A multi-item scale for open strategy measurement

Recent trends in strategic management and the strategy-as-practice stream of research have led to a proliferation of studies on open strategy. However, there is a general lack of research focused on valid and reliable measures of open strategy. In this paper, we developed and validated the open strategy scale to measure open strategy constructs derived from two dimensions—transparency and inclusion. We used the mixed methods composed in the multi-phase model of scale development. As a result, we have proposed a multi-item scale to measure the strategy openness. Our results demonstrate the validity and reliability of the scale proposed. The main implication of this research is that the scale may serve as both—an integrated tool for assessment of the overall level of open strategy development and an instrument for more detailed analysis of constructs to reveal the room for improvement or investigate the effect brought by managerial decisions.


Introduction
Recently, researchers have shown an increased interest in the open strategy (OS) stream of research (Adobor 2021;Brielmaier and Friesl 2021;Ohlson and Yakis-Douglas 2019;Seidl et al. 2019). The OS concept established by Whittington and coauthors (2011) emerged from contesting the approach present in strategic management, assuming that the strategymaking process is secretive and elitist, reserved for a select, narrow group of top managers. The OS concept starts from the premise that an organization's strategic processes should involve internal and external stakeholders (Chesbrough and Appleyard 2007). This opening of the strategic processes to a broader range of stakeholders occurs through two fundamental dimensions of the OS concept-inclusiveness and transparency (Baptista et al. 2017;Hautz et al. 2017;Heracleous 2019). Inclusiveness can generally be perceived as the number and type of stakeholders involved in a company's strategic practices. In turn, transparency can be considered in the context of the amount and type of information disclosed by the company to its stakeholders.
Although a growing body of studies has contributed to exploring the OS process (Adobor 2019;Dobusch et al. 2019;Luedicke et al. 2017), only a few have approached the measurement of its dimensionstransparency and inclusion (i.e., Morgan et al. 2018;Tacer et al. 2018) but still using the different context of such measurement. Thus, no comprehensive scale has been developed so far where the areas within those two dimensions are intertwined. That is the research gap we want to fulfill by providing a helpful scale to measure the OS by exploring its constructs. This study aims to outline the constructs and items that could be further used for measurement. This paper begins by reviewing the multiple perspectives within the literature where the frameworks for understanding transparency and inclusiveness are explored. We discuss the existing approaches to their measurement to reveal the necessity of more comprehensive scale development. In the following sections, we describe the theoretical framework that creates the core constructs of our study. We further explain the multi-phase scale development model, illustrating the tools and methods used. Finally, we describe the scale purification and validation stage. At the end of our study, we provide the final scale that could be used to measure the level of strategy openness and formulate some implications for the researchers and practitioners.

Theoretical framework for the development of open strategy measurement scale
Open strategy concept In the conventional approach to strategy, it is assumed that the strategy-making process is exclusive and reserved for a restricted group of top managers and, if necessary external consultants (Andrews 1971;Ansoff 1965;Chandler 1962;Hambrick 2007;Hambrick and Mason 1984;Montgomery 2008;Pettigrew 1992). In addition, according to Whittington and coauthors (2011), who based on the works of Makadok and Barney (2001) and Vicente-Lorente (2001) if the strategy has to ensure that the company achieves and maintains a competitive advantage, its key assumptions should be kept secret because asymmetries and ambiguities of information generate opacity and hinder competitors imitate successful strategies. Whittington and coauthors (2011) propose to go beyond this clichéd pattern of thinking about strategy and suggest a shift toward 'open strategy'-the more open form of strategy-making with more transparency inside and outside organizations and more inclusion of different actors internally and externally. The open strategy was defined as 'an openness in terms of inclusiveness, in other words, the range of people involved in making strategy; and an openness in terms of transparency, both in the strategy formulation stage and, more commonly, in the communication of strategies once they are formulated' (Whittington et al. 2011, p. 532).
The dimensions of OS-transparency and inclusiveness, proposed by Whittington and coauthors (2011) are commonly accepted and widely investigated by authors concerned with the issue of strategy and strategic management (Adobor 2020;Appleyard and Chesbrough 2017;Baptista et al. 2017;Cai and Canales 2022;Dobusch et al. 2019;Gegenhuber and Dobusch 2017;Hautz et al. 2019;Hutter et al. 2017;Luedicke et al. 2017;Mack and Szulanski 2017; Ohlson and Yakis-Douglas 2019; Seidl et al. 2019;Stjerne et al. 2022). In papers on OS dimensions, authors focus primarily on the manifestations and forms of these two dimensions. If any other concepts are analyzed, they concern the sub-dimensions that make up transparency and inclusiveness (see, e.g.: Dobusch et al. 2019;Seidl et al. 2019).
Although much has already been investigated, an unsatisfying level of knowledge and understanding of opening up the strategy-making process is still reported (Belmondo and Sargis-Roussel 2022; Heracleous 2019; Splitter et al. 2019). As it may bring several benefits (Gast and Zanini 2012;Matzler et al. 2016;Stieger et al. 2012;von Krogh and Geilinger 2019;Whitehurst 2015;Whittington et al. 2011) by adopting higher inclusion and transparency, it is worth exploring the meaning and measurement of the OS constructs.

