Statistical Analysis: the Use of Mediator and Moderator Variables

The use of mediator and moderator variables
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ABSTRACTThe research aimed at defining and clarifying the difference in the use of moderator and mediator variables in a conceptual model. Various procedural steps were taken to identify the utilization of the two in a model. The research revisited various scholarly literatures in assessing the mediator and moderator variables. Moderator variables tend to express the causal relationships between variables while the mediator variable simply extenuates the relationship of variables in a conceptual model. Primary data was collected from interviews, surveys, and consultations which targeted a particular niche of data analysis professionals on the variables in question. The evaluation found that there are indeed significant differences in the two variables in question. If statistical analysts fail to understand the difference of the two or if these variables are used interchangeably, the results will be prone or inferential or statistical errors. The research concluded that it is practical for researchers to identify with the degree of implementing the two.
Keywords Mediator, Moderator, Exogenous, Endogenous, Collinearity, Multi-Collinearity.
1. INTRODUCTIONMediator and Moderator variables are often used interchanged without regard to their actual difference and meaning. This, when employed in researches, results to inconclusive analyses and consequent findings which cannot be relied upon or be utilized owing to reduced credibility.

It is also important to consider how widely these variables occur and by extension the numerous divergent fields in which they can be utilized. As such, it is paramount for any academic or professional research to consider the proper use of these variables (O’Neill, 2003). To this end, this research will consider the enumeration of Moderator and Mediator variables both conceptually as well as strategically, to highlight the differences inherent to the same. Mediator and moderator variables occur in such phenomenon as control and stress, personality traits and behavioral tendencies Baron & Kenny (2004). Their sociological applications range from health applications, such as the examination of the effectiveness of a treatment plan for patients, to the corporate world, when examining the factors that influence employee productivity and overall company success. The use of regression analysis in research that involves mediator and moderator variables has meaningfully improved our understanding of phenomena that exists around us. As such, it is essential that researchers, in the universal pursuit of knowledge, be diligent in the use of mediator and moderator variables to arrive at concise, reliable and credible findings.

1.1 Mediator Variable
This describes a variable that causes mediation between independent as well as dependent variables. Simply put, a mediator variable extenuates the correlation that exists between a dependent variable and an independent one. In such scenarios as there is complete mediation between the independent and dependent variable, this is referred to as a complete intervention resultant from the mediator variable. It is worth noting that in such instances, the original variable does not have any influence on the outcome of the process and furthermore, on the variable obtained from the process. Partial intervention is a scenario in which there is incomplete intervention by the mediator variable. The process of mediation results into a mediation model, which is described as the mediation resultant from the presence of a mediator variable. The mediation model describes the phenomenon in which the outcome of the process is caused by the mediator and not the other way around. This causal relationship described by the mediator variable applies to a wide variety of fields, among them psychology. For instance, the internal state of mind of any individual is affected by the external or physical environment surrounding them. The mediator variable can describe the connection between the two.
Moderator Variable
The moderator variable defines the influence of the causal relationship that exists between an independent variable and a dependent one. As such, it is often regarded as a third variable and is denoted with the letter M. A regression coefficient is used to measure the causal relationship between a predictor variable and a product variable with regard to the moderator variable present Kosar and M. Mehdi Raza Naqvi (2015). Since the moderator variable describes the strength of the connection linking a dependent and an independent variable, then it can have an amplifying or a weakening consequence on the product outcome. The moderator variable can also be enumerated as an interaction or categorical variable that is quantitative in nature and has an influence on the direction of, or the degree of the relationship between x and y variables. In this case, x and y representing dependent and independent variables respectively. It affects the zero-order relationship that exists between the predictor and product variable.
Collinearity
In such scenarios as the mediation resultant from the existence of a mediator variable in any process is perfect, then the mediator variable and the independent variables are correlated to one another. This is known as collinearity. Due to collinearity, one variable can be predicted from the other with a significant degree of accuracy owing to the strong nature of their correlation. It is vital to consider that collinearity only affects any analysis with regard to individual variables; mainly dependent, independent and mediator variables. As such, a regression model comprising of collinearly sound dependent, independent and mediator variables may effectively ascertain how well the process achieved the product variable but cannot provide any indication of the nature of the individual variables, for instance, and redundancies or inefficiencies that may exist amongst the same.
