Understanding Organizational Citizenship Behaviour through Organizational Justice and its Consequences among Vietnamese’s Universities Employees

This paper aims to investigate the impact of organizational justice components on job satisfaction, organizational commitment, and organizational citizenship behaviours (OCB) of employees in the higher education sector of Vietnam. Although many research studies have been conducted in organizations on the topics of organizational justice, as well as organizational commitment, and organizational citizenship behaviour, there is a shortage of these topics in higher education institutions as well as in Asian context. Therefore, this article attempts to fill this literature gap. A total of 317 employees from various universities in Vietnam participated in this study, and a self-administered survey was conducted, which was modified based on suggestions from the universities' management team following interviews. The collected data were analyzed using the partial least squares structural equation modeling (PLS-SEM) technique. The results showed that procedural justice and interactional justice had a significant impact on both job satisfaction and organizational commitment, while distributive justice only affected job satisfaction. Furthermore, the study found that job satisfaction and organizational commitment significantly affected OCB. However, this study had a limitation in terms of the narrow sample size, which only included participants from universities. Future studies should broaden the sample size to include participants from vocational colleges. On paper, the study shows the effects of organizational justice on OCB through the mediating roles of individual work outputs, which received inadequate attention in previous studies.

and the organization they work for [23]. It also describes employees' perceptions of their job responsibilities and the organizations they are in. Employees with high job satisfaction will demonstrate superior job performance, positive work attitudes, high motivation, and a reduction in absenteeism and turnover. The job descriptive index instrument, developed by Smith et al. [24], contains five components: (1) job characteristics; (2) compensation and benefits; (3) attitudes toward supervisors; (4) relationships with colleagues; and (5) opportunities for advancement. The model of job satisfaction with five aspects has been used by many researchers in their studies [23,25].

2-4-Organizational Commitment
Becker [26] introduced the concept of organizational commitment, which explains the relationships between an individual and his or her organization by using the side-bet theory. According to this theory, an individual commits to an organization because he or she has hidden investments in the organization, which keep him or her there. The term "side bet" represents the values or benefits that would be lost if the individual were to leave the organization, such as job titles or pride in being a member. Porter et al. [27] described commitment as an individual's attentive and independent attitude towards the organization, along with behavioural intentions. On the other hand, Meyer et al. [28] proposed a model of organization commitment consisting of three factors: affective commitment (attractiveness in organizational activities), continuance commitment (willingness to stay in the organization), and normative commitment (feeling of employees in the organization). Inheriting the above, the researchers added to the definition of commitment by highlighting its importance as a key factor in enhancing performance and reducing absenteeism and turnover rates. It is also seen as revealing a person's singularity to the organization [29], as well as a sense of pride in being a part of the organization [30], and a tendency to dedicate one's loyalty and dedication to the organization [31].

2-5-Organizational Citizenship Behaviour
The term "organizational citizenship behaviours" was introduced by Bateman and Organ [32], which refers to the optional and voluntary contributions made by employees that are not directly related to their specific job responsibilities. Over the years, it has become an important field for many organizational behaviour researchers. Organ [5] suggested the five-factor conceptualization of organizational citizenship behaviours. These factors include altruism (providing support to colleagues); conscientiousness (ensuring compliance with regulations); courtesy (consulting others before making decisions); civic virtue (showing concern for important organizational issues); and sportsmanship (refraining from complaining about minor issues). These factors provide a comprehensive understanding of the various ways in which employees can positively contribute to their organizations beyond their formal job duties. The study of organizational citizenship behaviours (OCB) has received significant attention among researchers in the field of organizational behaviour. While some studies have supported a three-factor model of OCB by merging the components of "altruism" and "courtesy" into the "helping" dimension [33,34], the majority of researchers continue to support the original fivefactor model. Hence, in this study, OCB will be investigated using the widely accepted five-factor model [35].

