A cubic regression model to measure the impact of accidents on the number of incidences in the State of Kuwait

The regression analysis theories play a crucial part in safety traffic applications. A cubic regression model was specified in this article to fit the annual traffic incidents in Kuwait during the period 2002-2017 based on annual traffic in Kuwait. Estimation results using the least square estimation and the goodness of fit using the sample autocorrelation function are used to demonstrate the appropriateness of the estimated cubic regression model. As a result, the cubic regression model is supported using the residual analysis through the sample ACF, the sample partial ACF, and the normal probability plot NPP figures of the residuals .

Introduction
Policymakers often have an essential question to ask whether the implementation of speed limits, seatbelt laws, or a sudden increase in population due to a random event(s) impacts the extent and security of trafficrelated accidents and the number of incidences.
Traffic accidents form one of the most common modern-day problems that cause deaths and injuries. Today, Traffic Incidences are placed at the top of the list in several countries due to causing high mortality rates and severe injuries. Gulf countries, furthermore, report very high numbers as they suffer from substantial losses, including economic and social impacts and other economic problems related to traffic and the environment in general. Furthermore, most traffic accidents sufferers are young people, which causes a deterioration in a vital part of the population.
Several countries in the Gulf have recognized the importance of traffic safety and the typical association with social and economic growth, public policies, and developed plans to increase the overall traffic safety level. A set of individual budgets have been allocated to overlook projects and plans, including studies in traffic safety, enactment of the advancements in infrastructure, treating harmful accidents, and increasing general traffic safety awareness.
In the past, Gulf states faced an apparent movement towards more democracy, openness, and freedom, resulting in progressing economies and increasing incomes. It subsequently led to an increase in the demand PEN Vol. 9, No. 4, September 2021, pp.23-30 24 to acquire vehicles of different types, and Kuwait's case was not any different. With increasing numbers of vehicle acquisitions, Kuwait suffered from traffic problems such as traffic congestion, environmental pollution, and traffic accidents which is the primary cause of the increase in the youth mortality rate impacting the Kuwaiti Society and economy negatively.
Consequently, it becomes necessary to study the traffic problem analytically and statistically to find the root of the problem and reduce traffic accidents and state the positive economic and social effects associated with them.
This paper aims to specify a mathematical model to study the annual total number of traffic incidences in relation to the total annual number of traffic accidents in Kuwait. More specifically, a cubic regression model was considered, and estimation was done using the least square estimation (LS) method. The goodness of fit using sample autocorrelation function (ACF) and partial ACF was also used to prove the potentiality and suitability of the proposed cubic regression model in fitting the annual traffic accident data's impact on the total annual number of incidents in Kuwait during the period 2002-2017.

Literature review
Traffic accidents in all societies cause one of the most significant social and economic problems. However, different societies have differences in the quality and quantity of the accidents subject to differences in the drivers themselves despite various intersecting factors leading to these accidents. The road type in terms of appearance, extensiveness, trees, rocks, obstacles, and various other factors. Also, the different categories of drivers coming from different educational, demographical characteristics, and psychological characteristics play a major part in traffic accidents. A few previous studies having an indirect or direct relation to the paper's problem will be reviewed.
[5] has pointed out a direct connection between the drivers' cultural and educational level and traffic accidents. He believed that individuals do not feel obliged to obey the public systems and traffic rules in the absence of police officers as drivers may lack driving ethics.
The intersections on the roads which do not have clear signages for drivers are one of the leading causes of traffic accidents [1]. Also, the vehicle's maintenance level affected the accident percentage in the area, necessitating a regular patrol and maintenance of the vehicle to minimize traffic accidents resulting from it. [12] delivered an inclusive analysis of the modeling techniques and used it to analyze traffic accidents, the severity of the injuries they cause, driver and pedestrian behavior, and the roadway accidents' operational considerations related to.
According to [4], it is indicated that traffic accidents would be fewer among the higher educational level category due to improved skills and road ethics. Additionally, the negative psychological trends and emotional factors concerning social situations in daily life led to an unstable and turbulent psychological state causing it to be a significant factor in accidents.
The selection of the statistical method is expected to change the impact of an event that has been reported in the literature. Two statistical techniques were used in [13], which addressed risk compensation, the effect of the 1985 seat belt-use law in Illinois. One is related to a before and after method, and the other is related to the analysis of intervention using Autoregressive Integrated Moving Average ARIMA techniques. The developed time series intervention models revealed no statistically significant increase in traffic accidents. Unlike the before-and-after method, the developed time series intervention models revealed no significant change in traffic accidents. Nevertheless, the reported conclusions in that study opposed those reported by [6], [7], [8], [9], who used the traditional before-and-after analysis; in [13], it was claimed that the model misspecification and correlated error terms played against regression techniques.
Other studies have aimed to find the effect of the 55-mph speed limit on traffic accidents in the literature. A domestic speed limit of 55-mph was forced during the 1973 energy crisis in the USA. Meanwhile, numerous studies have assessed the influence of such a speed limit on traffic accidents (TRB, 1984 The impact of a reduced speed limit on the inclination of traffic accident rate has been addressed by [11]. The study specifically dealt with the time intervention when the speed limit was reduced, which significantly impacted traffic accidents.
The study on the traffic in Kuwait determined the leading causes analytically and statistically [2]. He provided probability and statistical models associated with the study's data from the year 2002 up to the year 2013. Also, he aimed to detect the economic and social effects on Kuwait's society, besides the institutions and government role, to decrease repetitive violations and accidents by using policies, rehabilitation programs, and laws.
A method capable and convenient to fit the traffic accident data which departed from the traditional beforeand-after regression techniques and the time series analysis and developed a method capable of fitting the yearly traffic accidents in Kuwait using a convenient lognormal diffusion process was carried out by [3].
[10], specified a rigorous mathematical model to investigate the effect of the Gulf crisis in 1990, imposing numerous families that went back to Jordan on the monthly total number of traffic accidents there. A stochastic diffusion model was specified and estimated in that study. They found that the Gulf crisis did not significantly influence the total number of traffic accidents. [14], proposed a different method for estimating the frequency of accidents at various severity levels, specifically the two-stage mixed multivariate model, which mixes both accident severity and frequency models. The accident, traffic, and road characteristics data from the M25 motorway and adjacent main roads in England have been collected to show the two-stage model's use. It was noticed that the two-stage mixed multivariate model is an encouraging technique to predict accident frequency concerning their site ranking and severity levels.

Statistical analysis
The statistical analysis to calculate the appropriate statistics was founded using SPSS statistical package, such as the following: 1) We use some descriptive statistical measures to calculate the minimum value, maximum value, sample mean and sample standard deviation, in addition to confidence intervals to calculate the 95% confidence intervals for Kuwait's yearly traffic incidence and accidents.
2) We use the regression analysis to fit the effect of the yearly traffic accident data on the annual total number of incidents in Kuwait during the period 2002-2017 and predict the annual number of incidences for the period from 2018 to 2022.

