The Mediating Role of Psychological Well-Being in the Relationship Between the Psychological Contract and Professional Engagement

This study was conducted using structural equation modelling to examine the relationship between the psychological contract, psychological well-being, and professional engagement. The sample of the study included 416 teachers who were selected using a disproportionate cluster sampling method from primary and middle schools in Turkey. In analysing relations between variables, mediation testing was performed using the structural equation model and the bootstrap method. The results of this study showed that professional engagement is both directly and indirectly affected via psychological wellbeing by the psychological contract. How teachers perceive the psychological contract is an important variable that shapes their psychological well-being and professional engagement. Accordingly, school administrations should meet these teacher expectations and display attitudes and behaviours that encourage teachers to take active roles in school-related decisions, thereby further increasing the professional engagement of their teachers.


Highlights:
• In the study, the antecedents of professional engagement were examined.
• Psychological contract and well-being affects teachers' professional engagement.
• Well-being mediates the relationship between psychological contract and professional engagement.
Engagement is defined as an individual's physical, cognitive, and emotional association with their job and co-workers (Handa & Gulati, 2014;Kahn, 1990). Engagement also encompasses qualities such as job performance energy levels, willingness, mental resoluteness, and endurance (Bakker & Demerouti, 2008;Schaufeli & Bakker, 2004). Professional engagement is thus the attitude that an individual takes toward their job and includes the expectation of performing the roles assigned to them in the best possible way (Kozikoglu & Ozcanlı, 2020). Professionally engaged employees are engrossed in and focused on their jobs and tend to increase their commitment to their jobs over time (Schaufeli et al., 2002). The topic of professional engagement has been widely researched in the field of education (Kozikoglu & Senemoglu, 2018;Rusu & Colomeischi, 2020). The teaching profession requires content knowledge and specific competencies, as well as competencies related to positive human relationships and problem-solving. Teachers draw upon both their cognitive and emotional capabilities in educational activities (Crosswell & Elliott, 2004). Klassen et al. (2012) state that the number of studies on education has increased in recent years, with a particular emphasis on topics such as the impact of professional engagement on student learning outcomes; overcoming stress and burnout related to the job; and contributing by taking an active role in school-related decisions. Teachers who are dedicated to fulfilling the requirements of their profession and who focus on the work they do are evaluated in the context of professional engagement (Granziera & Perera, 2019). Psychological well-being is also a predictor of professional engagement (Rusu & Colomeischi, 2020;Shimazu et al., 2012) as teachers with high levels of professional engagement perform their jobs at a higher level (Spilt et al., 2011).
People work to live peaceful and healthy lives and aspire to be content while doing so. This idea of contentedness is related to well-being, which is represented by two main approaches: subjective (hedonic) and psychological (eudaimonic). The concept of subjective well-being (SWB) was developed in the 1980s by Diener and is defined as one's evaluation of one's own life. This valuation can be in terms of cognitive states such as satisfaction with one's marriage, work, and life, or it can be in terms of ongoing affect (i.e., the presence of positive emotions and moods, and the absence of unpleasant affect) (Diener et al., 1998). Ryff (1995) defined psychological well-being (PWB) as "the striving for perfection that represents the realization of one's true potential" (p. 100). Based on a thorough review of previous related theories, Ryff (1989) introduced the concept of PWB with six main components: self-acceptance, positive relations with others, autonomy, environmental mastery, purpose in life, and personal growth (Ryff, 1989;Ryff & Keyes, 1995). An individual's level of PWB can be assessed by considering all of these components together.
The psychological foundations of teachers play an important role in achieving the goals of educational organizations. Therefore, the number of studies that directly address teacher well-being has increased in recent years (Aelterman et al., 2007;Konu et al., 2010;Collie et al., 2015). These studies have mostly examined psychological well-being within negative contexts such as stress and burn-out (Spilt et al., 2011). Teaching is a difficult and stressful profession which by its nature requires communication with different groups and types of people (Kyriacou, 2001;Klassen & Chiu, 2010;McInerney et al., 2015;Stoeber & Rennert, 2008). This inherent stress inevitably affects psychological well-being (Chan, 2013;Skaalvik & Skaalvik, 2009). Another concept that is closely related to psychological well-being is the psychological contract. Some factors included in the psychological contract do in fact positively affect teacher psychological well-being, including schools meeting the expectations of teachers and fulfilling their promises to teachers (Dollansky, 2012;Ryan & Deci, 2001;Weiland, 2021). Psychological well-being improves the professional engagement of teachers and aids in the retention of these teachers within the profession (Spilt et al., 2011).
Social exchange, equality, and meaning-making form the basis of the concept of the psychological contract (Guest, 2004). The psychological contract includes both an employee's expectations of and responsibilities to an organization as well as an organization's expectations of and responsibilities to the employee (Lunenburg & Ornstein, 2008;Rousseau, 1995;Rousseau & Tijoriwala, 1998). As such, the psychological contract operates at two subdimensions: as an operational contract and as a relational contract (Millward & Hopkins, 1998). The operational contract can be defined as a financially-focused short-term psychological contract in which the obligations of the parties are clearly defined (Coyle-Shapiro & Kessler, 2000). The relational contract is the identification of employees with the organization; in other words, their adoption of the organizational goals as their own (Millward & Brewerton, 1999).
The professional performance of teachers is an important factor that determines the success of educational systems (Abe & Adu, 2014;Andriani et al, 2018;Somech & Wenderow, 2006;Sudarjat et al., 2015). In addition to external or school-level factors, the psychological state of teachers may significantly impact professional performance. Studies on the psychological contract have shown that teacher perceptions of the psychological contract can have a positive impact on the educational environment (Dollansky, 2014;Ryan & Deci, 2001). Therefore, the strategic goals of a school-and how teachers can achieve them-should be clearly explained to teachers. Similarly, efforts should be made to earn the confidence of teachers that their reciprocal expectations of the school administration will be fulfilled (Rousseau, 1990). The fulfilment of teachers' obligations to schools depends on the fulfilment of the school's obligations to the teachers (Gokyer, 2020;Weiland, 2021). This is evaluated within the scope of the psychological contract.
As previously mentioned, research has emphasized that psychological well-being enables teachers to become more engaged in their work (Greenier, 2021;Rusu & Colomeischi, 2020) and that the psychological contract plays an important role in this engagement (Spilt et al., 2011). However, what these studies fail to consider is the mediating effect of psychological well-being on the psychological contract and professional engagement. There is also a limited amount of research on these factors within the context of education, leaving the question of the mediating effect unanswered. Therefore, it is necessary to examine the mediating role of psychological well-being in the relationship between the psychological contract and professional engagement in both international and national contexts. Based on this, the present study aimed to examine the relationships between the psychological contract, psychological well-being, and professional engagement. The subsequent hypotheses formed on the relationships between variables were tested with the structural equation model (SEM) in this study.