3-1-Organizational Justice and Job Satisfaction
The relationship between organizational justice and job satisfaction has been a topic of investigation for decades. Colquitt et al. [36] found that distributive justice is a significant predictor of job satisfaction, while Masterson et al. [37] demonstrated that both procedural and interactional justice have a positive impact on employee job satisfaction. Moreover, Zainalipour et al. [38] established a strong positive correlation between job satisfaction and organizational justice. A meta-analysis of the subject also confirmed the high correlation between organizational justice and job satisfaction [39].
Lambert et al. [40] have indicated that distributive justice is linked to overall employee satisfaction. Evidence from the study indicates that employees report higher levels of satisfaction when they are satisfied with the performance appraisal system and the rewards received. Distributive justice is a key predictor of job satisfaction and outcomes, and the research found that it tends to be a stronger predictor of personal outcomes than procedural justice [41].
DeConinck's [42] study of the linkage between organizational justice and job satisfaction indicated a very high correlation between distributive justice and job satisfaction. Procedural justice focuses on individual concerns about how rewards are defined and how evaluation systems are conducted. When procedural justice is transparent and fair, it can motivate people to work hard and increase satisfaction. Conversely, if it is not transparent and fair, it can lead to depression, vindictiveness, and decreased job satisfaction, potentially harming the organization. Recent studies have agreed that procedural justice has a positive effect on job satisfaction and suggested that the fairness of managers' decisions plays a role in employee job satisfaction [43].
Interactional justice is considered a key aspect in workplace settings due to its relationship with unfair and fair treatment [44]. Greenberg & Cropanzano [45] defined interactional justice as "the interpersonal treatment employees receive from decision makers and the adequacy with which the formal decision-making procedures are explained".
Interactional justice could be separated into two subcategories, named interpersonal justice and informational justice [36]. Greenberg [46] suggested that information justice mainly focuses on why a particular outcome of an activity appears a certain way and that interpersonal justice represents the extent to which people treat employees in decent, polite, and respectful ways. Chan and Lai [47] found that interpersonal fairness is clearly and positively related to employees' satisfaction with supervisors and that information equity is positively and significantly related to employee satisfaction with respect to job performance appraisal and satisfaction with supervisors.
From the above arguments, we postulate the hypotheses as follows: Hypothesis 1: Distributive justice is positively related with job satisfaction.

Hypothesis 2:
Procedural justice is positively related with job satisfaction.

Hypothesis 3:
Interactional justice is positively related with job satisfaction.

3-2-Organizational Justice and Organizational Commitment
Organization justice is considered a precursor to organizational commitment. When employees perceive procedural justice, they are more likely to believe in the caring and well-being of the organization, which motivates them to stay with their current organization [48]. In a study of 128 employees at a medical college, Bakhshi et al. [49] explored the significant relationship between organizational justice and organizational commitment.
Evidence suggests that organizational justice is perceived as an important predictor of both job satisfaction and organizational commitment. This could be due to the fair procedures used in decision-making and the feeling that employees are well-regarded and valued members of the organization. When employees are motivated, they are more likely to strengthen their relationship with their current organization [48].
In a recent study investigating the relationship between organizational justice and organizational commitment Jang et al. [50] found that an increase in organizational commitment is a result of distributive and procedural justice. This result is somewhat inconsistent with a previous study by Lambert et al. [51], which agreed that all forms of organizational justice (distributive, procedural, and interpersonal justice) had a positive impact on organizational commitment.
Based on this, the following hypotheses are proposed:

Hypothesis 4:
Distributive justice is positively related with organizational commitment.

Hypothesis 5:
Procedural justice is positively related with organizational commitment.

Hypothesis 6:
Interactional justice is positively related with organizational commitment.