Statistical measures and confidence intervals
To study the suggested cubic regression model, we obtained the yearly observations of Kuwait's total incidence and accident data from 2002 to 2017 from the Kuwait Traffic Police Department, as shown in Table  1 below. We summarized the statistical measures and the confidence intervals using the SPSS analysis for the above data in Table 1, as shown in the following Table 2:

Cubic regression model
Assume the dependent variable Y to be the yearly total number of traffic incidents and the independent variable X to be the annual total number of accidents; then the cubic regression model is given by are regression model parameters. And  is independent sequence and identically normally distributed with zero mean and unit variance 2  . Now, using the least square estimation method, we get the fitted cubic regression model as follows: Where the estimated values of the model parameters can be found using SPSS software. Now, the following results are obtained using the SPSS analysis for the data in Table 1: The independent variable is Accidents. The above results show that the correlation coefficient is 0.959, which indicates that the two variables under investigation are highly correlated. Also, the coefficient of determination is 0.920, which suggests that the cubic regression model is explained by 92% of the variation, resulting in the cubic regression model accurately fitting the data.
We find the estimated parameters using the least square estimation method, as shown in the above output. Thus, the estimated cubic regression model is given by

Residual analysis
In this section, we checked the goodness-of-fit of the suggested cubic regression model using a test based on the sample autocorrelation function ACF and the sample partial ACF as well as the normal probability plot of the rescaled residuals ( ) . Assuming the residual be as follows (c.f. [3]): Let and be the mean and the standard deviation of the residuals respectively in this case and ). Thus, the rescaled residuals are then defined by (c.f. [3]): Rescaled residuals ( ) were used to assess the goodness-of-fit of the estimated cubic regression model. Precisely, the residuals should be independently distributed with mean zero and constant variance. The sample autocorrelation function of ( ) and the values with the bounds ( ) checks the compatibility with independence. If more than 5% of the values sit out of the limits, then the residual's independence is rejected. Figure 2 shows the sample autocorrelation function of . It is also evident that the model's residuals pass the independence test, which supports the overall goodness-of-fit of the projected cubic regression model.

Prediction of future incidents
For prediction purposes, we first should predict the future annual number of Kuwait traffic accidents. In this case, the average annual rate of increase is computed and found to be equal to 1.085 and then by multiplying it with the number of traffic accidents for the year 2017 to get the number of traffic accidents in the year 2018, and by multiplying it with the number of accidents for the year 2018 to get the number of accidents in the year 2019, until we forecast the number of accidents in the year 2022. Using the fitted cubic regression model obtained in equation (3) above, we get the predicted annual total number of incidences from 2018 to 2022.
Therefore, Table 3 below shows the actual and predicted annual traffic incidents data from 2018 to 2022. Also, Figure 5 shows the predicted annual number of incidents for the same period. Note that the total number of traffic accidents from 2018 to 2022 is predicted recursively using the yearly increase rate, as stated earlier.

Concluding remarks
This paper aimed to specify a mathematically sound model to study the annual total number of traffic incidences in relation to the total yearly number of traffic accidents in Kuwait using a cubic regression model, and estimation was done using the least square estimation (LS) method. The goodness of fit using sample autocorrelation function (ACF) and partial ACF was also used to prove the capability and appropriateness of the suggested cubic regression model and fit the yearly traffic accident data's impact on the total annual number of incidents in Kuwait during the period 2002-2017. It was found that it is reasonable to fit the annual total number of traffic incidents data based on the total number of traffic accidents in Kuwait by using a cubic regression model, which is supported by the residual analysis through the figures of the sample ACF and the sample partial ACF as well as the normal probability plot of the residuals . Therefore, this study provides a capable and convenient methodology to fit the effect of traffic accident data on the traffic incident data in Kuwait. In terms of future research, this method could be helpful to study the impact of using traffic control devices on certain transportation services and introducing mandatory laws for traffic in Kuwait.


extfieldsofstudy: Physics Business

text:
Optimal Clearing Model of Centralized Market Considering Path Constraints

China’s electricity market is now still in the mode of “Unified market and two-tier operation” including provincial and inter-provincial market. The inter-provincial market is divided into the medium and long-term market and spot market. This study takes the inter provincial spot market as the research object, and proposes a unified optimization clearing algorithm for inter provincial spot market considering path constraints. The proposed method is able to handle AC-DC hybrid electricity network, and sort and determine the trading pairs using power flow tracing algorithm. The power market software PLEXOS and practical market data are used to simulate the proposed model, and the results show the accuracy and effectiveness.

provincial and spot markets, is gradually formed. The number of provinces participating in the inter provincial spot market will continue to increase, and the provinces that do not participate in the inter provincial spot market, such as JingIinTang area, Fujian and so on, will be gradually included.
Thirdly, the market is becoming more and more complex. In order to improve the operation efficiency of the market, the inter provincial spot market and the regional peak regulation ancillary service market will be gradually integrated in the future. The CRIP market will be an AC -DC hybrid market in which the power flow directions on AC lines are not unidirectional.
Based on the above considerations, this study proposes a unified optimization clearing algorithm for inter provincial spot market considering path constraints, such as node power flow balance, line power flow constraints, line ramping constraints, trading path constraints, etc.
The main features of the model are as follows: first, it supports the solution of complex AC / DC hybrid network with uncertain power flow direction, adopts the unified clearing method, constructs the mathematical unified optimization equation, and does not set the fixed path. Secondly, it is compatible with the current fixed path trading mode, and develops the path constraint algorithm to support the clearing method on the fixed path at present. Thirdly, the power flow tracing algorithm is innovated and developed, which can solve the power flow path from sending province to receiving province, which is convenient for transaction matching and settlement.

Model
The topology of the proposed CRIP spot market is taking the provinces or price areas due to congestion in the province as the base node, and building cross regional AC / DC hybrid network. Under the conditions of transmission security constraints and price constraints, the participated power resources are uniformly and optimally allocated with the goal of maximizing the social welfare.

2.1.Optimization goal
The goal of the optimization is to maximizing the social welfare, where the Welfare = Purchasing cost -Generation cost -Transmission cost. The equation is shown as follows. Where at a specific time interval, X , is the clearing power output of purchaser i at band b of its bidding curve, and P , is the corresponding price on band b, and there is a total number of n purchasers. X , is the clearing power output of generator i at band b of its bidding curve, and P , is the corresponding price on band b, and there is a total number of m generators. X is the clearing power output of line k and P is the wheeling charge of line k.
In order to implement the power flow tracing method, the transmission clearing power output variable X is decomposed into multiple sub-variables, shown as the following equation.

, , 2
In which, variable x i, j, k indicates the power energy transmits from generator i, flows through transmission line k and finally reaches to purchaser j.

2.2.Constraints
The node power injection constraint, the line flow constraint, transmission and ramping up and down constraints and path constraint are considered.

2.2.2.Line constraint
The clearing power on a specific line should be within its ATC limits. , , 4

2.2.3.Ramping constraint
The power ramping between two consecutive time intervals should be within the transmission line maximal adjusting capability.

2.2.4.Path constraint
If there is a fixed trading path s between generator i and purchaser j and line k is part of the trading path, the variable x i, j, k will be included in the model and be computed. If not, the value of x i, j, k will be forced to zero.

Simulation Results
A case study is carried out by using a set of practical data on one operation day of CRIP spot market. The total power bidding by generators is 37.619 million kWh, while the total power bidding by purchasers is 620.965 million kWh. The electricity market simulation software PLEXOS is used to model the CRIP market. The schematic diagram of the model is as follows. Figure 1 Diagram of Inter-provincial Spot Market In the above diagram, the lines include both AC and DC lines There are 33 bidding data from sending end and 16 bidding data from receiving end. A total of 47 lines was modeled, including parameters of loss rate, wheeling charge, power flow limits and etc. A unified optimizing clearance algorithm was applied by PLEXOS.

3.1.Case 1 -Compare actual results and simulated results
By setting the path constraint in the above proposed model, the comparison results are shown as the following tables.  The results are basically consistent, which verifies that the unified clearing algorithm considering path constraints can achieve the optimization goal as the same as matching clearing method.

3.2.Case 2 -Compare different market clearing methods
In this case, the high-low matching clearing algorithm and proposed unified clearing method are compared. The comparison results are shown as following. The unified optimization clearing algorithm optimizes the global variables, improves the transmission utilization rate, and further promotes the renewable energy consumption. Based on the unified clearing method, the trading volume was 13 million kWh; based on the fixed path matching clearing, the trading volume was 12.1 million kWh. It can be seen the unified clearing method was more effective than the fixed path matching clearing, and increase the trading volume by 900 thousand kWh.