The Present Study
A key element of most definitions of the psychological contract within the context of professional engagement is the reciprocal relationship between an organization and its employees. Therefore, reciprocity is the basic explanatory organizational element related to the concepts of the psychological contract and professional engagement. The basic approach of most studies of the psychological contract is to understand how employees react to an employer's behaviours (Coyle-Shapiro & Kessler, 2002).
Both the psychological contract and professional engagement are based on the Social Exchange Theory developed by Blau (1964) (Birtch et al., 2016;Cropanzano et al., 2001). Professional engagement, which is a motivational and psychological condition, is shaped according to the employees' perception of the psychological contract (Rayton & Yalabik, 2014) and their psychological well-being (Bakker & Schaufeli, 2015;Rusu & Colomeischi, 2020). Thus, a model for the correlation between the psychological contract, psychological well-being, and professional engagement was generated within the present study based on this conceptual framework (see Figure 1).
Insert Figure 1 near here In the conceptual model presented in Figure 1, the independent variable of the psychological contract is assumed to increase psychological well-being and professional engagement. Additionally, teacher perceptions of the psychological contract affect professional engagement directly as well as indirectly via psychological well-being.
Previous studies on psychological well-being have shown that burn-out, professional engagement, and job satisfaction are related to psychological well-being (Bakker & Oerlemans, 2011;Fredrickson, 1998;Garg & Rastogi, 2009;Mäkikangas et al., 2015). Shimazu et al. (2012) state that there is a significant positive correlation between psychological well-being and professional engagement.
Similarly, another study determined that psychological well-being is a premise variable of professional engagement (Brunetto et al., 2012). Hence, proposed that "psychological well-being is positively correlated with professional engagement." (Hypothesis 1).
The professional performance of teachers is one of the most important factors in determining the success of educational systems (Abe & Adu, 2014;Andriani et al., 2018;Somech & Wenderow, 2006;Sudarjat et al., 2015). The degree of professional performance may be affected by school-level factors such as ethical leadership but can also be related to personal and professional factors such as the attitudes, beliefs, and behaviours of teachers. Previous studies found that the psychological well-being of teachers increases when expectations are met in line with the psychological contract (Dollansky, 2012;Dollansky, 2014;Ryan & Deci, 2001;Van Petegem et al., 2005;Weiland, 2021). Therefore, proposed that "the psychological contract is positively correlated with psychological well-being." (Hypothesis 2).
The psychological contract consists of an organization's expectations of their employees-such as commitment, following the rules, and doing their job well-and also allows for employees to develop and contribute to the knowledge and skills of the organization (Rousseau, 2004). When expectations are met, employees feel good psychologically (Roothman et al., 2003) and will dedicate themselves to their jobs physically, cognitively, and emotionally, with their performances positively reflecting this investment (Handa & Gulati, 2014;Kahn, 1990). Therefore, it can be asserted that teacher perceptions of the psychological contract are closely correlated with professional engagement. In this regard, proposed that "the psychological contract is positively correlated with professional engagement."