3-3-Organizational Commitment, Job Satisfaction and Organizational Citizenship Behaviour
In their study of organizational citizenship behaviour and job satisfaction, Foote and Li-Ping Tang [52] found that when employees are satisfied, they tend to express higher OCB, which can be seen as a way for them to repay the organization for its good treatment of them. This idea has been supported by various studies, which have found that employees are more likely to exhibit positive behaviour when they are satisfied with their organizations, while dissatisfaction can lead to a decrease in commitment [52][53][54]. According to research conducted by Markovits et al. [30] as well as Irshad and Naz [55], Gunlu et al. [56] found that job satisfaction is positively related to organizational commitment. Organ et al. [57] argued that satisfied employees are more likely to exhibit higher OCB because they want to repay the organization for its good treatment of them. This idea has been strengthened by subsequent research, which has found a positive and significant relationship between job satisfaction and OCB [53,54,58].
O'Reilly and Chatman [59] have found that there is a positive relationship between organizational commitment and different types of organizational citizenship behaviours. The results of Schappe's [60] study indicated that organizational justice and job satisfaction have significant stimuli on organizational citizenship behaviours. Rana et al. [61] argued that employees who committed to organizations were more likely to exhibit citizenship behaviours. Furthermore, Organ and Ryan [62] in their meta-analytic study of OCB supported the view that organization commitment can be a predictor of organizational citizenship behaviour. Crane et al. [63] found that employees who perceive that their abilities and performance are valued by the organization received a fair reward that was suitable for their contribution. Several studies have supported this notion and agreed that employees who feel fairness in distributive reward are more likely to display citizenship behaviour [64]. In their research in higher education, Awang and Wan Ahmad [65] found that academic staff tend to perform organizational citizenship behaviours toward their colleagues, leaders, and organizations when they feel fairness in distributive justice. Organ [66] believes in the "fairness" of the organization, especially the beliefs about the fairness of pay and benefits, supervisory treatment, and rules that apply to the workplace. The greater the extent to which these attributes of the organization are judged to be fair, the more likely it is that individuals will feel and express some degree of positive affect about the organization, and the more likely it is that they will express some of this affect in fashions that are positive or beneficial behaviours with respect to the organization and its management. Conversely, cognitions or beliefs about the organization that are predominantly negative will tend to inhibit spontaneous, non-task gestures that benefit the collective enterprise. Awang and Wan Ahmad [65] concluded in their paper "The Impact of Organizational Justice on Organizational Citizenship Behaviour in Malaysian Higher Education" that interactional justice has a significant influence on organizational citizenship behaviour. Based on the results consistency with DiPaola and Hoy [67], the informal praise may be the best commendation for them to exhibit organizational citizenship behaviour. Recently, many studies have used social exchange theory as the main theory to build a conceptual model for explaining the relationship between justice and organizational citizenship behaviour [68]. Research guided by this framework has generally been supportive, according to Kuenzi et al. [69]. Lehmann-Willenbrock et al. [70] found that procedural justice predicted organizational citizenship behaviour, whereas De Lara [71] obtained similar results for interactional justice. Cohen and Keren [72] reported significant effects of organizational citizenship behaviour on all three of the major dimensions of organizational justice.
Based on these findings, the following hypotheses are proposed: Hypothesis 7: Employee's job satisfaction is positively related with organizational citizenship behaviour.

Hypothesis 8:
Organization commitment is positively related with organizational citizenship behaviour.

3-4-Research Framework
Based on the literature reviews and previous empirical studies, the research framework has been synthesized. The model conveys the impact of organizational justice on organizational citizenship behaviour through the mediating roles of job satisfaction and organizational commitment.

4-Methodology
Most previous studies on the relationship between organizational fairness and OCB have been conducted in Western contexts with individualistic cultures. However, Vietnam has a collectivistic culture where perceptions of fairness and organizational behaviour are quite distinct. Hence, a qualitative step is deemed necessary to complement the quantitative research. A number of managers participated as interviewees to articulate their perceptions of the citizenship behaviours that they expect from their employees. The questionnaire was refined through a combination of previous studies and insights gathered from the interviews. The respondents were selected from higher education institutions, and the data was analyzed using partial least squares structural equation modeling.

4-1-Measurement of Constructs
Qualitative and quantitative methods are put together to combine the advantages of both research methods.
The interviews were carried out by participants selected from senior management roles, including Principals, Human Resources Managers, and Deans. There were a total of 12 interviewees, comprising 3 Vice-Chancellors, 5 Heads of Human Resources, and 4 Deans from International University-Vietnam National University Ho Chi Minh City (IU-VNU-HCM), Ho Chi Minh City University of Economics and Finance (UEF), and Ho Chi Minh City University of Technology (HUTECH). The majority of the interviewees concurred that employees should exhibit behaviours such as fulfilling office duties and achieving the Key Performance Indicators set by management, participating in academic guidance for high school students, organizing excursions with students, establishing connections between enterprises and universities, participating in student activities, and supporting curriculum evaluations. Furthermore, employees are expected to uphold and implement the organizational culture by attending events throughout the academic year.
The questionnaire consisted of two sections, including demographic variables and key observed variables, using a 7-point Likert scale, with the range starting from 1 (strongly disagree) to 7 (strongly agree). The concept of organizational justice was assessed using twenty items, spanning its three dimensions of distributive, procedural, and interactive justice, as proposed by Leventhal [73], Bies and Shapiro [18], Shore et al. [13], and Thibaut [74]. Job satisfaction was measured with eight observed items, focusing on the satisfaction of the job, supervision, promotion, co-worker relations, and compensation, based on the work of Smith et al. [24,75] and Aboramadan et al. [76]. Organizational commitment was evaluated using sixteen items, as per the framework established by Meyer et al. [28] and Meyer et al. [77]. Finally, OCB was measured by eighteen items focused on its five dimensions, including four items for each of altruism, conscientiousness, sportsmanship, and civic virtue factors, and three items for the courtesy factor contributed by Podsakoff and MacKenzie [34] and Lee and Allen [10].