1.4 Multicollinearity
In such situations as the independent variable effectively describes all the alterations in the process that are caused by the existence of the mediator variable, then there does not exist a unique variable that explains the dependent variable. This phenomenon is regarded as multicollinearity. Multicollinearity cannot be avoided by the researcher as it arises from the mediational analysis of the product variable, the dependent variable, the independent variable and the mediator variable.
Exogenous variables
In the context of a mediation model, exogenous variables refer to those who do not have identifiable and explicit causes. It is easy to highlight these in the model since they are the once which have no arrows going towards them. They are also known as independent variables.
1.6 Endogenous variables
In the mediational model, these variables are defined as those who are affected in a causal manner by other variables. As such, within the context of the mediational model, they are represented by the variables having arrows pointing towards them. Owing to this, every endogenous variable should have a regression model fitted. They are also known as dependent variables.

2. LITERATURE REVIEWA thorough desk study conducted on the statistical occurrences described by mediator and moderator variables was invaluable at providing a base comprehension of these variables. As such, the examination of journals, books and articles revealed the following considering the moderator and mediator variables.
2.1 Conditions requisite for a Mediator variable
As cited by Kosar and Mehdi Raza Naqvi (2015).For a variable to be termed as a mediator variable, it is necessary for it to satisfy certain specified conditions. First of which, is that a variable is considered a mediator variable if the change that occurs in the independent variable correlates to a substantial alteration in the other variable. Second, is that there must exist a causal relationship describing a substantial alteration in the other variable resulting in an alteration or change in the dependent variable. The first two conditions enumerate that the causal relationship extends in a linear progression from the independent variable to the other variable, which is then established to be the mediator variable, and onto the dependent variable. In such a scenario as this progression is not clear, then the other variable cannot be described as a mediator variable.
A mediator variable is termed so particularly in such a process as the variable in question substantially affects the link between the independent and dependent variable O’ Neill (2003). This is to say that in any mediation process, the presence of the mediator variable is important to the outcome of the process. Without it, the relationship between the dependent and independent variable would be weak, non-reflective of a mediation and non-existent at all. The process of complete mediation involves the effect of the independent variable on the dependent ones, described by a causal relationship that results in the product variable. As such, this underlying relationship, where it is strongly defined by another variable that is neither the dependent, independent or product variable, is then considered to be the mediator variable.
2.1.1 Assumptions made in Mediation
Continuous Measurement: The first and the perhaps most significant assumption made in mediation are that there should be continuous measurements Ro, (2012). This implies that all the variables, independent variable, dependent and mediator variable, ought to be examined on a continuous scale. Normality: this assumption asserts the importance of all the variables’ following of a normal distribution. Linearity: this assumption asserts the fact that all the relationships that exist between the variables exist in a linear manner. Independence: in mediation, it is assumed that the errors observed are independent of each other. As such, the errors identified with one variable are not and cannot be associated with another.
2.1.2 Consistency of Mediator variable and the use of Instrumental Variables
Delgado and Vazquez (n.d.) asserted that the consistency with which the mediator variable is measured insignificant to the overall efficiency of the research and by extension, the credibility of the research. To this end, in such research as the mediator variable has not been adequately and efficiently measured, then the effect of the mediator variable can be underestimated with regard to the relationship it holds with the dependent variable or the independent variable. In other scenarios, the inconsistency in the estimation of the mediator variable could result in the overestimation of the relationship defined between it and the other variables, or between the independent, dependent and product variables. In any case, the findings of any such research would be substantially inconclusive and consequently would not be useable in any academic or professional capacity.
Kosar and M. Mehdi Raza (2015) cited that there exists a correctional procedure for any inconsistency with the measurement of the mediator variable. This correction is exceedingly necessary as without it, the data gathered would exhibit significant bias which is less than ideal as any research should present a neutral and perspectival approach. As such any error in the measurement of the mediator variable can be remedied by the use of an instrumental variable. In such a scenario as the relationship between the mediator variable and the dependent variable and the product variable exhibits a nature which cannot plausibly reflect the true relationship between the two, then the instrumental variable is utilized. In this respect, the instrumental variable creates a change in the mediator variable to reflect better the relationship that is pragmatic or that can exist in actuality. It is important to note however that the instrumental variable does not cause an independent warping or alteration of the dependent or product variable such that it maintains the initial inherent nature of the process. Instrumental variables are essential to the correction of an error in the measurement of mediator variables, especially in instances where there is a correlation of a regression manner between the error and the mediator variable.