Transparency and inclusiveness-related scales in previous studies
In the following section, we outline a brief summary of prior research to explore the broad scope of the transparency and inclusiveness concepts. We have reviewed how those constructs have been measured in previous studies to identify the existing approaches and perspectives employed and the scales used. We have discovered that the authors addressed transparency and inclusiveness using one view, investigating the information being revealed (what?), the receiver (who?), the circumstances of application (where?), or the processes or approaches used to implement the construct (how?).
While describing transparency, the information visibility was addressed with limited conclusions regarding the causality of the relationship between those two constructs (ter Hoeven et al. 2021). Several scholars have measured the motives and receivers of the revealed information by employing the stakeholder's perspectives (Dapko 2012;Rawlins 2009), investigating the efforts to be transparent. However, the perspective was limited to one type of stakeholder, which impacted the conclusions provided. Another avenue that was developed considered the processes where transparency was applied. In most cases, it concentrated on the supply chain perspective (Awaysheh and Klassen 2010; Caridi et al. 2010;Morgan et al. 2018;Wang and Wei 2007;Williams et al. 2013) as the visibility of the process is a natural way to build the long-term relationship with the suppliers. Besides different scales used, the main limitations concerned the variables affecting the level of visibility within the supply chain. Finally, we shall mention trust and networking, which were analyzed within the relational perspective that could be highlighted as another stream of research (Eggert and Helm 2003). Among the limitations, we may point to the differences between types of transparency revealed according to the nature of each relationship investigated.
While describing inclusiveness, the field of interest is narrower as the researchers focused mainly on participants involved in different processes. The internal perspective was investigated in the social domain, with belongingness and uniqueness being addressed (Chung et al. 2020). Among the limitations of such an adopted approach, the authors mention the cautiousness of making causal inferences. Moreover, user involvement (Ramani and Kumar 2008;Tacer et al. 2018) and broader stakeholder orientation (Feng et al. 2010;Yau et al. 2007) were also employed. Finally, Covin et al. (2006) contributed to the conceptualization of inclusiveness by measuring strategic decision-making participation. Again, the authors mentioned the lack of causal relationships between the researched variables among the limitations. Moreover, we may also find studies that offer the theoretical conceptualization of the inclusion measures that need further validation (Avery et al. 2008;Downey et al. 2015).
Based on that analysis, we may suggest that both concepts are multidimensional, so defining their conceptual domain implies the need to identify, conceptualize and validate their sub-dimensions. We have also addressed the calls for future research to explore the additional antecedents and outcome variables and provide a deeper understanding of causal relationships that may occur. Therefore, we developed a comprehensive scale, integrating different perspectives addressed in prior studies.

