the antecedents of their collaboration leads to several insights, which will be discussed next. In answering the first research question of this study, we identify three distinct clusters with respect to motives, barriers, and channels of knowledge transfer between the two organizational actors. The most numerous cluster includes the insecure open innovators (37.75% of the total), which have the values of the three antecedents around the medium level. The responsive open innovators follow (34.69% of the total), expressing a high level of the values of the considered antecedents. Finally are the low open innovators (27.55% of the total) which indicate the lowest level of the values of all analyzed antecedents. The distribution of the members within the three clusters is relatively similar, which offers support to the assertion that open innovation advances from a closed to an open approach through various degrees of openness [21,33].

A firm’s decision to engage in open innovation with universities is informed by various motives, which may be often perceived as anticipated benefits [49]. In this study, the main motivation for open innovation is represented by the OiM1 construct for both responsive and insecure open innovators, while the low open innovators express the OiM3 as their principal motivation (Figure 2). Not surprisingly, the first two groups are concerned with access to external knowledge and new ideas for carrying out their innovation activities, which are considered important for the development of new products or processes [50]. However, they have to prepare themselves on how to support this process [51], as industry and universities have very different organizational goals. Regarding the latter group, its members are oriented toward increasing the efficiency of product developments, which can improve performance and give a competitive advantage to the firms they belong [20].

Considering the high degree of sophistication and complexity of collaboration between the two organizational partners, their relationships in an open innovation context may face various barriers that have to be addressed by industry. According to Figure 2, OiB4, OiB1, and OiB3 were reported as the main challenges for the first, second, and third clusters, respectively. While the experience of prior collaboration may help insecure open innovators in overcoming some of the organizational and managerial barriers (e.g., differences in research priorities between industry and university), the others are sensitive to different influences such as legislation and regulations of the higher education systems [52]. Therefore, they may feel insecure in dealing with such challenges. Moreover, greater attention is required in overcoming intellectual property protection barriers in the context of the openness paradox as innovation often involves knowledge sharing, while protection may be sought to appropriate its benefits [53]. Surprisingly, awareness and connections were reported as the most important barrier in the case of responsive open innovators, although they were located in the relative proximity of universities. Perhaps their prior collaboration with universities did not fulfill expectations of an open innovation approach. Following the suggestion of Laursen and Salter [28] for a deep search across many potential university partners that are more oriented toward such an approach, may help to mitigate these barriers. Finally, the barriers related to the uncertainty of collaboration are of particular concern for low open innovators who might consider the associated risks of the open innovation phenomenon as having a great impact on deviation from their desired performance. Employing a risk management approach such as that described by Madanaguli et al. [54] may assist these innovators in becoming more open.

While different channels facilitate the interaction between industry and university [10,17], and many of them the flow of knowledge in open innovation [55], we found OiC2, OiC4, and OiC3 as the most important ones for Cluster1, Cluster2, and Cluster3, respectively (Figure 2). Starting with insecure open innovators, they were more concerned with transferring knowledge through informal links and networks since they may facilitate direct contact with academic partners. Thus, the employment of such channels may help these innovators to build up more easy relationships and often become more open in their innovation approach [55]. As Fernández-Esquinas et al. [23] pointed out, universities are one of the most important sources of tacit knowledge which usually means specific knowledge residing in the minds of people, which can significantly enhance the results of innovation activities. Therefore, training and employment were found to be the greatest interest to responsive open innovators, which was also observed as being successfully used to capture such knowledge [23]. With regard to low open innovators, they rated research collaborations and consulting as the most influential channels, which is not surprising as such channels have been indicated as quite closed in the context of open innovation [55].