2.2 Moderated Regression Analysis
In applying efforts to identify the variable describing the strength or course of the link between the independent and dependent variables in any process, the moderated regression analysis is used to highlight the moderator variable Walters, (2012). This can adequately be enumerated by the example that follows:
Given that;
  (1)  (2)  (3)
When evaluating the nature of the relations between the independent variables and the moderator variable is not significant in statistical analysis, then Z ceases to be a moderator variable and instead becomes simply an independent variable. However, in the case that the interaction between the independent variables and Z is statistically substantial, then the equations describe a process that encompasses moderation.
2.2.1 Assumptions made in the use of Moderator Variables
As enumerated by Schwarzer, (2008), there exists a Causal variable relationship: This assumption asserts that it is essential that the independent variable in any process ought not to be related to the moderator variable. It implies that no special relationship can be extrapolated from an independent variable and a moderator variable which are correlated. The independent variable in any research should be clear of any relational connection that may exist between it and either the product variable, the dependent variable, or the moderator variable. Contrary to this, it is, however, paramount and critical that the moderator variable exhibit correlation with the dependent variable. If any strong correlation exists between the independent variable and the moderator variable, then there arise estimation problems with the data.
Measurement assumption: in most statistical cases, the moderator is representative of the degree of interaction that exists between the causal variable and the product variable. As such, there must be a significant degree of transformation of the independent variable to the dependent one on the moderator variable for moderation to be supported. This being said, in such cases as there is little or no significant relations between the moderator variable and the independent variable, then the process will exhibit the fact that moderation is not supported.
Causal assumption: This hypothesis states that suppose X represents the independent variable, then when X variable has not been randomized, then causation has to be assumed. It is also important to note that where the causation existent between the independent variable X and the dependent variable Y, then the moderator variable can affect the causation in a reverse manner.
2.2.2 Linear and Nonlinear Measurement
In any regression equation involving a moderator, where there exists a correlation between the dependent variable Y and the linear independent variable X, then there will be an observation of a change in the Y variable with any modification of the mediator variable Walters, (2014). In a non-linear model, then changes in the moderator variable may not issue a corresponding linear change in the dependent variable.3. METHODOLOGYThis research focuses on the statistical applications of mediator and moderator variables. As such, most data compiled from the same is resultant from extensive studies on secondary sources which comprise journals, books, and articles written by previous scholars regarding the matter. This information is crucial towards the comprehension and understanding of the matter of mediator and moderator variables, as through the scrutiny and examination of such data, can the actuality of the nature of the variables be determined? The desk study will incorporate sources from various fields of learning, which include, psychology, social sciences, and medicine. To attain the most widespread view of the literary information present on the matter, it was necessary to consider the use of scholarly sites and sources such as Google Scholar and JSTOR, as well as physical searching of books in the library. It is only through the evaluation of the past findings that it is possible to adequately and definitively define the differences that exist between mediator and moderator variables and by extension, the areas in which they are supposed to be utilized.
The research also utilized the consultation with persons who hold particular expertise in conducting statistical research and data analysis visa vie mediator and moderator variables. This may include such persons as professors and professionals in research institutes. Interviews and surveys will be conducted on said people to attain as much information regarding the subject as possible. To this end, the interviews will comprise of targeted inquiries of the experience the individual has had in all researches conducted on the variables in question, any problematic areas, and strategy used to overcome the same.
4. DISCUSSIONFollowing the undertaking of the research into the nature and characteristics of the mediator and moderator variables, it is thus necessary to explore the means by which they are tested for and applied in statistical context. As such, this segment will constitute the formulation of a mediational hypothesis, the tests to ascertain presence or absence of mediation and moderation, and the steps and procedures taken for the moderation and mediation analysis, with regard to various case studies.
4.1 Mediational Hypotheses
The mediational model, which is intrinsically established from the mediator variable, can be described and analyzed statistically, however, statistics can not describe the mediation that is produced by the variable itself. In order to comprehend the meditational model, it is first paramount to address the existence of a mediational hypothesis. This described a state where an independent variable is affecting a dependent one, whereby the mediator variable highlights this relationship. It is noteworthy that in meditational hypotheses, an independent variable can still affect the independent variable. However, the dependent variable cannot affect the independent variable even in the context of a process involving a mediator variable Liu et.al. (2013). In pursuit of this, it is essential to evaluate the findings of two principle scholars, Baron and Kenny. Upon evaluations of the mediator variable, and the formulation of mediational hypotheses, they concluded on four steps highlighting a procedure for the testing of various mediational hypotheses. As such, for any mediational hypothesis to be valid, they ought to satisfy the following requisites.