Transparency domain
A large and growing body of literature has investigated the concept of transparency, and different perspectives on its forms are distinguished. From the psychological perspective, Schnackenberg andTomlinson (2016, p. 1788) focus on the effect of information disclosure and define transparency as the 'perceived quality of intentionally shared information from a sender.' Based on that approach, the organizational perspective was developed as it includes the degree of visibility and accessibility of information provided by a company (Wilkin 2009). Such actions cover the intentional sharing of information that is usually not shared (Merlo et al. 2018). To make this process effective, information accessibility and clarity is required (Mittal 1999) aimed at lowering the level of uncertainty experienced by the various stakeholders (Ziamou and Ratneshwar 2002). Some transparency costs are involved as asymmetric information, or the early revealing of negative news can exceed the potential benefits (Almazan et al. 2009).
To make this process coherent and reduce the risk of misunderstanding, organizations are providing ready-made and desirable interpretations of strategic moves for their key stakeholders (Whittington and Yakis-Douglas 2012). As Wehmeier and Raaz (2012) observed, we may witness the growth of public expectations regarding organizational transparency, including sharing information about the strategy.
One of the challenges covers choosing the content of information shared. Berggren and Bernshteyn (2007) observed that organizations are increasingly making goals transparent rather than keeping them undisclosed, understanding that the transparency of goals enables the employees to understand the relation between the network of personal goals and performance, which may reduce the inefficiencies in strategy execution. However, openness should go beyond the goals as highlighted by Yakis-Douglas et al. (2017), who argued that it requires transparency and strategic Decision (March 2023) 50(1):51-71 53 information sharing. It is also described by Hautz et al. (2017), who point out that either the strategy formation or the content of the strategy are the core issues that should be revealed to make them deciphered by internal and external stakeholders. Such perspective referring to the visibility of information about an organization's strategy and possibly during its formulation process is also argued by Pittz and Adler (2016). Another aspect is the vast spread of strategic information within and outside the company. As mentioned by Holland et al. (2018), there is still an unsatisfying level of research aimed at operationalization and testing how organizational transparency is actually communicated using different message design features. One of them is clarity which may be achieved by providing extended explanations (Rupar 2006) and jargon avoiding (Kundeliene and Leitoniene 2015). Another is disclosure, which differs from the accessibility of information, as pointed out by Craft and Heim (2008). It requires decisions on where, when, and how the information is presented within a message, which is a much more advanced dilemma than just making it accessible. The last dimension that should be analyzed is ensuring accuracy, which requires designing the communication process to ensure the perception that the information provided by the organization is observable, valid, and truthful (Bernstein 2012).
The managerial practice used in the communication process aimed at ensuring a higher level of transparency may vary from selective disclosure throughout signaling (Heil and Robertson 1991) to a more advanced process based on selecting, simplifying, and summarizing the strategic data (Christensen 2002). As a result, as highlighted by Albu and Ringel (2018), a communication process aimed at greater strategy transparency may turn into a detailed investigation and trigger new forms of data ordering, sorting, and aggregating practices.
Although the challenges and advantages are reported, the precise guidelines on how to augment the transparency with the strategy are still scarce. Moreover, we still observe limited research discussing the performance benefits of giving the stakeholders access to objective information. Some results show that a considerable value of transparency efforts, even if it involves the disclosure of 'bad news,' almost doubles the performance compared to the non-disclosure approach (Brandes and Darai 2017). However, some authors argue that such an effect cannot be analyzed separately without including the other essential success factors, such as the pre-existing level of trust in the work environment (Akkermans et al. 2004).
As a result, transparency is treated as a challenge to be managed within different areas-starting from the specific mindset, where revealing sensitive strategic information is included in the communication process where the key stakeholders are involved (Merlo et al. 2018). Therefore, as the conceptualization of transparency is perceived as the internal or external visibility of information about an organization's strategy (Chesbrough and Appleyard 2007), our transparency dimension includes two core constructs-information content and communication process, which are further explored.

Inclusiveness domain
The second dimension of the OS concept is related to inclusiveness. Inclusiveness can be perceived as an organizational activity in which the strategy-making process is revealed to stakeholders (internal and external) to use the feedback they provide Whittington et al. 2011). Inclusiveness enables an organization to access internal and external knowledge sources that have traditionally not been included in a strategy-making process (von Krogh and Geilinger 2019). Although a strategy-making process opened up to large numbers of stakeholders is usually slower than the classical approach, it leads to better decisions, engagement, and execution (Whitehurst 2015).
Considering inclusiveness in the context of OS, it is essential to focus on the scope of stakeholders involved in strategizing process. An organization has to decide which external and internal actors should be engaged. The traditional approach to the strategymaking and execution process limits the group of actors involved to internal stakeholders only (Covin et al. 2006;Radomska and Kozyra 2020), most notably for a restricted group of top managers (Hambrick 2007;Pettigrew 1992). Meanwhile, inclusiveness considered in the context of OS assumes opening up the strategy-making process for a broader scope of stakeholders (Barroso-Castro et al. 2017), including external ones (Chesbrough and Appleyard 2007;Henisz et al. 2014;Laine and Vaara 2015). So, when embarking on the strategy opening process, an organization must decide which stakeholders should be included and how to select them (Vaara et al. 2019). It is also important to decide how deep and persistent relations should be established. Mack and Szulanski (2017) claim that inclusion can 'involve stakeholders in work groups or task forces in which there are information sharing, interactions, and joint decision-making among members' (Mack and Szulanski 2017, p. 386). But there are other forms of inclusiveness; for example, social media is treated as a platform through which individuals can participate in creating and shaping strategy (Baptista et al. 2017), conducting open dialogue with stakeholders who constantly interact with each other and with an organization (Signori 2017) or crowdsourcing technology, used to involve a large number of stakeholders who can participate in and communicate about the strategy-making process in transparent, virtual environments (Aten and Thomas 2016). Nowadays, establishing relationships with stakeholders is supported by new technologies, allowing to organize virtual participation. This kind of participation allows individual actors to exchange knowledge, concepts, ideas, and emotional support (Casaló et al. 2007;Koh and Kim 2004).
The organization may want to use stakeholder engagement only for selected activities (e.g., new product development) or maintain continuous contact with stakeholders (e.g., to update the strategy). Once an organization decides to engage stakeholders in strategic processes over the long term, the challenge remains to ensure their commitment to the strategymaking process (Mantere and Vaara 2008;Stieger et al. 2012). Therefore, it seems crucial to discover how to stimulate employees' motivation and willingness (Díaz-Fernández et al. 2014; García-Cruz and Valle-Cabrera 2021) and other stakeholders (especially external ones) to get involved in the company's life.
Including stakeholders in creating a company's strategy is based on networking activities, a common managerial practice (Starkey et al. 2000). Skillful building the relationship with stakeholders is significant in implementing various types of changes. As shown by (Mohrman et al. (2003), successful change implementation is linked to a mixture of different types and levels of networks. Therefore, we may claim that in the case of opening-up strategy making process, building and developing internal and external networks seems to be especially useful as 'the strategy process is an intensely social process where participating individuals and their strategic activities concerning idea generation, initiative development and strategic re-integration are embedded in networks of social relationships' (Hautz 2017(Hautz , p. 1958. Organizations creating networks of social relationships with internal and external stakeholders have to answer several questions: what kind of stakeholders to engage in strategic processes, under what conditions; which principles to consider (or not); how to communicate with different stakeholders, and finally-how deep and persistent relations should be established. The answers to these questions will help to determine whether strong or weak social network ties are being created while they both play, albeit different ones, a role in change implementation (Mohrman et al. 2003). Based on the previous research on OS, we may outline that inclusion concerns either internal or external consultation (Schmitt 2010) or even co-strategizing (Doz and Kosonen 2008). Thus, our conceptualization of the inclusiveness dimension would embrace two constructs: the actors being included, i.e., stakeholders and practices of inclusion, i.e., networking.
Based on the arguments provided, we may outline the initial set of constructs that should be considered while adopting the OS concept. As transparency and inclusion are applied at the same time, we may distinguish-the information content (what is communicated?), the communication process (how it is shared?), networking (how to include?), and stakeholders (who is included?). The theoretical model is presented in Fig. 1.