4-2-Data Collection and the Sample
Statistics from the Ministry of Education show that the ratio between public and private universities is close to 3:1. Therefore, the researchers focused on achieving a 3:1 participant ratio, following the sequence of public and private universities. The data for this study were obtained from universities in The questionnaire was sent to the participants in paper and electronic forms. The survey was conducted from March 15 to April 5, 2022, and obtained 325 respondents. After screening the answers, only 317 responses were valid for further analysis. The data showed that 214 participants were from public universities, representing 67.5% of the total sample, while 103 participants were from private universities, indicating that the targeted ratio of sample was achieved.

4-3-Statistical Methods
In partial least squares structural equation modeling (PLS-SEM), the optimization of variance is elucidated by endogenous latent variables, rendering it a suitable methodology to examine the hypotheses of the present study. Kaplan [78] suggested that "structural equation modeling (SEM) represents a class of methodologies that aim to explicate hypotheses concerning the means, variances, and covariances of observed data through a smaller number of "structural" parameters defined by a hypothesized underlying model. Furthermore, PLS-SEM is particularly useful when dealing with complex research models and small sample sizes [79][80][81]. Prior to model evaluation, reliability analysis is an obligatory procedure whereby the accuracy of the scales is tested. All of the aforementioned procedures are indispensable for obtaining realistic and accurate research outcomes. After satisfying the criteria for the measurement models, the structural model evaluation step must be undertaken, which involves investigating the models using PLS-SEM.

5-1-Sample Characteristics
The data collected from the study revealed that out of the total 317 participants, 49.2% were male and 50.8% were female. Regarding educational qualifications, individuals holding doctoral and postdoctoral degrees accounted for 20.5% of the sample, whereas those holding master's and bachelor's degrees comprised 50.2% and 29.3% of the sample, respectively. Approximately 50% of the participants were lecturers, with the remainder comprising managers and academic staff. In terms of work experience, 177 respondents had less than five years of experience, while 140 individuals had worked for more than five years at their current organization, including 62 people who had worked for over 10 years. A summary of the characteristics of the respondents is presented in Table 1.  Table 2 presents the descriptive statistics for the variables under study. The findings indicate that the respondents exhibited a favourable inclination towards organizational citizenship behaviours, as evidenced by a high mean score for OCB (M = 5.796, SD = 1.037). Moreover, other constructs such as organizational commitment, job satisfaction, and interactive justice also exhibited a mean score greater than 5.0. However, the mean score for distributive justice was the lowest among all constructs (M = 4.950, SD = 1.331), with the mean score for procedural justice being only marginally higher, indicating dissatisfaction among university employees with respect to these justice-related factors. The present study examined the outer loadings of the indicators to assess whether they met the required standards. The results indicated that all outer loadings were greater than the critical value of 0.7, falling within the range of 0.700 to 0.946. The internal consistency of the constructs was evaluated using Cronbach's α, and the results revealed that the inner loadings of all variables exceeded the threshold of 0.7 [82].