Conclusions
In this research, it proposes a unified optimization clearing algorithm for inter provincial spot market considering path constraints. The proposed model supports the solution of complex AC / DC hybrid network with uncertain power flow direction and is compatible with the current fixed path trading mode. Moreover, the power flow tracing algorithm is innovated and developed, which can solve the power flow path from sending province to receiving province, which is convenient for transaction matching and settlement. Simulation shows the accuracy and effectiveness of the proposed method. The proposed method can be taken as reference for future inter-provincial market design to better promote the renewable energy and optimize the allocation of power resources in large-scale range.


STIMULATION OF INNOVATIVE BEHAVIOR THROUGH THE INCLUSIVE LEADERS AND ENGAGED WORKERS

. Based on social exchange theory, this research introduced a model to understand factors that contribute towards inclusive leadership (IL) and its effect on innovative work behavior (IWB) with employee engagement (EE) as a mediator. Although the connection between IL and IWB is previously established. However, few studies have tested the potential mediation effect of EE particularly in the IT sector. Therefore, this investigation provides new insights as to how IL stimulates the innovation through the meditating impact of EE. Data collected through questionnaire were then analyzed through structural equation modeling. 116 participants have provided the data for this study. We found a positive association of IL with IWB, while the mediating effect of EE was also empirically established. This study is novel because it explained how IL can persuade their subordinates to exhibit positive behavioral outcome (i.e. IWB). Furthermore, the current study also might help the policymakers to devise effective leadership training programs so that their managers may adopt IL style and make the employees more engaged and innovative.

Introduction
Today's era of intense competition has made it essential for organizations to stay competitive and innovative as compared to their rival firms. This can be achieved through an engaged and innovative workforce. Organizational innovation highly depends on the employees' innovative work behavior (IWB) and it provides a competitive advantage to the firms (Mansoor et al., 2020). Employees' IWB includes development, promotion, and implementation of novel ideas (Janssen, 2000). IWB is an extra role behavior of employees that is practiced in the turbulent business environment. Therefore, new challenges can be effectively met in a dynamic environment (Scott & Bruce, 1998). Agarwal (2014) found that the organizations are very much inclined to discover antecedents of employees' IWB. Scholars have highlighted multiple antecedents of IWB at organizational levels. It was discovered that the organizational innovation can only be achieved through the inclusion of innovative workers.
Leadership is perceived to be among the most pivotal factor in the stimulation of creativity and innovative more innovative. EE is considered a critical success factor particularly in the service sector organizations, because engaged staff can better serve the needs of the customers (Nazir & Islam, 2017). Recently, researchers have identified the need to further explore the possible impact of EE on leadership-innovation relationship (Karatepe & Olugbade, 2016). Therefore, the current investigation posits that the EE can possibly mediate the association of IL and IWB. This study has two research questions.
RQ1: How does IL promote the innovation among their employees?
RQ2: Does EE mediate the relationship of IL and IWB? To contribute to the existing literature, this study provides useful insights regarding how IL promotes employees' IWB. It tries to unearth which practices and measures are required to persuade the employees so that they can make the firm successful through innovative ideas. Additionally, this investigation explains how a leader can stimulate innovation among their workforce. Besides, this research has also explored the mediation effect of EE, which enriches leadership literature by identifying the IL as an antecedent of EE. Lastly, drawing upon social exchange theory, this investigation tries to explore the role played by IL in the promotion of IWB through the development of EE. This will further enhance the understanding of policymakers regarding the suitable leadership style required to stimulate employees' IWB.

Inclusive leadership and innovative work behavior
In today's business world, stimulation of innovative behavior is considered as the most important function of the leadership (Amin et al., 2018;Hakimian et al., 2016). IL is vital to create a climate for innovation within the organizations, which ultimately promotes IWB of workers (Ashikali et al., 2020). The leader, who follows the inclusion approach, would engage their followers in the goal development process. Additionally, inclusive leaders would also ensure the availability of all the resources required to achieve the firm's objectives (Khan et al., 2020). Agarwal (2014) identified the important role played by IL in making the employees innovative and creative. The inclusion of employees in the key decision making enhances their ability to perform. Hollander (2012) explained that IL encourages its followers to become risk-takers, as this would lead towards the implementation of novel ideas. As a result, employees present and implement their ideas without the fear of consequences. Javed et al. (2017) conducted research in the Pakistani textile industry and found that the IL significantly promotes IWB. Similarly, Mansoor et al. (2020) identified that the culture of inclusion created by the inclusive leaders stimulates the employees' innovation. Therefore, this research posits the following hypothesis: Hypothesis 1: IL positively influences the employees' IWB.

Inclusive leadership and employee engagement
Recently, EE has gained a lot of attention from practitioners and academicians (Chen et al., 2020;Zheng et al., 2020). Several organizational outcomes depend largely on the EE (Bakker & Albrecht, 2018); hence, this became the primary reason for continued interest from various scholars. Therefore, organizations are striving to develop and retain engaged workers so that they could help the organizations to gain success in the turbulent business environment. Moreover, IL offers a encouraging work environment that develops extra role behavior such as EE (Choi et al., 2015). Wang et al. (2019) conducted a study on Chinese nurses and found that the IL positively promotes their level of engagement with the work. Similarly, Cenkci et al. (2020) found that the workers' engagement depends largely on the inclusiveness and fair dealing of organizational leaders. Based on these arguments, we posit the hypothesis as under: Hypothesis 2: IL positively influences the EE.

Employees' IWB and employee engagement
The full commitment of the workers to perform their job tasks refers to the EE. Therefore, EE is directly associated with the job commitment. Likewise, it was empirically established that the empowered employees become more engaged with their work, as workers perceive that they are trusted by their top management. This positive perception makes the workers more loyal and committed to the firms. Resultantly, they are much more inclined to stick with the company and keep doing better. Furthermore, it was also found that the EE becomes an antecedent of IWB (L. Miller & A. F. Miller, 2020). Similarly, a study conducted by Al-Ajlouni (2020) found that the employees exhibit IWB when they were more engaged with their job. So, this research posits the following hypothesis: Hypothesis 3: EE positively influences the employees' IWB.

Mediating effect of employee engagement
IL shows accessibility to their followers to make them more engaged in decision making and goal setting. Inclusive leaders not only involve the workers in decision making, but they also appreciate the input received from them. Nembhard and Edmondson (2006, p. 948) mentioned this as "their voices are generally valued". The positive perception created through IL would certainly enhance the commitment level of individuals. Carmeli et al. (2010) categorized IL as one type of relational leadership. Like other relational leadership styles, IL also promotes positive behavior among the workforce. Lisbona et al. (2018) suggested that the engaged employees demonstrate a higher performance level as compare to those who have less commitment to the organization. Likewise, Choi et al. (2015) mentioned that IL generates positive organizational outcomes such as higher performance, EE, and innovation. It was suggested by Lisbona et al. (2018) to further examine the impact of EE as to how it influences the employees' IWB. Hence, this investigation posits the hypothesis: Hypothesis 4: The interlinkage of IL and employees' IWB is mediated through EE.
The following theoretical model (Figure 1) is proposed to check the relationship between IL, IWB, and EE.

Sampling and data collection
The current investigation has obtained the data from the workers of Pakistani IT firms through the application of cross-sectional research design. These firms are selected due to hyper-competition and complex business environment prevailing in the IT industry, which has made it essential for the organizations to direct their attention towards employees' IWB (Javed et al., 2019).
In order to select the participants, the lead author contacted ten IT firms and explained the purpose and importance of the study. Three firms were agreed to provide data for the research. Therefore, all the questionnaires were sent through online mode because IT professionals may find it more convenient due to their continuous internet usage. Additionally, the COVID-19 pandemic situation made it more feasible to collect the data online. 150 questionnaires were sent on the official email addresses provided by the human resource department. Finally, 116 responses were included in the data analysis, and 34 responses were rejected due to the incomplete responses. Table 1 provides details regarding the sample.