Development of the multi-item open strategy scale
The main advantage of employing the scaling techniques has already been outlined, as it provides the ability to measure the complexity of concepts investigated using multiple indicators (De Vaus 1996). Therefore, the analysis is more context-specific with greater precision, specifically ranking or classifying the groups and identifying subsequent differences or similarities observed (Green et al. 1988). In our study, three stages were taken to develop and validate the open strategy scale (OSS). The phases and procedures are described in Table 1. As Bearden et al. (1993) proposed, in the first stage, the theoretical definition of the construct's concepts employed in this study has been precisely outlined and delineated based on a systematic literature review. The OS was operationally defined to have two characteristics-transparency and inclusion, which were further discussed and plotted within the theoretical framework where the initial four constructs were described, namely information content, communication process, stakeholders, and networking. To enhance the statements' accuracy, readability and adequacy, a professional workshop with experts was included to refine the initial items. It included nine experts, seven academics specializing in strategy development and strategy implementation, and two

Networking
-creating cooperation networks -opening the strategy creation process -inclusion as an own initiative -leading role in building the relations Fig. 1 The theoretical model. Source: own work correlation coefficients between items assessment of dimensionality through exploratory factor analysis (EFA) and confirmatory factor analysis (CFA)

Test of unidimensionality
Scale validation Reliability analysis-assessment of reliability and internal consistency Validity analysis-assessment of convergent and discriminant validity Nomological validity analysis-assessment of correlations between constructs Source: own work academics-practitioners representing the strategic advisory services. The main goal of this step was to propose a set of items consistent with the literature and unequivocal. The selection was based on purposeful sampling to gain deeper insights into the investigated constructs. The initial multi-item scale consisted of six items tapping the information content, six tapping the networking, four tapping the communication process, and five tapping the stakeholders. The items were related directly or indirectly to the roots, obstacles, and activities aimed at opening up the strategy-making process in terms of transparency and inclusiveness. Further, an evaluation of items and data categorization (Charmaz 2000) of the construct's domain was performed (Bearden et al. 1993). The result of this study was twofold. Firstly, we were able to delineate the constructs definitions precisely. Secondly, as a result of the previous stage, we revealed that one construct, called stakeholders inclusion, is enough to integrate the previous two, as it covers both the participants of the process (stakeholders) and how it is communicated (communication process). That integration of constructs contributes to the qualitative stage of our study as we opted for model parsimony reflected in the theoretical simplicity (Aarts 2007). The simplified version of the instrument was then applied to a validation sample for purification (Netemeyer et al. 2012). As a result, we had 21 items proposed and grouped into 3 constructs that were further analyzed: information content (INF), networking (NET) and stakeholders inclusion (STI).
The items were derived to rate the level of agreement or disagreement within a questionnaire format, and to provide an extensive range of scoring, a Likert scoring from 1-5 was used. The statements were selected to reflect the attitude toward the investigated concept. The responses ranged from strongly agree to strongly disagree. The full version of the initial OSS items is included in Appendix.