Given the above considerations, understanding how firms in these clusters operate is also vital for the future of their collaboration with universities. Regarding the low open innovators, most of them in our sample are SMEs mainly involved in low-tech industry (e.g., jewelry industry). Although these firms are geographically clustered, they may prefer internal development to keep their unique and exclusive identities by avoiding the disclosure of the techniques or design of their products. This may prevent the adoption of state-of-the-art technologies such as 3D metal printing or sustainable materials that are often available in university labs. While a balance between in-house development and selective openness to accelerate innovation should be found by these firms, universities may also offer them a tailored approach through a secure project-based collaboration based on emerging technologies such as blockchain. With regard to the responsive open innovators in our study, most of them belong to firms operating in medium or high-tech industries. They are generally competing in a world-class manufacturing environment, where they should maintain a knowledge base similar to that of universities to easily access, absorb, and implement the knowledge of these organizations. In this way, cutting-edge technologies such as artificial intelligence developed by universities can be adopted faster, while the latter organizations have the possibility of real-world application of their research. In between there are insecure open innovators, which represent a mix of low or medium-tech firms that mainly operate in a more traditional manufacturing environment. They are more reluctant about opening up their innovation activities at a higher level as their collaboration could be influenced by the asymmetry of knowledge. As a result, its transfer rate and pace of innovation may be slowing down, which could influence the overall impact of their partnership.

When responding to the second question of this study, we noted differences in how open innovation is interpreted among firms of different sizes and industry classes in their collaboration with universities. To begin with the firm’s size, we found mixed evidence based on the marginal effects in Table 4. First, both indifferent and responsive open innovators tend to belong to large firms. A possible explanation is that large firms have more capabilities to build relationships and innovate more openly with universities but they are also able to dedicate large resources and have a greater structure to internally innovate [56]. Moreover, such a mixed effect of the large firm on open innovators is in line with other studies. For example, the findings of Bellucci and Pennacchio [57] sustain the hypothesis that firms used more knowledge from universities with the increase in their size. Nonetheless, above a certain level, large firms may have their own knowledge to conduct performant in-house development, which results in only marginal advantages from collaboration with universities in an open innovation context. However, this finding needs future investigation as the marginal effects were statistically insignificant for these two clusters. Second, insecure open innovators are likely to work within SMEs, which have less internal formalized innovation approach, and distinctive network characteristics and may face more resource constraints [26]. Following on from the size of the firms, industry intensity was also assessed considering the marginal effects in Table 4. Our results show that responsive open innovators are more likely to be associated with high-tech firms, while low open innovators are more related to low-tech ones. Therefore, these findings should be seen in the context of the relative strengths which are specific advantages to the firms, i.e., the resource and behavioral advantage for large and SMEs, respectively. On the one hand, large firms are recognized as having more resources at both human and financial levels that allow them to search for appropriate university partners, interact with researchers, and engage in open innovation that may need time and take risks to deliver useful results [25]. Operating in a highly technologically intense environment where they have to deal with rapid technological change, high-tech firms tend to be more predisposed to collaborate with universities. As a result, universities are considered to play a central role as external sources of innovation in high-tech industry [28]. Thus, large and high-tech firms are more likely capable of investing in their relationship with universities on a continuous basis, which allows a better development of their absorptive capacity compared to SMEs, i.e., their capacity to identify promising ways of collaboration with such organizations. On the other hand, SMEs usually have fewer resources to carry out open innovation activities, but they are characterized by behavioral conditions such as flexibility, adaptability, and agility. While these conditions may support them in exploring universities’ knowledge and technologies in open innovation, they may still have fewer opportunities to mitigate the market and financial uncertainties risks associated with such context. Moreover, universities may be a less important external knowledge source for low-tech SMEs that mainly interact with other potential sources (e.g., customers) [58]. In addition, environmental changes are more often a concern for SMEs in their collaboration with universities, since such firms are more sensitive to changes in competition strategy, acquisition, or even closure of business [25].