Measures
We adopted standardized questionnaires for the data collection purpose. Unless otherwise stipulated, a five-point Likert scale was used to measure the dimensions. Employees' perception of IL was assessed through the scale developed by Carmeli et al. (2010). This scale has comprised of nine items. The value of Cronbach alpha was 0.87. This scale identifies the perception of employees as to what extent they think their managers are exhibiting IL behavior.
IWB was measured through the 9 item scale of Janssen (2000). The value of Cronbach alpha was 0.83. This scale was also used by Mansoor et al. (2020) in his study. For measuring EE, we used the scale developed by Schaufeli et al. (2006). The responses were obtained through the 7 point Likert scale ranging from "Never = 0" to "Always = 6. " The Cronbach alpha was 0.81. Through this scale, the researchers have tried to guage the level of engagement within the employees.

Results
This investigation has used the structural equation modeling technique through SmartPLS version 3 for testing the proposed hypotheses. Due to its predictive nature, SmartPLS was used in this study (Hair et al., 2017). It also provides more reliable results even when the sample size is small (Henseler et al., 2015). Table 2 presents Cronbach alpha values, which depict the reliability of the instruments. The values of Cronbach alpha ranged from 0.84 to 0.90; therefore, it satisfies the desired level of >0.70 as per recommendation of Fornell and Larcker (1981). The values of AVE and Composite reliability have also fulfilled the criteria set by Fornell and Larcker (1981). Thus, we established the composite reliability and convergent validity of the scales. (HTMT) were used to determine the discriminant validity of measurement scale. Kline (2015) proposed that the HTMT value should be < 0.85 for establishing the discriminant validity. Table 3 presents the values of HTMT which are well below the recommended value of less than 0.85. Thus, it confirms the discriminant validity of the scale. From the below presented table (Table 4), it can be seen that values of factor loadings are above .70 which establishes convergent validity.

Structural model
The bootstrapping procedure was applied to examine the hypothesized theoretical model. Firstly, we test the impact of inclusive leadership on innovative work behavior and employee engagement. Results revealed that inclusive leadership significantly and positively impacts the IWB and EE; therefore, both hypothesis 1 (IL positively influences the employees' IWB) and hypothesis 2 (IL positively influences employee engagement) are accepted. Furthermore, the interlinkage between EE and IWB was also found significantly related. Hence, hypothesis 3 (Employee engagement positively affects the employees' IWB) was also supported. The mediation effect was tested by following the procedure suggested by Nitzl et al. (2016). The indirect impact of inclusive leadership on employees' IWB through EE is significant and positive, but it is reduced in size (Table 5). Therefore, it shows that the EE has partially mediated the association between IWB and IL. Through this, the hypothesis 4 (i.e. The association of IL and IWB is mediated by EE) was also supported.

Discussion and conclusions
This investigation aimed to highlight the impact of IL on employees' IWB with the intervening role of EE. All the hypothesized relationships were supported in our study. It was found that the IL promotes IWB among employees and EE mediates this relationship. The positive association between IL and employees' IWB stresses the need for an inclusive organizational culture for the promotion of innovation. Inclusive leaders involve their subordinates in decision making and keep them abreast of full knowledge related to the organizational goals. As a result, employees come up with the innovative thoughts without the fear of negative consequences. Moreover, IL makes people more confident and they can freely implement their creative ideas. This result also matches with other studies (e.g. Ashikali et al., 2020;Mansoor et al., 2020).
This investigation has also revealed that IL affects the behavior of employees through the intervening role of EE. The mediating role of EE depicts that the employees feel obligated towards their organizations because of the inclusive behavior shown by its leaders. Inclusive leaders promote a culture of cooperation which makes the people more involved with their tasks and organization. Therefore, it makes sense that the engaged employees would exhibit positive behavioral outcomes in the form of IWB. Although it is empirically established that the IL positively influences multiple behavioral outcomes; however, scholars (e.g. Younas et al., 2020;Zeng et al., 2020) stressed the need to further explore this relationship through the inclusion of different meditating variables. Hence, this research has responded to the call for research from various scholars and analyzed the mediating role of EE.
This study found that the IL significantly influences employees' IWB and the mediation impact of EE on the IL-IWB relationship was also established. This research has offered valuable insights to the managers of the IT industry in specific and other related industries in general. The exhibition of IL style would enable the firms to become more innovative and competent. Organizational success depends largely on the innovative capabilities of its workers. Therefore, this investigation has identified a suitable leadership style i.e. IL, which may stimulate innovation among their staff. Thus, this research offers both theoretical and practical contributions.

Theoretical implications
The current investigation has contributed to the literature of leadership by identifying the role of EE as an intervening variable. Although the effect of IL on employees' IWB is previously established; however, the mediating effect of EE makes it more clear as to how IL stimulates innovation among the workers. Additionally, our research has established the direct association between EE and IL. Therefore, it enhances the understanding of IL style and presents a new perspective to look into this relational leadership style (Uhl-Bien, 2006). Furthermore, this research has established the mediation effect of EE in the IL-IWB relationship. This result may direct the attention of other scholars towards the testing of EE as a potential intervening variable in the association between IL and other outcomes related with the firm. Finally, this is one of the pioneering study which has explored the relationship of EE, IL, and IWB specifically in the Pakistani IT sector.

Managerial implications
Hyper-competition has increased the need for the adoption of innovative practices to remain competitive. Leadership encourages employees to become more innovative (Ashikali et al., 2020). Therefore, this research provides several practical implications for the organizational policymakers. First, the managers should demonstrate accessibility to hear the issues faced by the workers. Managers should also make all necessary resources available for the individuals so that the workers could implement their novel ideas. Additionally, this research has revealed that the employees would exhibit IWB when they are encouraged through the IL style. Hence, it is recommended for the supervisors to adopt the necessary elements of IL (i.e. accessibility, openness, and availability).
Secondly, the outcome of this study emphasizes the effective management of human resources, specifically related to the IT industry. This industry requires those workers who possess intensive technical knowledge and potential for coming up with creative ideas. Therefore, this research provides useful insights to conceptualize the effective way of leading those individuals through the concept of IL. Leaders exhibiting IL style would promote a conducive environment in which people can share and implement the creative solutions without the fear of consequences.
Thirdly, we recommend that the top management should promote those IT managers who exhibit IL style. Furthermore, training programs should be initiated to make the managers familiar with IL style. Lastly, this study has highlighted the role of EE as an important predictor of positive behavioral outcomes. Therefore, organizational policymakers must adopt measures to increase the level of EE. To do so, supervisors should cultivate an environment of openness and make themselves accessible whenever the need for consultation emerge among the employees. In this manner, personnel would perceive that they are important and valued for the organization and this will consequently increase their engagement level.

Limitations of research and directions
Despite of its contribution, this research also has some potential limitations which would become future directions for other researchers. Our study has collected data from one source i.e. employees. Thus, future studies should collect data from both the managers and employees. Moreover, this research was conducted with small sample size due to the impact of COVID-19 pandemic. Therefore, future research should test this model in a bigger sample size in order to generalize the outcome of their investigation. In addition, intrinsic motivation can also be used as a mediator in the future studies. Lastly, there is a need to test this model across different cultures and industries, as the current study was conducted in the Pakistani IT industry.