Sample design and data collection
To test the scale proposed, we designed a study and collected relevant data. As we wanted to investigate the strategic management process, all respondents-CEOs, owners, strategy managers, and board members-were considered responsible for executing strategic management processes. A direct questionnaire interview was used to conduct the study, and the survey was carried out by applying the paper-andpencil interviewing method.
The research sample contained 150 Polish jointstock companies based on the Polish capital, and approximately half (50.7%) were listed on the Warsaw Stock Exchange and the New Connect market. All sampled companies were involved in various businesses but in almost equal portions connected with the production, merchandising, and services sectors. One respondent represented each company. Out of the total sample, 70% of questionnaires were completed by CEO or president, and the remaining by a member of the Board of Directors (17%) or vice president (13%). Responders were mainly male (67%), and in minority female (32%). The sample is balanced concerning the company size, and it consists of an equal portion of small, medium, and large companies.

Preliminary data analysis and refining the open strategy scale
Our preliminary data analysis relies on between items correlation analysis (see Table 2). We analyzed the correlations between items a priori assigned to the relevant conceptual dimensions (as presented in ''Appendix'') and correlations between these items and items belonging to other constructs. As pointed out in the study of Tian et al. (2001), items should be correlated with other items grouped a priori within one construct, i.e., corrected item-to-total subscale correlations should be at least 0.50. Additionally, items should not have higher correlation coefficients with items belonging to the remaining dimensions than with items included in the dimension to which they belong (Bearden et al. 1989). Adopting the abovementioned requirements related to the magnitude of between items' correlation coefficients, we excluded the following items from further analysis: INF1, NET1, NET2, STI1, STI3, STI8, and STI9. As a result of eliminating these items, the reliability coefficient alpha of each construct improved substantially. However, we decided not to exclude the following four items: INF2, NET4, NET5, and STI4, although the corrected item-to-total subscale correlation coefficient, as reported in Table 3, was slightly below the required limit of 0.5. We decided to proceed further with these items because excluding them  Correlation coefficients equal to at least 0.2 are statistically significant at the significance level of 0.05. Correlation coefficients between items apriori assigned to the construct are presented in bold. Following the study of Tian et al. (2001), we excluded from the further analysis items which have not been correlated enough with the remaining items in the construct, i.e., having multiple correlation coefficients of approximately at least 0.5. Based on the above rule, we excluded: INF1, NET1, NET2, STI1, STI3, STI8, and STI9. The summative statistics for each construct are included in Tables 2 and 3 Decision (March 2023)  In the next step, we employed all remaining items. We grouped them, as previously, in a priori-defined three constructs: information content (items INF2 to INF6), networking (items NET3 to NET6), and stakeholders inclusion (items: STI2 and STI4 to STI7). These items build a trimmed pool of items, which we next proceed through confirmatory factorial analysis (CFA) and explanatory factorial analysis (EFA). We calculated the coefficient of Kaiser-Mayer-Olkin (KMO) and Bartlett's test of sphericity to check whether factor analysis can be performed. The KMO in our sample equals 0.88, and the p value corresponding to Bartlett's test is almost 0. The KMO index ranges from 0 to 1, with at least 0.50 considered suitable for factor analysis (Tabachnick and Fidell 2013). The Bartlett's test of sphericity should be significant (p \ 0.05) for factor analysis to be suitable (Tabachnick and Fidell 2013). Both measures in our sample satisfy these limits. We used CFA to test the open strategy scale formulated a priori and EFA to investigate the structure of the items observed a posteriori. If the scale is reliable and valid, the results of CFA and EFA coincide, as demonstrated in the paper of Patil et al. (2008). Considering not large sample size (N = 150), we selected from the list of fit measures typically used to evaluate the fit of the structural equations model (subject to CFA analysis); these measures are less affected by the sample size. As suggested by Hu and Bentler (1999), we investigate the following indices combination: non-normed fit index (NNFI) introduced by Bentler and Bonett (1980), comparative fit index (CFI) of Bentler (1990), standardized root mean square residual (SRMR) introduced by Bentler (1995), and root mean   1954;Kaiser 1960) and Catell's scree test (Cattell 1966). When analyzing the loadings of factors yield from EFA, we set the cutoff point of at least 0.6 loading magnitude, taking into account the consequences of the relationship between the loadings magnitude and the fit measures of SEM investigated by Shevlin and Miles (1998) i.e., the higher the loadings, the better model fits the data. The results of the CFA and EFA analysis are displayed in Table 3. All CFA parameters are statistically significant. However, the fit measures indicate small misspecification (i.e., NNFI of 0.93 and CFI of 0.948 are slightly below the cutoff point of 0.95). The associated EFA results suggest that the probable source of misspecification generates item STI4. The EFA loading of STI4 on the STI factor equals 0.504, which is too low compared to the cutoff point of 0.6. Moreover, this item's remaining loadings are insufficient; therefore, item STI4 is excluded from the scale and further analysis. The remaining items have loadings above 0.6 which we assumed as sufficient. The number of factors extracted by EFA, based on Guttman-Kaiser criterion of eigenvalue equal at least 1, i.e., three factors with eigenvalues of 5.95, 1.37, and 1.13, and their loadings (beside item STI4) cover hypothesized structure of the constructs: information content, networking, and stakeholders inclusion. As a result of our analysis, our final model consists of three constructs and the following items: information content (items INF2 to INF6), networking (items NET3 to NET6), and stakeholders inclusion (items STI2 and STI5 to STI7). In the next step, we evaluate the a priori hypothesized latent structure.