5-2-Measurement Model Results
During this process, two items related to OCB, namely recommending qualified individuals for organizational roles and volunteering for overtime or business trips, were eliminated. Additionally, six out of sixteen items from the organizational commitment scale, including three reversed items (C4, C6, and C12), were excluded. Table 3, the values of Cronbach's α ranged from 0.907 to 0.963, and the values of composite reliability ranged from 0.924 to 0.969, thereby indicating high reliability of the data. Furthermore, the AVE values for all constructs were examined to be greater than the minimum requirement of 0.5, ranging from 0.607 to 0.841. Thus, the convergent validity was well established by the measurement model. Discriminant validity is a crucial criterion to be measured in order to understand the extent of variance in each variable in the model. The results presented in Table 4 revealed that the square root of the AVEs for each construct was greater than the cross-correlation with other constructs, consistent with the guidelines proposed by Fornell and Larcker [83]. Therefore, the measurement model exhibited acceptable discriminant validity.

5-3-Structural Model Assessment
The present study employed various statistical tools, including coefficient of determination, collinearity assessment, effect size, and direct effect, to test the assumptions. Collinearity was evaluated using the variance inflation factor (VIF), where a VIF value greater than 5.00 indicates collinearity. The results indicated that all VIF values were smaller than 5, suggesting the absence of collinearity.
To estimate the predictive precision, R-squared was utilized. The results showed that the R-squared values were significantly close for job satisfaction (R-squared = 0.681), association with organizational commitment (R-squared = 0.440), and organizational citizenship behaviour (R-squared = 0.346). These findings indicate that the three dimensions of organizational justice account for 68.1% of all variance in job satisfaction and 44% of all variance in organizational commitment. Moreover, job satisfaction and organizational commitment together explained approximately 35% of the variance in organizational citizenship behaviour. Hence, the results of R-squared suggest that the structural model demonstrated a high level of predictive accuracy.
Furthermore, F-square was utilized to evaluate the impact of independent constructs on dependent constructs [82]. The F-square values demonstrated a small (0.02), moderate (0.15), and large (0.35) impact of independent variables on the dependent variable, respectively. These results suggest that all constructs had a moderate effect, ranging from 0.066 to 0.274.
Finally, the coefficient significance was examined using PLS-SEM with the nonparametric bootstrapping method, where a sample size of 317 cases with 1,000 subsamples was employed. T-values were estimated to inspect the statistical significance of the coefficient.
The findings of this study reveal that all three components of organizational justice have a positive influence on job satisfaction. Specifically, the impact level gradually increases with procedural justice, followed by distributive justice and interactive justice. Interestingly, it was observed that procedural justice has the largest impact on organizational commitment (OC), whereas the effect of interactive justice is weaker, and the relationship between distributive justice and OC is not supported by the analysis results. Furthermore, both job satisfaction and OC have a strong positive effect on organizational citizenship behaviours (OCB), with job satisfaction showing a larger impact than OC. Although the relationship between distributive justice and OC is not supported, distributive justice can still positively influence OCB through job satisfaction. Therefore, the study concludes that all components of organizational justice have some impact on OCB.