Author contributions
Adil Mansoor and Sazali Abdul Wahab conceived the study and were responsible for the design and development of the data analysis. Adil Mansoor and Sarwat Jahan were responsible for data collection and analysis. Adil Mansoor wrote the first draft of the article.

Disclosure statement
The authors do not have any conflict of interest.


From toilet to table: value-tailored messages influence emotional responses to wastewater products

Background Products made from recycled organic materials are an important part of a circular economy, but the question is whether they will be adopted by the public. Such products can elicit strong emotional responses and public resistance. As a case in point, we studied products made from sewage waste, such as recycled toilet paper, which can serve as material alternative to wood and plastic when making household items (e.g., tables). In an experimental study, we investigated the role of values in emotional responses to such wastewater products, and whether emotional responses were influenced by value-tailored messages. We expected that people would experience positive emotions towards products that supported their values, especially when the messages emphasised the benefits of these products for their values (e.g., when the products were presented as good for the environment). We presented participants with one of two messages describing wastewater products as having positive implications for either biospheric values (i.e. positive consequences for the environment) or hedonic values (i.e. positive consequences for personal enjoyment). We predicted that the relationship between values and positive emotions would be stronger when the messages emphasised the positive implications of wastewater products for one’s core values. Additionally, we predicted that emotions would be associated with acceptability and intentions to purchase the products. Results The more strongly people endorsed biospheric values, the more positive emotions they reported towards wastewater products. As expected, this relationship was stronger when the environmental benefits of products were emphasised. Hedonic values were significantly but weakly associated with more negative and more positive emotions, and this did not depend on the message framing. However, we found that emphasising pleasurable benefits of wastewater products reduced positive emotions in people with weaker hedonic values. Positive and negative emotions were significantly associated with higher and lower acceptability of the products and intentions to purchase the products, respectively. Conclusions Our findings have implications for the effective marketing of wastewater products. For people with strong biospheric values, emphasising the positive environmental consequences may promote wastewater products. Such biospheric messages do not seem to make the products less (or more) appealing for people with strong hedonic values, who do not generally have strong emotional responses to these products. We discuss the theoretical implications of our findings and avenues for future research. Supplementary Information The online version contains supplementary material available at 10.1186/s13068-021-01931-z.

Introduction
There is an urgent need for production and consumption systems worldwide to become more sustainable in order to combat climate change and environmental destruction [18]. An approach that is currently being widely promoted is to transition away from a linear economy (i.e. "take, make, use, dispose") towards a more circular economy, which aims to reduce energy usage, reuse materials and minimise waste as much as possible [9]. As part of this transition, it is important to encourage consumer adoption of products made from recycled resources. However, recycled materials have the potential to elicit strong negative emotions in consumers. This is particularly the case for products made from sewage waste, such as recycled water (e.g., [10,30,39]) and materials made from recycled toilet paper (e.g., see the website, Cell-vation; https:// www. cellvation. com). Public resistance to wastewater products and other recycled products could impede a successful sustainable transition [18,36]. It is therefore important to better understand the psychological bases of emotions elicited by these products, as well as the relationships between emotions and product acceptability and adoption.
Emotions play a key role in consumer satisfaction with products, as well as consumers' willingness to purchase and use products (e.g., [27]), see also a special issue in the Journal of the Association for Consumer Research for a collection of recent research on this topic; [26]. Only recently has more attention been paid to the potential negative emotions elicited by environmentally friendly products, which can affect their uptake and use. For example, in one study, besides positive emotions, such as happiness and enthusiasm, plant-based plastic bottles elicited negative emotions, such as nervousness and worry, and both positive and negative emotions were related to purchase intentions [15]. Additionally, in another study, clothing made from recycled plastic elicited disgust, which was associated with lower purchase intentions [20]. Given that emotions can be related to consumers' willingness to purchase and use products, it is important to understand what causes emotional responses to products. Thus far, this has received little attention in the research literature, so we aim to address this gap. We propose that emotional responses to products depend on the perceived implications of these products for people's core values [24].
In the current research, we investigated how people who endorse different values to varying degrees respond emotionally to wastewater products. More specifically, we examined whether people who prioritised different values had different emotional responses to products made from recycled toilet paper, when different valuetailored messages were used to promote these products. We also investigated the relationships between emotions, acceptability of the products and intentions to purchase the products. In addition to providing theoretical insights into the role of values in emotional responses towards wastewater products, this research also offers practical insights into strategies for increasing positive emotions and reducing negative emotions, which can be related to their acceptability and adoption. That is, investigating which kinds of emotions are elicited by wastewater products, and the role of different values in these emotional responses, could be informative for considering how to effectively market these products (e.g., [17]; [19,39]).

Values and emotions towards sustainable innovations
Values can be defined as "concepts or beliefs that pertain to desirable end states or behaviours, transcend specific situations, guide selection or evaluation of behaviour and events, and are ordered by relative importance" ( [32], p. 4). Values determine what people find important in life. Four types of values have been found to particularly influence attitudes and behaviours in the environmental domain, namely, altruistic (concern for other people), biospheric (concern for nature and the environment) egoistic (concern for money and resources) and hedonic (concern for personal pleasure) values [34]. For example, when evaluating energy production systems, individuals who strongly endorse biospheric values are more likely to attend to consequences for the environment, find them more important, and consider them more in decision-making [34,35], whereas individuals who strongly endorse egoistic values are more likely to attend to personal consequences and find them more important [23].
It has been proposed that values can underlie emotional responses towards sustainable innovations [24]. Specifically, appraisal theory posits that people first evaluate a situation according to the characteristics that are goal relevant and goal (in)congruent (or alternatively, value relevant and value (in)congruent), which then, in turn, can elicit emotions [6]. Therefore, emotional responses to an innovation could depend on how people perceive the (in)congruence of the innovation's specific characteristics with their core values [24]. For example, if one has strong biospheric values, then perceiving an innovation to have characteristics that support biospheric values (e.g., if the innovation produces less carbon emissions) could elicit positive emotions. In contrast, perceiving an innovation to have characteristics that conflict with biospheric values (e.g., if the innovation produces more waste) could elicit negative emotions.
Wastewater products are interesting for investigating the role of values in emotional responses to sustainable innovations. On the one hand, wastewater products may elicit positive emotions such as happiness and excitement because they benefit the environment. On the other hand, these products may also elicit negative emotions such as fear and disgust because they originate from sewage. As such, we suggest that wastewater products may have strong implications for two values in particular: biospheric values and hedonic values. Specifically, we expected that people with stronger biospheric values would experience more positive emotions and less negative emotions towards wastewater products, because these products are more environmentally friendly than conventional products. In contrast, we expected that people with stronger hedonic values would experience less positive emotions and more negative emotions towards wastewater products, because these products originate from sewage systems and may be seen as contaminated, non-pleasurable, and disgusting. These emotions are likely to be associated with preferences and choices. There is some initial evidence to support our reasoning. Specifically, research on behaviours that are environmentally friendly but potentially less pleasurable (e.g., taking shorter showers, eating less meat, owning fewer cars and not leaving electric devices on standby) has shown that endorsing biospheric values is positively related to engaging in such behaviours, whereas endorsing hedonic values is negatively related [34]. However, the role of emotions in these processes has not yet been explored.