Test of unidimensionality
The refined OSS should exhibit a latent structure of a higher-order factor model in which each of the three dimensions is the first-order factor. These factors collectively are accounted for by a higher-order factor. Statistically, such a model is equivalent to a threefactor correlated model. Following the approach of Tian et al. (2001) to evaluate this latent structure, we estimated six competing models: a one-factor model (i.e., assuming all items load on one single factor), a three-factor orthogonal model (i.e., assuming no correlation between three factors), a three-factor oblique model (i.e., assuming a correlation between the factors), and three two-factor oblique models in which all possible pairs of factors were combined to form a single factor that was correlated with the remaining factor. The goodness-of-fit measures of competing models are presented in Table 4. Among all competing models the three-factor oblique model fits the best the data and satisfy required limits, i.e., NNFI = 0.953; CFI = 0.963; SRMR = 0.051 and RAMSEA = 0.05. All CFA parameters (see Table 5) are statistically significant at a significance level lower than 0.01. The model is presented in Fig. 2. Based on the assessment results, we conclude that the completed evidence in the sample is in favor of the hypothesized measurement three-factor model of the OSS.
Having the CFA result for the three-factor oblique model, we employ EFA again and compare these analysis outputs to further test the refined OSS. The CFA and EFA results for the refined OSS are presented in Table 5. Considering the EFA results, the respective items load their factors significantly-all have values above the required level equals 0.6. Moreover, these loadings have visibly higher values with the factor they belong to than the remaining factors ensuring the discriminant validity. The CFA results and EFA results coincide: EFA extracted three significant factors, and CFA confirms the evaluated three-factor oblique model fits the data very well.
At the end of this stage, as a result of applied methodology resulting in 8 items reduction, our OSS consists of 13 items grouped into three constructs. It provides a desirable 'simple structure' as recommended by Bearden et al. (1989) and Pritchard et al. (1999) and represents a parsimonious explanation of open strategy. Moreover, a final number of items assigned to one construct (i.e., 5, 4, and 4 items, respectively) fulfills the requirements based on statistical model identification. A minimum of three items per construct minimizes problems with model convergence or unstable solutions (Hair et al. 2017).

Reliability assessment
The average assessment of the strategy openness in the sample was 3.38 and ranged between 3.14 and 4.37 for separate items, while the standard deviation was 1.27 and ranged between 1.03 and 1.51 for separate items. On average, the correlation coefficients between items for the information content construct equals 0.56, networking 0.40, and stakeholders inclusion 0.51. All correlations coefficient, as depicted in Table 2, are positive. The multiple correlation coefficients R calculated for all items included in the measurement scale, presented in Table 5, are about 0.5 and above this level. The magnitude and the direction of correlation observed in the sample suggest that responders tend to similarly assess information content, networking, and stakeholders inclusion dimensions of OS.
Reliability statistics confirm this statement. Cronbach's alpha for the entire scale equals 0.88, and for included in the scale constructs are 0.85 for information content, 0.71 for networking, and 0.81 for stakeholders inclusion.
Additionally, composite reliability (CR) for these constructs equals 0.89, 0.82, and 0.86, respectively. As Nunnally (1978) recommended, Cronbach's alpha should be a minimum of 0.7, while the composite reliability (Nunnally and Bernstein 1994) cutoff value for general research purposes is 0.8. Comparing our sample estimates of internal consistency to just recalled standards, we gathered evidence to confirm the OSS's reliability-the items included in the relevant construct jointly measure the same concept exhibited in this construct. This tendency replicates in all constructs: information content, networking, and stakeholders inclusion. however, the networking construct seems to reflect the lowest reliability, but its internal consistency measures are still acceptable.