4.1.1 Baron and Kenny’s Mediation procedure
The first in the procedure comprises the establishment that the initial variables have a correlation with the final variable. This essentially ensures that the independent and dependent variables at the beginning of the process undergo a change which results in the product variable. The existence of this change is essential to the validity of the mediational hypothesis, as it establishes that there is indeed a mediating variable. The final mediational model will thereby describe the mediation process. In this regard, the researcher has to ascertain that the independent variables affect the dependent ones, through the process of the mediating variable for his/her mediational hypothesis to have satisfied the first requisite.
Baron and Kenny consequently proposed that it is necessary for the original variable to have some correlation with the mediator variable. In essence, it is crucial that the researcher enumerates that there is indeed a relationship that exists between the independent as well as dependent variables. To do this, the researcher has to consider the mediator variable as a product or final variable and highlight the existence of an effect between the initial variables and the mediator variable. To this end, it is paramount for the researcher to establish that the initial variable is the causal variable within the process, both with regard to the mediator variable as well as the product variable. This is to say that without the presence of the original variable, both the product, as well as the mediator variable, would not exist. There is an exception to this step, as there are scenarios whereby the mediator variable is resultant from the product variable. This is only possible in instances where the original variable is a manipulated variable. In this respect, since the mediator variable as well as the product variable is not manipulated variables, then they can be causal variables towards each other irrespective of the initial variable in the mediational hypothesis.
The third step in the procedure described by Kenny and Baron (2004) is that any researcher who seeks to propose a mediational hypothesis must prove a correlation existing between the product variable and the mediator variable. This correlation is largely founded on the notion that both the product as well as the mediator variable is functions of the initial or original variable. With respect to the entire process, the researcher must exhibit a causal relationship between the initial variable and the product variable through the mediational variable. Baron and Kenny suppose that the original variable has to exhibit some control parameter through which the mediator variable and the product variable are arrived at. The final step in the Baron and Kenny mediational hypothesis requisites procedure is that there must be complete mediation across all of the variables; original variables consisting of both independent and dependent ones, the mediator variable and the product variable. The fourth step is only satisfied if the effect attained from the original variable over the outcome variable is zero, with regard to the controlling of the mediator variable. Researchers often employ these steps in the check for validity of their mediational hypothesis. This being said, where all steps outlined by Baron and Kenny are met then the data obtained by the researcher is consistent with mediational hypothesis while if only the first three are met then, the data exhibits partial mediation.
4.2 General Steps were undertaken in the Testing of Moderation
The effects of a moderator variable are often established through the use of hierarchical multiple regression. In the testing of moderation, it is essential to look at the interaction effect that exists between X and M and whether or not this effect can be considered as substantial in the prediction of Y variable. This being said, in order to show that there exists a moderation effect on the correlational model between two variables X and Y, it is critical that one exhibits that any change that occurs in the moderator variable M, has a definite and significant effect on the dependent variable Y through interaction with the independent variable X. To this end, the following steps should be followed;
First and foremost, there is a need to standardize all the available variables M.A (2013). This is done in order to make it simpler to make interpretations afterward and to alleviate the existence of multicollinearity.
It is then necessary to code categorical variables and subsequently create the terms for the initial variables, i.e. independent and dependent variables as well as terms for the moderator variable and the product variable. The level of coding is however only dummy coding.
It is then paramount that one fits a regression model, otherwise known as block 1, which will comprise the prediction of the product of the variable Y from the initial variable X and the moderator variable which is denoted by the letter M. At this point, ascertain that both the model in general denoted by the symbol R2 as well as the effects ought to be substantial.
Following this, it is necessary for one to add the interaction effect resultant from the moderator variable, to the preceding model denoted by, block 2, and check to see if any substantial alterations have been evident in R2. It is then important to consider whether there has been any major modification with the introduction of the original interaction term. If there is a major change in both scenarios, then one can safely conclude that moderation is existent within the process being evaluated.
If the initial variables and the moderator variable are not significant with the added interaction term, then it can be concluded that complete moderation has taken place.