Tailoring messages to audiences
It may be possible to make product evaluations more positive by appealing to people's values, via messages indicating that product has positive consequences for their values. Marketing messages are commonly used to advertise the benefits of products to consumers, in order to elicit more favourable responses and positive emotions. We argue, however, that the effectiveness of such messages is likely to depend on how these messages connect with the audience's values. We propose that product communications (or message frames) that indicate positive implications for people's core values may elicit more positive emotions towards the relevant product. Several studies have indeed found that valuetailored appeals aimed towards a specific audience tend to be more persuasive. For example, environmental campaigns (e.g., reducing plastic bottle use, or saving paper) are more convincing when the campaign messages are tailored to align with the audience's biospheric or egoistic values [2], [37]. Most research thus far has not specifically examined the effects of hedonic message frames (i.e. a specific form of self-enhancement message). Thus, there is a need for more research on the role of emotions, as well as the impact of hedonic message frames. This might be particularly relevant for wastewater products, given that these products likely have negative implications for hedonic values, and could produce negative emotions.
Since wastewater products have implications for biospheric values, one obvious marketing strategy for wastewater products is to appeal to the audience's biospheric values, by using biospheric message frames that highlight the environmental benefits of the products (e.g., that the products reduce waste). Hence, whereas people with strong biospheric values are likely to already experience positive emotions to wastewater products, this effect may be more pronounced when the positive impacts of these products are emphasised. Importantly, although stronger hedonic values could be associated with negative emotions towards wastewater products (given the implications of lower enjoyability), positive emotional responses could potentially be increased with hedonic message frames that highlight the personal pleasurable benefits of the product, such as its modern design. Thus, we tested the effects of framing wastewater products as having benefits for the environment (i.e. a biospheric message frame), or as having benefits for personal enjoyment (i.e. a hedonic message frame), for people who support biospheric and hedonic values to varying degrees.

The current research
We first investigated whether emotional responses to wastewater products depend on people's biospheric and hedonic values. We predicted that the stronger the audience's biospheric values, the more positive (H1) and less negative (H2) emotions people would experience in response to wastewater products. Conversely, we predicted that the stronger the audience's hedonic values, the less positive (H3) and more negative (H4) emotions people would experience in response to wastewater products. We then examined whether the effects change when the messages describe wastewater products as congruent with either biospheric or hedonic values. More specifically, we predicted that the relationship between biospheric values and positive emotions would be stronger for the biospheric message frame (e.g., emphasising these products reduce plastic waste and greenhouse gas emissions), relative to the hedonic message frame (e.g., emphasising that the products will enhance your interior and draw attention) (H5), and that the relationship between hedonic values and positive emotions will be stronger when the pleasurable benefits (versus environmental benefits) of the products were emphasised (H6). We did not make any directional hypotheses about the moderation effect for negative emotions. Lastly, we examined how emotions related to acceptability and intentions to purchase the products. We predicted that stronger positive (negative) emotions would be associated with higher (lower) acceptability of the products and intentions to purchase the products (H7). We tested these hypotheses in an online experimental study conducted in the Netherlands.
Thus far, most research on the acceptability of wastewater products has focused specifically on responses to recycled water (for a review, see [8]. In the current research, however, we focused on products made from wastewater materials. These are products made with cellulose fibres from toilet paper in wastewater, which during production can be mixed with other materials such as biodegradable bioplastic. These wastewater products can range from facade elements, asphalt, acetic acid, plant pots, telephone holders to table tops. The products are sustainable because they are made from recycled cellulose, saving natural resources and reducing emissions (e.g., see the website, Cell-vation; https:// www. cellvation. com). In addition, waste from these new products is also reduced, because the cellulose is biodegradable [1]. Hence, these products support the circular economy. The specific wastewater products studied in the current research were made from the recently developed material "Recell ® ". To make Recell ® , cellulose fibres from toilet paper are extracted from wastewater, and dried and sanitised so they are safe for use. The fibres are then turned into pallets or fluff, which is used to make various household products (e.g., a plant pot or a table top).

Results
Means, standard deviations and bivariate correlations between all variables can be found in Additional file 1: Tables S1 and S2. We ran hierarchical linear regression analyses to test our hypotheses regarding the main effects of values on emotions, and the moderating role of message framing on the relationship between values and emotional responses to the products. 1 , 2 For positive emotions (see Table 1), there were significant main effects of biospheric values, hedonic values and message framing for both products. As predicted, the more strongly that people endorsed biospheric values, the more positive emotions they reported in response to the products (supporting H1). The relationship was non-significant for negative emotions (see Table 2; not supporting H2). Conversely, the more strongly that people endorsed hedonic values, the more negative emotions towards the plant pot (partially supporting H4), and the more positive emotions towards both products (not supporting H3) they reported. In general, the biospheric frames elicited more positive emotions than the hedonic frames.
As expected, these main effects were qualified by significant interactions between the values and the message framing for positive emotions. When the interaction terms were entered, there was a significant change in the explained variance, indicating a moderation effect. We conducted simple slopes analyses using PROCESS with 5,000 bootstrapped resamples [11], Model 1) to examine the interactive effects on positive emotions, run These findings provide support for H5: the relationship between biospheric values and positive emotions appeared to be accentuated when the environmental rather than hedonic benefits of the products were emphasised (see Fig. 1). Conversely, the effect of hedonic values on positive emotions was stronger when the pleasurable benefits were emphasised than when the environmental benefits were emphasised. Unexpectedly, however, the significant interaction between hedonic values and message frame seemed to be primarily driven by individuals with weaker hedonic values: individuals with relatively weak hedonic values tended to express less positive emotions when viewing the hedonic frames compared to the biospheric frames, whereas individuals with relatively strong hedonic values expressed a similar degree of positive emotions to both frames (see Fig. 2). More specifically, for the plant pot, weaker endorsement of hedonic values was associated with less positive emotions when the pleasurable benefits were emphasised, b = 0.25, t(314) = 3.31, p < 0.001, but not when the environmental benefits were emphasised, b = 0.06, t(314) = 0.93, p = 0.35. Similarly, for the table top, weaker endorsement of hedonic values was associated with less positive emotions when the pleasurable benefits were emphasised, b = 0.28, t(314) = 3.40, p < 0.001, but not when the environmental benefits were emphasised, b = 0.04, t(314) = 0.60, p = 0.55. Therefore, these findings do not seem to provide support for H6.
For negative emotions, there were no significant interactions between biospheric values and message framing, or between hedonic values and message framing, for either product (see Table 2).

Discussion
This research examined the role of values and valuetailored messages in emotional responses to wastewater products. Given the possible implications of wastewater products for both the environment and one's personal comfort, we focused on the role of biospheric and hedonic values that reflect a concern with the environment and personal comfort, respectively. We predicted that individuals with stronger biospheric values would report more positive and less negative emotions in response to wastewater products, whereas individuals with stronger hedonic values would report less positive and more negative emotions. Additionally, we predicted that the relationships with positive emotions would depend on value-tailoring, that is, presenting the products as having positive implications for the relevant values. We hypothesised that value-tailored messages would increase positive emotions towards the products. We also examined whether emotions, in turn, were associated with acceptability of wastewater products and intentions to purchase wastewater products. Overall, the hypotheses were partially supported. We provide further explanation of the results separately for biospheric and hedonic values below.

Biospheric values and emotions towards wastewater products
Biospheric values were associated with more positive emotions towards the products (i.e. supporting H1). Importantly, as expected, we found that this relationship was stronger when the product messages emphasised the positive environmental consequences of wastewater products (i.e. the positive implications for biospheric values; supporting H5). Thus, it appears that, in general, the stronger their biospheric values, the more positive emotions people have towards wastewater products, and this is even more likely when the benefits for the environment are emphasised in the product messages. Interestingly, we did not find a significant relationship between biospheric values and less negative emotions towards wastewater products (not supporting H2). This could have been because our selected products did not elicit very strong negative emotions in the first place. Specifically, the low mean scores and low variance for the measures of negative emotions suggest that the specific products that we included may have not been 'disgusting' enough to generate sufficient variation in the negative emotion responses, or that the emotion terms selected to represent negative emotions were too strong for the products. For instance, 89% of participants chose "Not at all" when asked if they feel uncomfortable when imagining using the table top. Thus, the specific products chosen for the current research seem to have produced a floor effect for the measure of negative emotions. Previous research has found that people can be distressed about [39], and unwilling to consume [30] treated wastewater. However, the wastewater products included in the current research may not have been considered as disgusting as recycled water, because these products do not have to be ingested or come into contact with the body (see also, [13,20]). Therefore, we would recommend that a wider range of products are included in future studies, particularly products that involve a high degree of physical contact or are used for oral consumption (e.g., drinking cups or straws).