Convergent validity
Each construct of the proposed OSS-namely information content, networking, and stakeholders inclusion is built out of items, i.e., INF 2-INF6, NET3-NET6, and STI2, STI5-STI7, which are observable variables. These items converge into three latent variables-one for each construct-and the question arises to what extent the aggregated latent variable explains the variation of the items included in the relevant construct. The standard measures of convergent validity are composite reliability (CR), average variance extracted (AVE), and factor loadings of EFA and CFA. The composite reliability was already discussed in the previous section. CR measures for all the open strategy scale constructs are at the aboverecommended level of 0.8 (Cronbach 1951). It means that items included in the particular construct are highly correlated, creating a good foundation for replacing them with one latent variable. Indeed, the average variance explained by extracted factors equals 0.63 for information content, 0.54 for networking, and 0.60 for stakeholders inclusion. All these measures are at the above-recommended level of 0.5 (Cheung and Wang 2017). Finally, we investigated the factor loadings of EFA and CFA models. As depicted in Table 5, all factors of EFA calculated for the scale's items load the factor they belong to substantially and, at the same time, do not load the remaining two factors substantially. EFA loadings are above the value of 0.7, and the value of variance extracted, amounting to 62,53%, corresponds to the most frequent values of these statistics observed in the research (Peterson 2000).
On the other hand, the standardized parameters of the CFA model estimated in our sample vary between 0.50 and 0.86. Although the popular cutoff value is 0.7 (Joe F. Hair et al. 2011), we decide to retain items with factors lower than 0.7 but higher than 0.5 for the following reasons. First, the EFA factors are substantially high, and all are higher than 0.7. Second, the deletion of the items with lower loadings reduces Cronbach's alpha, composed reliability, and goodness-of-fit measures for both CFA and EFA models. In such circumstances, lower loadings are acceptable (Joe F. Hair et al. 2011).

Discriminant validity
Discriminant validity generally holds when items belonging to the construct correlate with the latent variable (factor) of the construct to which they belong and, at the same time, weakly correlate with the remaining latent variables (factors) extracted for the remaining constructs. It can be investigated on both: EFA loadings and CFA loadings. To verify the discriminant validity of the proposed OSS, we first assessed the cross-loadings produced by EFA analysis (Gefen and Straub 2005). As reported in Table 5, EFA loadings show the intended pattern, i.e., in general, items load the construct factor to which they belong substantially higher than the remaining factors. The AVE values calculated for each construct are visibly higher than the identical measure of average variance explained calculated for the remaining two factors. AVE for information content equals 0.63, while identically calculated average variance explained for the remaining two factors, namely networking and stakeholders inclusion, equals only 0.12 and 0.27, respectively. The same holds for the second construct-networking; AVE for this construct equals 0.54 while the average variance assigned to the remaining two factors equals 0.12 and 0.15. The last construct, i.e., stakeholders inclusion, has an AVE of 0.60, higher than 0.20 and 0.16. Secondly, we employed in this study the Fornell-Larcker's criterion (Fornell and Larcker 1981), which we adapted to the values of the correlation coefficient (Henseler et al. 2015). For this purpose, we calculated the squared root of AVE based on CFA loadings and compared these values with the absolute value of the correlation coefficient reported in Table 2. The discriminant validity is established if the following condition holds: ffiffiffiffiffiffiffiffiffiffiffi ffi AVE j p [ max r ij . The squared roots of AVE for the following constructs are 0.75 for information content, 0.63 for networking, and 0.72 for stakeholders inclusion. The maximum correlation coefficient between the items loading information content and remaining items equals 0.6, and the respective correlation coefficient for the Networking equals 0.4, and Stakeholders Inclusion 0.5. The additional argument supporting the discriminant validity is the magnitude of the correlation coefficients between factors extracted by EFA. These correlations are: r(INF, STI) = 0.53, r(INF,NET) = 0.42, and r(NET, STI) = 0.44, and are accurate. The magnitude of the correlation coefficients supports the conclusion that the three constructs of the proposed OSS measure together one underlying concept. However, each construct separately captures a unique part of this one concept. As argued above, we have enough evidence to sustain that the proposed OSS demonstrates discriminant validity.