(Hypothesis 3).
Psychological well-being of teachers is positively affected by the psychological contract (Dollansky, 2014;Weiland, 2021), enabling them to make a greater commitment to their profession (Brunetto et al., 2012;Greenier, 2021;Rusu & Colomeischi, 2020). It has been determined that psychological well-being is affected by various factors at the teacher and school level and has a positive impact on organizational outcomes such as performance and commitment (Handa & Gulati, 2014;Spilt et al., 2011;Wadhawan, 2016). On the other hand, there have been studies investigating the mediating role of psychological well-being (Ahmed & Malik, 2019;Baroni et al., 2018;Hossein Zei & Sahami, 2017). In conclusion, proposed that "psychological well-being is a mediating role in the relationship between the psychological contract and professional engagement." (Hypothesis 4).

Method
The proposed model for the correlation between the psychological contract, psychological wellbeing, and professional engagement (see Figure 1) was tested using SEM.

Study Model
The study was conducted using a correlational model, where the goal was to determine the presence and direction of the correlation between two or more variables (McMillan & Schumacher, 2010). In this case, the quasi-causal relationship between the variables of the psychological contract, psychological well-being, and professional engagement was examined.

Sample and Procedure
The sample of the study included 416 teachers who were selected using a disproportionate cluster sampling method from primary and middle schools in Gaziantep, Turkey in the 2020-2021 academic year. Of the teachers included in the study, 240 (57.7%) were female, 176 (42.3%) were male, 153 (36.8%) were aged between 21-30, 170 (40.8%) were aged between 31-40, and 93 (22.4%) were aged 41 and older.
Pre-interviews were conducted with administrators of the schools to be included in the sample in order to obtain necessary permissions for their teachers to be used in the study. After that, packages containing the data collection tools were distributed to 570 teachers within these schools, of which 443 were returned. Twelve forms were incompletely or incorrectly filled out and were thus not included in the study. Of the remaining 431, 11 were excluded from the set as outliers, and 4 fell under 13.82, the critical value for Mahalanobis distance (Pallant, 2005). Analyses were conducted on data collected from 416 forms. The population size was calculated using the formula, and 416 teachers were found sufficient for a 95% confidence interval and α = .05 significance level (Field, 2009).