Hedonic values and emotions towards wastewater products
Hedonic values were weakly associated with negative emotions towards the plant pot, but not the table top (i.e. partially supporting H3). Hedonic values were also significantly associated with positive emotions (not supporting H4), especially when the product messages emphasised the pleasurable benefits of the products (i.e. the positive implications for hedonic values). Contrary to what we predicted in H6, however, this relationship seemed to be driven by weaker hedonic values. Specifically, weaker hedonic values were associated with less positive emotions when the pleasurable benefits were emphasised, relative to when the environmental benefits were emphasised, whereas stronger hedonic values were associated with similar levels of positive emotions in both message frames.
The relatively weak relationships between hedonic values and emotional responses towards wastewater products suggest that these kinds of products-or, at least, the products included in the current research-are probably not perceived as having major implications for hedonic values. This is unlikely to be due to different overall levels of endorsement of hedonic values in the sample, since both hedonic and biospheric values were endorsed by participants to a similar degree. The explanation that the current products did not have strong implications for hedonic values is also plausible because we found very low scores on negative emotions-which suggests that most people did not feel disgusted, anxious or uncomfortable in response to the products. Future research could include more disgusting products.
Another potential reason why hedonic values did not strongly predict emotions, is that the hedonic message frame may not have been relevant enough in this context. That is, the hedonic frames may have been generally less appealing than biospheric frames. For example, it could be the case that messages emphasising the environmentally friendliness of wastewater products are simply more convincing and intuitive (because this would be a primary reason to use such materials), whereas messages emphasising their pleasurable qualities may be seen as confusing, or even disingenuous (since these products might not be experienced as typically pleasurable in nature). Additionally, emphasising the origins of the materials could have had an unexpected effect of making the products seem more special and unique (given that products made from recycled toilet paper are relatively uncommon), whereas emphasising the pleasurable aspects of the products could have unexpectedly made the products seem more generic and conventional (i.e. just describing a product as 'unique' does not necessarily make it actually appear unique, because this is a very common marketing strategy). Alternatively, perhaps the hedonic frame may have immediately led people to consider the potential negative hedonic aspects of the products as well-although this explanation would still imply that stronger hedonic values would tend to have less positive emotions towards the products, which was not supported.
Unexpectedly, it appeared that individuals with weaker hedonic values, tended to express less positive emotions to the products when the hedonic frame was employed, relative to the biospheric frame, whereas individuals with stronger hedonic values did not differentiate strongly between the frames in their emotional responses. This suggests that when message frames are used that try to appeal to values that people find less important, these frames could potentially backfire. Future research should try to replicate and clarify the reasons for this finding. One possible explanation is that the hedonic message frame contained content less relevant to hedonic values (e.g., "drawing attention" could communicate a status motivation, which is more relevant for egoistic values). Additionally, while the biospheric frame primarily communicated implications for one main value, the hedonic message may have contained mixed content relevant to both hedonic and biospheric values. For example, even just stating that the products are made from biodegradable plastic and reused toilet paper could imply that they are good for the environment, in addition to the hedonic content implying that they are also good for the self, which may have reduced the clarity of the hedonic message. Some previous research has found that combined messages (e.g., incorporating both biospheric and egoistic frames; van den [37] are less effective than singlevalue appeals, showing that messages tailored towards a specific value can be more effective than messages that attempt to appeal to multiple values. Future research could also further investigate the effectiveness of combined product messages incorporating both hedonic and biospheric content.
In the current research, we did not see negative effects of the biospheric frame for individuals with strong hedonic values. This may indicate that people can believe that products can be both sustainable and pleasurable, and there is not necessarily a trade-off between hedonic values and pro-environmental behaviours (e.g., [38]. Yet, overall, the hedonic messages in the current research seemed to be less effective for eliciting positive responses to wastewater products than the biospheric messages. The current findings make a unique contribution by being one of the first studies to investigate the role of hedonic values and hedonic messages in the context of consumer products that are likely to have negative implications for hedonic values, and elicit negative emotions. Most past research on value-congruent messaging and pro-environmental behaviours has not explicitly focused on hedonic values and messages, focusing instead on messages tailored towards either biospheric or egoistic values (e.g., [21],Van den [37], or not distinguishing hedonic messages from egoistic messages within a broader "self-enhancement" message frame (e.g., [4,12]). For example, Herziger et al. [12] describe "wellbeing enhancement and stress reduction" as "selfish" interests related to egoistic values, although, arguably, these messages could also communicate selfcare, which may be more relevant to hedonic values. Similarly, in the research by de Dominicis et al. [4], some of the content of the "self-enhancement" message frames appeared to be more hedonic in nature, such as people having fun at the beach. It can be quite difficult to disentangle egoistic and hedonic content when constructing messages that target solely one of these values. Indeed, even the hedonic frame in the current study could be viewed as containing egoistic elements (e.g., the reference to "drawing attention" could communicate a concern for one's status). Thus, future research could pilot-test the specific value-tailored messages, to ensure that they are communicating the primarily targeted value. Hedonic values and hedonic message frames may have different effects on emotions towards sustainable products than egoistic values and egoistic message frames, for one because people may not perceive caring about the environmental benefits and the personal pleasure derived from such products as mutually exclusive, while they might do so for behaviours that are good for the environment and good for saving money. It appears that more research is needed to study the unique effects of hedonic values and hedonic message frames in the value-tailoring literature.

Emotions, acceptability and intentions to purchase
We found consistent support for H7; positive emotions were associated with higher acceptability of wastewater products, and higher intentions to purchase wastewater products, whereas negative emotions were associated with lower acceptability of wastewater products, and lower intentions to purchase wastewater products. Emotions have been found to be highly intertwined with acceptability and are thus a relevant component in people's reactions. In this paper, we have chosen to focus on investigating emotions, in particular, because these types of products could presumably cause strong emotions (e.g., disgust). H7 predicted that emotions would be associated with intentions to purchase; however, we did not hypothesise that emotions would act as a mediator, as this would suggest that emotions come first in a causal chain, before intentions. This causal chain may not necessarily be the case (e.g., [22,31], and our design does not allow us to test causality or what comes first-emotions or intentions (rather, it is focused on testing the casual effects of value framing on emotions). Thus, we have focused on reporting the associations between emotions, acceptability and intentions. While we have run some exploratory moderated mediation analyses (see the Additional file 1), more experimental studies are needed to directly test the effects of emotions on intentions to purchase products.
The current findings are broadly consistent with previous research on the effects of message framing in responses to environmentally friendly products (e.g., [8,15,30]). Overall, our findings provide support that the implications of sustainable innovations for one's strongly held values play a role in the elicitation of emotions and the acceptance of these innovations [24]. The findings are also consistent with previous research that has demonstrated that message framing can shape emotional reactions to wastewater products, like recycled water (e.g., [10]. We have extended this literature by demonstrating the key role of values in emotional responses to wastewater products.