Nomological validity
Nomological validity refers to the degree to which specified a priori predictions on antecedents and/or consequents comprised in one nomological network containing the constructs of interest are confirmed (Bagozzi 1981). Technically, nomological validity is confirmed when all of the network's relations are supported in a single omnibus test of a model (Hagger et al. 2017). We employ the approach presented by Lee (2019) to test the nomological validity. We investigate the correlation coefficients estimated between the latent factors of the CFA model, as depicted in Fig. 2, and compare these estimates with predictions on formulated a priori relations between constructs determining the OSS. A relationship between stakeholders' involvement and networking has already been reported. For example, Heikkinen (2017) claims that addressing climate change requires involvement and collaboration among various stakeholders from businesses, governments, and civil society (a multi-stakeholder network). The relation between the information content and stakeholders' involvement has already been addressed. For example, Baptista et al. (2017) suggest more comprehensive access to strategic content and information to build stakeholder involvement.
To verify the nomological validity, we expect that all three constructs showed moderate to high correlations of 0.5 \ r \ 0.85 because we can formulate such a prediction based on the abovementioned studies. The estimated correlation coefficients between the constructs are: r(INF,STI) = 0.73; r(INF,NET) = 0.58; and r(NET,STI) = 0,71. All three correlation coefficients are within the predicted range, supporting the proposed scale's nomological validity. An additional argument is derived from the CFA model goodness-offit measures. As Hagger et al. (2017) claim, CFA allows testing formulated a priori networks simultaneously. In this context, the overall evaluation of model fit provides evidence as to whether the proposed model fits the observations to get an argument in favor of nomological validity. As reported in the section devoted to scale purification (see also Table 5), the estimated CFA model fits the data well. A good model of the proposed scale and the confirmation of predictions formulated separately for all relations included in the network are enough to conclude that the proposed OSS reflects nomological validity.

Conclusions
The OSS adequacy and accuracy As mentioned in the literature concerning OS, a gap exists in research focused on valid and reliable measures of strategy openness. In this article, we report on developing and validating the OSS that measures strategy openness through the lens of its two fundamental dimensions-transparency and inclusiveness. The OSS transparency dimension includes one core construct-information content (focused on the visibility of information about an organization's strategy). The inclusiveness dimension embraces two constructs-stakeholder inclusion (covers the participants of the strategizing process and how it is communicated) and networking (focused on practices of stakeholders' inclusion).
Our research shows that activities that reflect well on an organization's transparency in strategizing are related to the consultation process of the organization's strategic decisions with various stakeholders. Proposed OSS corresponds with the works of Heracleous (2019), Heracleous and coauthors (2018), and Lazarus and Mcmanus (2006), in which the perspective of dialogue with stakeholders as an essential element of transparency was analyzed.
Further, the OS practices describe the organization's transparency focus on keeping employees informed of strategic issues. We refer here to ensuring that employees know the company's strategy and strategic objectives and what is needed to achieve them. In addition, it is also essential to provide employees with regular information about the state of strategy implementation. The OSS aligns with the previous works concerning the content of information shared (Berggren and Bernshteyn 2007;Hautz et al. 2017;Yakis-Douglas et al. 2017).
According to our research, the inclusiveness dimension is well measured by the involvement of employees in the strategy creation process and considering their ideas in strategic decisions making. These findings also align with the works mentioning the qualitative depth of stakeholders' involvement in the strategy (Adobor 2020;Dobusch et al. 2019;Seidl et al. 2019).
Finally, based on our research, the inclusiveness dimension considered in the networking context is well-measured by an open approach to cooperation with a wide range of external stakeholders, including entities from other industries, by a willingness to ensure long-term cooperation and by established rules used to build relationships with competitors. The OSS corresponds with the work of Hautz (2017), where the strategy process is perceived as embedded in networks of social relationships, and the work of Seidl and Werle (2018), where the issues of inter-organizational collaborations are discussed.

Managerial implications
An essential contribution of the proposed OSS is that it may be used to identify the most crucial areas of transparency and inclusion development. That would allow us to prioritize the managerial decisions within each category of openness development and decide whether both dimensions are acquired at the same time. Having comprehensive knowledge would contribute to building organizational awareness and improve the decision-making process. Thus, the importance of using a combination of constructs proposed is also underlined. Finally, we may mention the contribution related to the analytical perspective, where an individual level of information content, networking, and stakeholders' engagement could be determined based on each subscale's score in the following criteria.

Limitations and further research
There are some limitations of our study that could be addressed in future research. First, we have not included the industry drivers that may impact the possibility of imposing higher transparency and could also influence the willingness to be more open. Among other limitations, we can mention the necessity to report or not reveal some data due to being listed on the stock exchange. Therefore, further research should be focused on scale validation in various samples where organizational and industry limitations would be included. It could also employ the international context as our research could be further duplicated on different markets to check the impact of international idiosyncrasies.

Declarations
Conflict of interest The authors have no relevant financial or nonfinancial interests to disclose.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. In our company, we hire external consultants who play a crucial role in the strategy creation process STI2 In our company, it is important to communicate the strategy to our employees STI3 Employees know the strategy mainly through informal contact with the CEO STI4 During the strategy communication process, we often use formal outlets (i.e., brochures, newsletters, posters, announcements) STI5 The company's future is an essential topic of discussion between the management team and employees STI6 We involve all employees in the process of strategy creation STI7 Ideas of different employees are taken into account when making critical decisions in our company STI8 In our company, the strategy also considers stakeholders' interests other than the owners STI9 In our company, all employees have the autonomy to decide how to implement the strategy