Instruments
A form to collect demographic information as prepared by the researcher, the Psychological Contract Scale, the Psychological Well-Being Scale, and the Teachers' Professional Engagement Scale were used as data collection tools.

Data Analysis
The data were analysed using the SPSS 22.0 and AMOS 23.0 programs. The conceptual model was tested with the analysis of the path formed using SEM to determine the direct and indirect effects of the psychological contract (independent/external variable) and psychological well-being (mediating variable) on professional engagement (dependent/internal variable). In addition to SEM, the bootstrap method was used to test the partial mediatory role of psychological well-being on the correlations between variables, and to determine the significance of the direct and indirect effects in this model by resampling with replacement from the same sample (Preacher & Hayes, 2008). In the present study, bootstrap test and estimates were done with 10.000 resamples, then the bootstrap coefficient was calculated, and confidence intervals were determined (MacKinnon, 2008). The correlations between variables were calculated with the Pearson product moment correlation coefficient. Statistical significance level was accepted at p < .05.
Before the analysis, multicollinearity assumptions were tested with univariate and multivariate normality. The skewness-kurtosis coefficients of each variable were calculated in the univariate normality assumption, and the values obtained were between -2.0 and +2.0. This result indicated that the data were found to have a normal distribution (George & Mallery, 2016). Within the scope of the multivariate normality assumption, the Mardia coefficient was lower than 1.96, the critical ratio (c.r) was lower than 5, and the multivariate normality assumption was met (Raykov & Marcoulides, 2008).
Binary correlations between the values were calculated and found to be below 0.80 for the multicollinearity assumption in this study. Additionally, the fact that the variance inflation factor (VIF) value was lower than 10 and the tolerance value was higher than 0.2 indicates that there was no multicollinearity assumption problem (Field, 2009). The maximum likelihood method was preferred in the analyses related to the prediction of parameters in the structural equation modelling where assumptions were met. The effect sizes of all direct, indirect, and total effects obtained as a result of the analyses were interpreted as follows: around .10 indicated a small effect, around .30 was a moderate effect, and around .50 revealed a major effect (Kline, 2011).

Descriptive Statistics and Correlation Coefficients
Descriptive statistics and correlation coefficients of the variables of the psychological contract, psychological well-being, and professional engagement are presented in Table 1.
Insert Table 1 near here In the interpretation of the arithmetic mean scores in Table 1, the fact that the psychological contract and professional engagement scales were answered on a five-point Likert type and the psychological well-being scale was answered on a four-point Likert type was considered. Accordingly, it can be seen that teacher perceptions of the psychological contract (M = 3.88, SD = .47) and professional engagement (M = 4.01, SD = .42) were high while perception of well-being (M = 3.84, SD = .43) was moderate. The coefficients of skewness for the psychological contract, psychological wellbeing, and professional engagement were found to be .07, -.52, and -.53, respectively, while the coefficients of kurtosis were found to be -.74, -.59, and -.14, respectively. Considering these correlation coefficients, there was a moderate positive correlation between the psychological contract and psychological well-being (r = .36, p < .01), the psychological contract and professional engagement (r = .45, p < .01), and psychological well-being and professional engagement (r = .48, p < .01).

Measurement Model
Before conducting the structural equation model test, a measurement model should be formed and the structural relationships between the variables should be examined (Schumacker & Lomax, 2004).
As a result of the analysis of the measurement model generated in this framework, Chi-square (χ 2 ) value was 1901.32, and the degree of freedom (df) was 845, χ 2 /df = 2.25, p = .000. The model fit values were the following: RMSEA = .05, SRMR = .06, GFI = .82, NFI = .84, IFI = .90, TLI = .90, and CFI = .90 (Hu & Bentler, 1999;Schumacker & Lomax, 2010). According to the t-test results of the model, factor loads were between .39 and .91 and statistically significant. Additionally, there was a moderate positive correlation between the variables. After the structural validation of the measurement model, the structural model was tested with the path analysis.