On the contrary, an event that the initial variables, independent X and dependent Y, and the moderator variable are not significant with the added interaction term, then through moderation has still taken place; one should also note that the main effects are substantial.
4.2.1 Example of research tested for moderation using Multiple Regression Analysis
A researcher may consider examining the level of depression experienced by a family of caregivers, represented by the dependent variable Y. This is affected by two independent variables represented by the severity or the nature of the impairment experienced by the patients (X1) and the nature and extent of the dysfunctionality evident within the family (X2). Upon examining the dynamics of the caregiving family, the researcher discovers that there is little correlation between the nature of impairment and the depression evident in the caregivers. Consequently, the researcher discovers that the relationship between the dysfunctional nature of the family and the depression experienced by the caregivers. As such, they are led to formulate a moderation hypothesis in that; the dysfunctional nature of the family moderates or influences, to a significant extent, the enhancement of the nature of the patient’s impairment on the depression of the caregivers. In doing so, the researcher has effectively introduced a third variable namely X3, which is essentially a moderator variable.
4.2.2 Testing for Moderation through Multiple Regression Analysis
In the event that the original and the final variables are continuous, moderation is tested for using multiple regression analysis. According to Baron and Kenny, most researchers assume that a continuous moderator variable changes the correlation of the exogenic and endogenic variables which occur in a linear manner. As such, using the example above and variables, then the original variables of the dysfunctionality of the family and the impairment of the patients, are entered into a regression equation. The interaction term is then entered, which is the moderator variable X3, described by the function (dysfunction * impairment). The researcher may choose to enter the data in various methods including a stepwise, simultaneous or hierarchical manner. However, it is important that the initial variables, the dependent variable, as well as the two independent variables, be entered before the moderating variable is input.
Following this, if R2 is altered in a significant manner, then a moderating effect is confirmed. Consequently, the hypothesis proposed by the researcher will be confirmed. However, if the change in R2, is not statistically significant, then it can be concluded that there is no moderating effect and the null hypothesis is proved to be true. For the attainment of statistical changes in R2, then the researcher has to follow subsequent steps. First of which is the establishment of the levels of low, medium and high for the independent variables of dysfunction and impairment. These are determined through Standard Deviation for these variables. Secondly, simple regression analysis will be conducted for each level of these initial variables on the moderator variable. Following the obtaining of these values, the regression lines are then plotted. These comprise of all the values of low, medium and high values, which is done so as to ascertain whether the moderation is a situation-specific event, or whether there is enhancing or whether there is a buffering effect on the dependent variable.
Through all these processes of testing for moderation, a researcher must be constantly aware of the fact that the issue of multicollinearity is ever present. As such, multicollinearity results to bouncing betas, which in turn result in inconclusive results. Though a problem continuously encountered, multicollinearity does have some measure of control. In this instance, it can be reduced by the centering of constant initial variables and moderator variables. To achieve this, one has to subtract the sample mean from the variable in question. By doing this, one can effectively achieve a deviation score which will comprise of an intrinsic mean of zero. The only means of reducing multicollinearity is the reduction or complete alleviation of the correlations that exist between the independent variables. By centering the beta terms, the degree of correlation was effectively reduced, which in turn eliminated any and all occurrences of multicollinearity.
4.2.3 Moderation testing using Structural Equation Modelling
Most researches conducted involving moderation usually utilizes multiple regression analyses. However, Structural Equation Modelling is founded on the method of maximum likelihood analysis, which can only be employed when these conditions are met; the model includes correlated residuals, the model comprises a non-recursive nature, and the model contains multiple highlighting variables for unobserved or otherwise known as latent variables Schwarzer(2008). The second requisite, regarding a non-recursive model, owes to the fact that a model containing reciprocal relationships is impossible to analyze through the use of regression methods. Structural Equation Modelling allows for the assimilation of errors which can be incident while preparing the statistical model. Structural Equation Modelling is also suitable in the respect that it permits the alienation of the confounding of aspects evident in the reciprocal nature of recursive dataset. Structural Equation Modelling is also efficient in the analysis of scenarios which present latent or construct variables which originate from different indicators. Other measurement techniques may not be able to note these unobserved variables efficiently. Researchers who seek to use SEM must first obtain extensive statistical training in various software used to handle the same. Principal among this analytical software is the EQS and LISREL VII.