Limitations and future research
It is important to note that the current findings are based on a single study, and more research is needed to replicate and support these findings. A further limitation to this study is that we were not able to demonstrate whether the hedonic and biospheric message frames had beneficial effects when compared to a control condition (e.g., a condition containing very basic information about the product, with little value-related content). A control condition would allow for testing which of the message frames was primarily driving the effects on emotions (or if both messages were having an effect). We therefore recommend that future research includes a control condition. Another limitation is that we did not measure the perceived implications of the products for participant's values. Thus, it cannot be concluded with certainty that people with stronger biospheric values had more positive emotions towards wastewater products because they perceived these products to have positive implications for their biospheric values (although the findings strongly suggest this). Future research could also include a measure of perceived value-congruence; that is, the extent to which participants think that a product has positive implications for their core values. Additionally, we were not able to conclude that the "hedonic" message frame was perceived as especially relevant to hedonic values. Future research could further test the effects of framing, particularly the hedonic framing; for example, by including clear value-relevant frames that have been pilot-tested. Alternative outcome measures also could be included in future research, such as relative willingness to pay (e.g., [29]), or behavioural measures; for example, by giving participants the opportunity to actually buy wastewater products. This would provide more evidence for the ecological validity of the findings and show that the manipulations are likely to have an impact on real-world behaviours.
Broader avenues for future research could include examining the role of other values, such as egoistic values or conservation values (i.e. valuing order and preserving the status quo; [33]). Previous research has found that purity and conservation values tend to be linked to trait disgust sensitivity (e.g., [14]; but see [5]), for a recent critique of this perspective). Therefore, it may be the case that 'disgusting' wastewater products evoke more negative emotions for people who hold strong conservation values than people who hold strong hedonic values.
Future research could also consider a more longitudinal perspective, rather than measuring reactions at a single time point. For example, disgust responses can change within individuals over time, a shift that can be intentional (e.g., via the motivated up-regulation or downregulation of disgust to behave in ways that are more consistent with one's values) or unintentional (e.g., from repeated exposure). For instance, there is recent evidence that people who work with meat (e.g., butchers, deli workers) exhibit adaptation of their disgust responses to meat over time [28]. In the current context, it is possible that individuals with stronger biospheric values may be motivated to down-regulate their disgust responses to wastewater products over time, because these products fit with their values. Also, arguably, the meaning of what is considered "disgusting" in society has changed a great deal over the course of history, and many culturally accepted innovations (e.g., fermented foods) could also be considered disgusting from a different cultural perspective [16]. Thus, disgust responses to circular economy products may be more amenable to change than is commonly assumed, and more research is needed in this area.

Practical implications
The current findings provide useful insights for how to promote wide adoption of wastewater products. Although stronger biospheric values can lead to positive emotional reactions towards wastewater products, it may be important to clearly explicate the implications of the products for these values to consumers, in order to maximise the positive effect (consistent with the literature on value activation; e.g., [35]. Companies who are developing wastewater products may be reluctant to promote these products as environmentally friendly, since they may be concerned that this would increase the salience of the product's origins and deter consumers from purchasing their products, particularly those with stronger hedonic values. The current findings suggest that this is not a major concern, participants holding strong hedonic values did not seem to have strong negative emotional responses to this type of wastewater product, even when the environmental benefits were emphasised. Thus, people do not seem to have large concerns about the implications of these products for their hedonic values. The findings also suggest that wastewater products are mostly appreciated for their environmentally friendly characteristics; in general, biospheric framing led to more positive emotions towards these products than hedonic framing, and there were more positive emotions elicited when the audience held strong biospheric values. Therefore, when audiences hold a variety of different values, it would likely be most beneficial to use biospheric message frames emphasising the positive benefits of the products for the environment. However, we should caution that we only included a small number of products and two types of values in the current research, and the hedonic frame did not produce the outcomes that we had expected. More research is needed to find out whether the findings would extend to other products, particularly products that require more physical contact, or how individuals respond based on their egoistic or altruistic values. Additionally, although the current research shows that biospheric frames can elicit positive emotions in people with strong biospheric values, it is less clear how we motivate people with low biospheric values to adopt wastewater products. This is another area for future research.

Conclusions
To conclude, this research shows that biospheric values were consistently related to experiencing more positive emotions (but not less negative emotions) in response to wastewater products, whereas hedonic values did not tend to be (or were only weakly) related to positive and negative emotional responses. Stressing the positive environmental consequences could help promote wastewater products by increasing positive emotions, particularly for people with stronger biospheric values, and these messages seem not to make the products less appealing for people with stronger hedonic values. In contrast, stressing the pleasurable personal benefits of wastewater products does not seem to have much of a positive effect on emotions (and they could even backfire for those with weak hedonic values). Progressing this field of research has important practical implications for promoting the adoption of wastewater products and recycled products more generally, by demonstrating how effective messaging strategies can depend on the values and emotions of the specific target audience. If we can encourage more people to purchase such products, this could help promote the transition to a circular economy, which could ultimately contribute to saving natural resources and energy, and reducing greenhouse gas emissions and waste.

Participants
The study was run with a sample from the general Dutch public. It was estimated a priori that 263 participants were required to detect a small to medium effect size of 0.05 (similar to effect sizes reported for emotions in research with a similar methodology; [7], when using a power of 0.80, an alpha level of 0.05 and 5 predictors (biospheric values, hedonic values, framing, interaction biospheric values x framing and interaction hedonic values x framing). To allow for the removal of low-quality responses, we recruited 331 Dutch residents via thesistoolspro.com who received credit worth €1 to spend at a web store, Bol.com, upon completion of the questionnaire. We excluded 17 participants due to either failing an attention check (14 participants) 4 or requesting to remove their data (three participants). 5 The remaining sample comprised 314 participants (141 men, 173 women) who ranged in age from 16 to 88 (M age = 53.80, SD = 15.36). 6 Compared to the general Dutch population, fewer men and more women participated, and the sample was relatively more highly educated and had a higher income. Therefore, the sample was not completely representative of the Dutch population (see demographics in Additional file 1: Table S3).

Research design
The research design was between-subjects with two conditions (a biospheric frame and a hedonic frame). Participants read short messages describing two products made with Recell ® ; a plant pot and a table top (all participants viewed both products). The first part of the text described how Recell ® is made, accompanied by two pictures of the raw material (pallets and fluff ) and a picture of each product (see full messages and pictures in Additional file 1). The second part of the text differed across the experimental conditions so that participants read one of the following messages (presented in English here, but in Dutch to participants).
Biospheric frame "Recell ® and the products made from it are environmentally friendly. First, because less energy is needed for treating sewage water. Next, the plant pot is made from Recell ® instead of oil-based plastic, which helps you to reduce plastic waste and greenhouse gas emissions. The table top is made from Recell ® instead of wood, which helps saving valuable trees and reduces your carbon footprint. " Hedonic frame The versatility of Recell ® creates endless possibilities for creating modern interior objects. For the plant pot, Recell ® is used to make granulate, which has a modern granite look that can fit nicely in the interior of your home. The refined table top made from Recell ® will be a very unique piece of furniture in your house, completing your interior and drawing attention. "

Procedure
The survey materials were prepared in English and then translated to Dutch (see messages and pictures in Additional file 1). The study was presented to participants as a study on the evaluation of different innovative products. We first measured participants' values, and then participants were randomly assigned to either the biospheric framing condition or the hedonic framing condition, in which they read short messages describing two Recell ® products emphasising either the environmentally friendly or pleasurable benefits of the products, respectively. After reading the product messages, participants reported their emotions towards the products, as well as their acceptability of, and intention to purchase the products.

Personal values
Personal values were measured with the shorter version of the Schwartz value scale (1992) developed by Steg et al. [34]. This scale consisted of 16 items measuring biospheric, hedonic, altruistic, and egoistic values. Participants rated the importance of each value as a guiding principle in their life, on a 9-point Likert scale from -1 (opposed to my values) to 7 (of supreme importance). The two subscales of interest were biospheric values (respecting the earth, unity with nature, protecting the environment, preventing pollution), α = 0.88 and hedonic values (pleasure, enjoying life, self-indulgent), α = 0.81.