Structural Model
It was found that the path coefficients between the variables were statistically significant as a result of testing the proposed model in this study; thus, all variables were added to the model at the same time. The path coefficients of the structural model tested were given in the mediation test in detail (see Figure 2). It was concluded that the goodness of fit values, which were χ 2 = 1901.32, df = 845, χ 2 /df = 2.25, p = .000, RMSEA = .05, SRMR = .06, GFI = .82, NFI = .84, IFI = .90, TLI = .90, and CFI = .90, were acceptable or close to acceptable values (Hu & Bentler, 1999;Schumacker & Lomax, 2010).

Mediating Test
First, the direct, indirect, and total effects were examined within the scope of the mediating test (MacKinnon, 2008). Results regarding the partial mediatory role of psychological well-being in the effects of the independent variable of the psychological contract on professional engagement were presented in this process. It was found that the psychological contract had a significant correlation with psychological well-being (β = .37, t = 3.83, p = .000) and professional engagement (β = .41, t = 3.81, p = .000). Moreover, the direct correlation between psychological well-being and professional engagement was statistically significant (β = .49, t = 6.23, p = .000). It was concluded that psychological well-being (mediatory variable) affected professional engagement without the independent variable of the psychological contract. These findings indicated that the mediation test would be suitable. Therefore, the partial mediatory role of psychological well-being in the correlation between the psychological contract and professional engagement was tested and the findings are presented in Figure 2.
Insert Table 2 near here   Considering Table 2, the fact that psychological well-being positively affected professional engagement (β = .49, p = .000) supports the H1 hypothesis while the fact that psychological contract positively affected psychological well-being (β = .37, p = .000) supports the H2 hypothesis.
Additionally, the fact that the psychological contract positively affected professional engagement (β = .58, p = .000) supports the H3 hypothesis. It was found that the standardized path coefficients between the psychological contract and professional engagement decreased as psychological well-being was added to the model and that the path coefficients became statistically significant following this decrease (β = .41, p = .000). In other words, the fact that the psychological contract affected professional engagement both directly and indirectly via psychological well-being provided evidence about the partial mediatory role of psychological well-being. Thus, the fourth hypothesis (H4) of the study was supported.

Bootstrap Test
After determining the partial mediatory role of psychological well-being, the significance of the change in the regression coefficients was tested by adding the standard errors of the variables into the calculation with the bootstrap method (MacKinnon, 2008). First, the partial mediatory role of psychological well-being in the correlation between the psychological contract and professional engagement was tested. The coefficients of the direct, indirect, and total effects obtained as a result of the analysis and the confidence intervals of these coefficients are presented in Table 3.
Insert Table 3 near here Considering the bootstrap coefficients and confidence intervals related to these coefficients in Table 3, it was found that the direct paths between the psychological contract, psychological well-being, and professional engagement were significant. Additionally, the psychological contract significantly and indirectly affected professional engagement (β = .17, 95% CI [.12, .26]). In line with the findings obtained, it can be stated that the psychological well-being of teachers had a partial mediatory role between their perception of the psychological contract and professional engagement.