4.2.4 Moderator testing using Analysis of Variance (ANOVA)
The use of Analysis of Variance is useful especially in cases where both the independent variable and the moderator variable exhibit dichotomous nature Baron & Kenny (2004). In such a case, a 2*2 ANOVA is used. This type is also known as a two-way ANOVA. In the case of the example used above, the researcher may want to employ evaluations into two different types of therapy offered by the caregiving family members. This can be in the form of individual therapy as compared to group therapy, which can be matched up against reported depression levels in the caregivers, whether happy or sad when administering care. Through the evaluation by the two-way ANOVA, the effects of the two types of treatments (individual and group), with regard to the interaction between the patient and the caregiver (cheerful or sad). If this interaction provides results which prove to be statistically substantial, then the hypothesis supporting moderator will be proven. Sample means for each situation, both for individual and group therapy is plotted against both states of happy and sad and visually demonstrated.
4.3 General Steps were undertaken in the testing for Mediation
Mediation, as cited above, is a product of indirect causality, where the product variable is arrived at owing to the transformational process involving a mediator variable M. In the pursuit of confirmation of a mediating variable, it is essential that we extenuate the fact that though a mediator is resultant from the original variable, the independent variable, and is consequently the causal agent for the product variable and the dependent variable, it inclusion in the model results in the loss of meaning of the original variable. As such, the following steps, should be followed:
First of all, it is crucial to establish the relationship that exists between the original variable and the outcome variable.
Secondly, it is essential that the relationship between the mediator variable and the original variable, usually the independent variable, be established as well.
Third, it is paramount that the researcher establishes a link between the mediator variable and the outcome variable with the consideration of the presence of the original variable.
Four, it is essential that the researcher establishes a reduction in the meaningful effect of the relationship between the initial variable and the product variable in the presence of the mediator variable.
4.3.1 Example of Research involving Mediation test
A researcher decided to conduct an evaluation of a certain population of women that have developed breast cancer. In this regard, the women became categorized broadly into two sections; those who practiced active means of coping with the breast cancer, while there were those who practiced passive means of coping with the issue of breast cancer. A considerable difference between these two categories of women undergoing breast cancer is that those practicing active coping indulge in activities that are in line with the treatment program and as such, experience healthier lives. Such activities include; exercising, taking all the prescribed medication in the manner described by the physician, the eating of balanced diets and to this end, the undertaking of healthy feeding habits that lead to good nutrition. As such, the researcher proposes that the practicing of active coping in it may not enhance life longevity. However, it acts as a mediator variable which enables one to undertake activities that promote longevity of life. As such, the independent variable includes treatment regime (A), while the dependent variable is the longevity of life of the person (C). The third variable is coping (B).
4.3.2 Mediational test using Multiple Regression Analysis
Before regression analysis can be applied to the example, it is significant that all the variables involved be evaluated for correlation amongst each other. First, the variable a representing treatment regime has to exhibit substantial statistical correlation with the dependent variable C which represents longevity. The mediator variable B, coping, also has to show correlation with the dependent variable C, longevity. Following this, three regression analyses were conducted. In the first, the substantiality of the path described by the relationship between A and B is established. Afterward, the substantiality of the path between the A and B is ascertained. Consequently, the path from B to C is determined using the independent variable and the dependent variable C as primary variables. The third step involves a simultaneous entry of variables instead of a stepwise one. This is primarily owing to the simultaneous entry allows for the control of A while the correlation between B and C is analyzed. This is also applied to the mediator variable while the correlation between the dependent and independent variable is examined.
The results of these are then observed and evaluated. In the event that the path described by A to C in the third step is resultant to zero, then it indicates that there is the substantial existence of a solitary central mediator. However, the contrary is usually the case, where that pathway described by A to C does not equal zero and thus indicates multiple cases of mediational factors. In the case provided by the example, the nurses would be conducting the research. In this regard, they would be involved in the examination of the mediation factors that reduce the path described by A to C. One can go a step further and examine how strong the mediator variable is by the evaluation of the change in the coefficient obtained from regression analysis experienced in the third equation as compared to the one, in the regression coefficient evaluation, experienced in the second one.