5.2. Concluding Remarks and Future Research

The resulting findings of our study have provided some meaningful implications to the existing literature. From an empirical point of view, these findings have shown that the antecedents of open innovation between industry and university shape the patterns of their collaboration in such context. Our study has proved the presence of different firm profiles based on the attitudes of industry towards the adoption of open innovation with universities. Considering not only motives for and barriers to this collaboration but also the channels of knowledge transfer, three different types of firms were identified: low, insecure, and responsive open innovators. In this way, our study offers support to the perspective that open innovation should be seen as a continuum that varies from closed to open through different stages of openness [21,33]. Furthermore, with regard to the tendency of adopting open innovation, our findings illustrate that high-tech firms are more predisposed to be responsive open innovators, while low-tech are more likely to be regarded as low open innovators. At the same time, mixed evidence was found regarding the firm’s size, with both indifferent and responsive open innovators being associated with large firms and insecure open innovators with SMEs.

Our findings also suggest at least two interesting recommendations for managing open innovation between industry and university. First, they reveal that there are heterogeneous open innovators, which address with different intensity levels their motives, barriers, and knowledge transfer channels of collaboration with universities. Moreover, distinctions exist on how different classes of open innovators are influenced by the size of the firms and industry type. Therefore, the managerial attention should not be oriented only to open the firm’s innovation processes. A deeper understanding of the patterns of their collaboration in such a context and the impact of different contextual characteristics on these patterns could help managers to better comprehend what affects their propensity to an effective collaboration with universities in open innovation. In this way, they could prescribe better strategies to implement open innovation with these partners that are expected to respond more effectively to different size and industry classes. Second, our study shows that fuzzy cluster analysis can be used to determine the differences between open innovators, which supports the suggestion of Marescotti et al. [59] that it can be employed as an ex-ante approach to investigate the impact of different strategy scenarios.

Considering the scarcity of existing research about the patterns of open innovation between industry and university, this study has been exploratory in nature. While revealing new insights into our understanding of such patterns, it comes with several limitations that also point toward future research directions. We begin with the sample size of the survey, which was relatively small and local-oriented. Although the sample size of the survey was relatively small, the sensitivity analysis pointed toward a sufficient cluster stability. However, firms operating in different regions may greatly differ in their characteristics that are often influenced by historical developments, local politics, and economy. As a result, they are expected to identify open innovation antecedents that better respond to their environmental differences, which may conduct to different patterns across such antecedents based on a cluster analysis. For example, Hertrich and Brenner [22] used a clustering approach to classify German lagging regions into different types with respect to innovation barriers and found that the cluster membership of the identified regions frequently changed during the analyzed period. They also reported a decrease in the economic situation, especially regarding the founding activity, among the main aspects related to the dynamics of these regions. The study of Fernández-Esquinas et al. [23] also employed a cluster analysis to create a typology of innovative firms considering channels of their interaction with universities in the peripheral region of Andalusia in Spain, supporting the requirement to adapt the knowledge transfer indicators to the regional environments. Within this context, replications are required by conducting studies with much larger sizes at both cross-regional and even cross-national levels before our findings become more general.

Next, our study addresses only manufacturing industries, while differences between manufacturing and services industries may also be worth analyzing as open innovation has a very wide scope. While services may use open innovation to grow their business, finding the path of their collaboration with universities in such a context is likely to be different from manufacturing firms because of the intangible nature of services. Open innovation in services may put greater emphasis on the employment of organizational and intellectual capital compared with the more relative tangible assets used in product and process innovations [60]. As a result, the influence of such factors in the context of service industries should also be investigated in future works. Future dynamic studies are also expected to track the evolutionary patterns of transition from low to responsive open innovators, explore the role of internal factors such as how organizational culture and leadership style influence across the open innovation continuum, or how a data-driven approach based on big data and artificial intelligence influences firms behavior within such continuum.

Lastly, an important challenge in applying a fuzzy cluster approach is related to the determination of an appropriate value of the fuzzification factor m in relation (3). The existing studies provide methods that indicate values of the fuzzifier factor m which are different from the typically employed value of 2 (e.g., [34]). Therefore, future research should examine if such methods lead to a different optimal value for this factor in the context of our study.