6-Discussion
The results of the Structural Equation Modeling (SEM) confirm the validity of the research model and hypotheses. Seven of the eight hypotheses were supported, while one was rejected. The results demonstrate that hypothesis 1 (H1), which described that there is a positive relationship between distributive justice (DJ) and job satisfaction (JS) among employees in higher education institutions (HEIs), was supported. This indicates that when employees perceive that the organization is fair in its distribution of compensation and benefits, they are more likely to be satisfied with their job. This finding coincides with that of Clay-Warner et al. [85] and Lambert et al. [86].
Similarly, Hypothesis 2 (H2), which suggests that procedural justice has a positive effect on job satisfaction, was also accepted. The results suggest that when employees believe that the organization's procedures are fair, they are more likely to be satisfied with their job. This supports the findings of Bidarian & Jafari [2] and Lambert et al. [86].
Following this, hypothesis 3 (H3) was also supported, indicating that increased perceptions of fairness in organizational interactions are associated with an increase in job satisfaction. The results show that interactions between supervisors and subordinates enhance job satisfaction. This finding is in line with the studies conducted by Martínez-Tur et al. [44] and Wang et al. [87]. Continuously, the results of the study provide support for the notion that organizational commitment is shaped by employees' perceptions of the fairness of their organization's HR procedures and supervisory practices. Specifically, hypotheses 5 and 6, which proposed a positive relationship between perceived justice in the distribution of rewards (PJ) and justice in the treatment of employees (IJ) with organizational commitment (OC), were confirmed. These findings suggest that when employees perceive that their organization's procedures and policies are fair and that they are treated justly by their supervisors, they are more likely to be committed to the organization. These findings are consistent with the study of Sun et al. [88], which indicated that employees who express greater organizational justice report higher trust in their management and supervisors and, subsequently, stronger job satisfaction, leading to higher organizational commitment. In addition, Aggarwal et al. [89] confirmed in their study a positive effect of perceived procedural justice and interactional justice on employees' organizational commitment (OC) and a negative effect on employees' turnover intentions.
However, Hypothesis 4, which posited a positive relationship between distributive justice (DJ) and organizational commitment (OC), was not supported by the study's results. This finding aligns with previous research, including Chang's [90] prior work, which suggested that procedural justice has a greater impact on organizational commitment than distributive justice. In collectivist societies like Vietnam, where group harmony and social relationships are highly valued, employees may place more importance on procedural justice and perceived fairness in their treatment by supervisors than on the distribution of rewards.
Next, the findings of this research accepted the hypothesis 7 (H7) that job satisfaction has a positive relationship with organizational citizenship behaviours of employees. It confirmed that satisfied employees will develop their behaviours as citizenship in organizations. This finding is similar to the studies of Zeinabadi & Salehi [91] and Organ [92].
Lastly, the hypothesis 8 (H8) is supported by the fact that organizational commitment has a positive relationship with organizational citizenship behaviour. It means that as employees have expressed their commitment to organizations, they will display their citizenship behaviours in the organization. This finding supports the results of Gautam et al. [29], Cetin et al. [93], and Musringudin et al. [94].
Overall, the present study's findings highlight the importance of procedural justice and supervisory fairness in shaping employees' organizational commitment, particularly in collectivist societies. Future research could explore the underlying mechanisms by which perceived fairness in HR procedures and supervisory practices influences employees' commitment to the organization, as well as how cultural and social factors may moderate these effects.

7-Conclusions
This study makes meaningful contributions to the literature on organizational behaviours in the higher education sector, particularly in Vietnam. Firstly, it provides a comprehensive understanding of organizational citizenship behaviours, which is a vital aspect of employee behaviours that is critical to the success of higher education institutions. The study specifically focuses on the context of Vietnam, a developing country with a collectivist culture, which presents unique challenges and opportunities for the management of higher education institutions. By highlighting the importance of organizational citizenship behaviours, this study provides valuable insights into how higher education institutions can improve their performance and achieve their goals.
Secondly, the study examines the relationship between organizational justice, job satisfaction, and organizational commitment. The findings demonstrate the ways in which organizational justice can influence these critical factors and provide guidance for higher education institutions on how to increase satisfaction and commitment among their employees. This is particularly relevant in the context of higher education institutions, which often face significant challenges in managing a diverse and dynamic workforce. The study provides useful information for managers and policymakers who are responsible for creating and implementing effective human resource practices.
Finally, the study draws a comprehensive picture of the relationships between organizational justice, job satisfaction, organizational commitment, and organizational citizenship behaviours. This is an important contribution to the literature, as previous studies have often focused on only one or two of these factors. The study highlights the interdependencies and interactions between these factors, which can help managers and policymakers design more effective strategies for promoting organizational citizenship behaviours in higher education institutions.
Based on the findings of this study, higher education institutions' boards of management can better understand the impact of organizational justice on organizational citizenship behaviours, as well as the job satisfaction and organizational commitment of lecturers and staff in their universities. The study also suggests that policymakers can develop and implement human resources practices to increase organizational citizenship behaviours in higher education institutions, which will lead to improvements in the overall quality of these institutions.
However, there are some limitations to this study. Firstly, the participants in this study are only from universities, which represents a narrow and limited sample. Future research should broaden the scope of the sample size to include vocational colleges as well. Secondly, the size of the sample in this research is not large enough to identify differences and associations between and among groups. Therefore, further study should explore the findings of this study and compare them between groups of participants. Finally, only Vietnamese higher education institutions are addressed by this study, and thus it is not enough to represent other cultures in Asia. Hence, in the next studies, researchers could investigate these findings in other contexts to better understand the broader applicability of the results.

8-2-Data Availability Statement
Data sharing is not applicable to this article.

8-3-Funding
The authors received no financial support for the research, authorship, and/or publication of this article.

8-6-Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.