4.3.3 Mediational test using Structural Equation Modelling
Structural Equation Modelling is essential towards the evaluation of unobserved or latent variables from multiple indicators. In a scenario where there are three latent variables, an unobserved initial variable A, an unobserved mediator variable B and A latent product variable C, unobserved variable constructs can be obtained using factor analytic methodologies. Following this, the mediational model is evaluated based on the fit of A to B to C. The interpretation follows the rule that where there is a significant mediational effect, then the relationship defined by A to C becomes non-significant, whenever B is in the model. As such, this confirms a mediational hypothesis in the process. However, in such cases as the relationship between A and C remains substantial and unaffected regardless of the presence of the third variable B, the null hypothesis regarding mediation is proven. In this scenario, the mediating variable has little to no effect on the causal relationship existent between the initial variable and the outcome variable, and as such, there exists no mediation in the model.
To attain these conclusions in Structural Equation Modelling, then the entire model is tested on two conditions; when A to C is not under constraint, and when A to C is under constraint. In this regard, constraining a path means that it is not estimated during the analytical process. In the event that a mediational effect has been evidenced, then the researcher has to evaluate the model with use of a chi-square. The chi-square test determines the significance and the goodness of the fit indices. The chi-square compares the theoretical model of the process, and the actual gathered data from the research. As such, the chi-square is critical towards the assurance that there is consistency and congruency between the actual and the theoretical. However, when a researcher chooses to employ the use of the chi-square, he/she has to consider conducting it in the most diligent manner as any errors will result in a cataclysmic deviation of the results from the actual. This is partial because the chi-square is greatly affected by the size of the sample. In such researches where the amount of data is significantly extensive, then one can utilize the goodness-of-fit index or the AGFI, which is similar to those above with the slight exception of being adjusted to better reflect the varying degrees of freedom existent in the model.
5. CONCLUSIONMediator and Moderator variables are extensively used in the world of research. This is predominately due to their immense applicability under various fields in the description of the relationship that exists between different variables. In the efforts of maintaining the integrity and credibility of the researches that employ these variables, it is essential that all researchers realize the divergence of these two. This is paramount as researchers who utilize these variables interchangeably often result in committing statistical as well as inferential errors. It is a cornerstone purpose of this paper to enumerate the need to adequately comprehend the nature of these two variables by scholars before they endeavor to start their research. Mediator and moderator variables are essential to regression analyses and owing to this; it is paramount that all researchers understand how to formulate mediational as well as moderation hypotheses Walters (2012). Furthermore, they scholars ought to know the procedures by which these variables are analyzed, steps which this research has sought to explicate in great detail. As such, it is important that all scholars who strive to undertake researches practice diligence when it comes to the use of mediator and moderator variables. When research is conducted and analyzed appropriately, it not only eliminates the possibility of erroneous conclusions and inferences but also paves the way for exhilarating new comprehensions of the world around us.
REFERENCESBaron, R. and Kenny, D. (2004). The moderator-mediator variable distinction in social psychological research: Conceptual, strategic, and statistical considerations. Journal of Personality and Social Psychology, 51(6), pp.1173-1182.
Delgado Pina, M. and Vázquez Inchausti, E. (n.d.). Moderator-Mediator Distinction: AnApplication on Top Management Team Literature. SSRN Electronic Journal.
Kosar, R. and M. Mehdi Raza Naqvi, S. (2015). Psychological Empowerment and EmployeeBehaviors: Employee Engagement as Mediator and Leader-Member Exchange asModerator. JOURNAL OF INTERNATIONAL BUSINESS RESEARCH ANDMARKETING, 1(6), pp.24-30.
LIU, X., ZHAO, J. and SHEN, J. (2013). Perceived Discrimination and Subjective Well-beingamong Urban Migrant Children: The Effect of Mediator and Moderator. ActaPsychologica Sinica, 45(5), pp.568-584.
MA, A. (2013). Relative Deprivation and Social Adaption: The Role of Mediator and Moderator.Acta Psychologica Sinica, 44(3), pp.377-387.
O’Neill, K. (2003). Moderator or mediator (1st ed.).
Ro, H. (2012). Moderator and mediator effects in hospitality research. International Journal ofHospitality Management, 31(3), pp.952-961.
Schwarzer, R. (2008). Models of health behavior change: Intention as mediator or stage as moderator? Psychology & Health, 23(3), pp.259-263.
Walters, G. (2012). Relationships among Race, Education, Criminal Thinking, and Recidivism:Moderator and Mediator Effects. Assessment, 21(1), pp.82-91.
Walters, G. (2014). Sex as a moderator and perceived peer pressure as a mediator of theexternalizing-delinquency relationship: A test of gendered pathways theory. Journal ofCriminal Justice, 42(3), pp.299-305.