Discussion
The present study aimed to investigate the effects of the psychological contract on the professional engagement of teachers and the mediating role of psychological well-being on these by employing SEM on a dataset of 416 teachers in Turkey. Empirically, this study not only confirmed previous findings on the considerable role of the psychological contract on professional engagement but also provided a clearer understanding of how psychological well-being may affect the professional engagement of teachers.
As a result of this study, it was found that the psychological contract and psychological wellbeing had a positive correlation with the professional engagement of teachers. This was an expected finding because the results of previous research on this subject showed that the psychological contract positively affected professional engagement (Fredrickson, 1998;Garg & Rastogi, 2009;Mäkikangas et al., 2015) and that the fulfilment of teachers' expectations by school administrations in line with the psychological contract is an important factor in increasing professional engagement (Rousseau, 1995;Spilt et al., 2011). According to another study, psychological well-being has a positive effect on the professional engagement of teachers. Besides, psychological well-being improves the professional engagement of teachers and aids in teacher retention within the institution as well as within the profession itself (Greenier, 2021;Spilt et al., 2011). Thus, it can be asserted that psychological wellbeing has positive effects on teachers' professional engagement.
Additionally, it was determined that the psychological contract affects professional engagement both directly and indirectly via psychological well-being. This result supports the findings of previous studies (Handa & Gulati, 2014;Kahn, 1990;Dollansky, 2014;Weiland, 2021). The psychological contract consists of the organization's expectations of its employees-such as engagement, following the rules, and doing the job well-and also the psychological expectations about allowing the employees to develop and contribute to the knowledge and skills of the organization (Rousseau, 1990). In instances where these expectations are met, employees will feel good psychologically (Roothman et al., 2003).
Further, in these cases, employees will dedicate themselves to their jobs physically, cognitively, and emotionally, with their job performance reflecting these efforts (Handa & Gulati, 2014;Kahn, 1990). Therefore, it can be asserted that the perception of the psychological contract is closely correlated with the psychological well-being and professional engagement of teachers. Additionally, the perception of the psychological contract increases teachers' psychological well-being (Dollansky, 2014;Weiland, 2021) and enables them to commit to their professions more deeply (Spilt et al., 2011). In short, the psychological well-being of teachers whose expectations are met within the scope of the psychological contract will increase and they will make a greater commitment to their profession.

Conclusion and Recommendations
The results of the present study revealed that teachers' perception of the psychological contract is an important premise variable that shapes their psychological well-being and professional engagement.
Accordingly, school administrations should meet teacher expectations and display attitudes and behaviours that encourage teachers to take an active role in school-related decisions, thereby further increasing the professional engagement of their teachers. This situation will also positively affect the psychological well-being of these teachers and increase their professional engagement. Teacher perceptions of receiving appropriate and/or promised recognition and compensation from school administrations for their work enables teachers to show a positive attitude towards the institution. The fair and honest practices of administrators and their efforts to meet the expectations of their teachers can comfort teachers psychologically and increase their level of professional engagement. Moreover, teachers with a higher level of professional engagement will show higher performance as well as contribute to the realization of educational goals. Future studies can examine other variables considered to be the premises of professional engagements such as the leader-member exchange, school culture, organizational justice, among others. In addition, qualitative studies can be conducted to determine the variables that might negatively affect the professional commitment of teachers.
The results of this study also have certain practical implications. First, it is important for school principals and teachers to meet mutual obligations by developing a relational psychological contract. As well, administrators should provide teachers with opportunities to participate in administrative decisionmaking and creative work environments where they can implement their ideas in order to increase their psychological well-being and professional engagement. Second, as professional engagement is shaped by perceptions of the psychological contract (Garg & Rastogi, 2009) and psychological well-being (Rusu & Colomeischi, 2020;Spilt et al., 2011), it is critical to determine which factors can contribute to increasing the level of compliance with the psychological contract of teachers and positively affect their psychological well-being, and to include practices with these factors in the school environment. Third, school principals should guide teachers in solving their work-related problems. In this way, teachers may become more connected to their work. Adopting a participatory management approach, fulfilling promises made, establishing fair and honest communications and behaviours with teachers, and ensuring psychological well-being among teachers are steps administrators can take to increase the level of professional engagement of their teachers.
The results of this study were limited by a few factors regarding research design and methodology.
Because the participant sample is not a representative sample of the whole country, the same results may not apply to other regions of the country. Future researchers can compare this study's findings with their studies at different school levels and residential areas. The relational model was used in this study.
However, this causes two critical limitations. First, the relational model explains the relationship between the three variables, but not the cause and effect relations. Second, when the scale is applied, a comprehensive perspective is gained, but this situation does not allow for obtaining detailed information.
Therefore, it is necessary to conduct qualitative and mixed-method studies on the subject. HLM or Multilevel SEM analyses can determine which variables affect the findings at the school level or teacher level. However, since the data collected were not suitable for multilevel analysis, these could not be conducted in this study.  The mediating role of psychological well-being Note. The path coefficient specified in parentheses (.58) is the value of direct impact before the psychological well-being mediating variable is added to the model.