Moderation and Mediation PDF

Moderation and Mediation Moderation Analysis  Moderation Analysis Parental support A moderator is a variable that specifies...

Moderation and Mediation Moderation Analysis  Moderation Analysis Parental support A moderator is a variable that specifies conditions under which a given predictor is related to an outcome. Answers the question, “when?” Confidence Academic Success Moderation implies an interaction effect, where introducing a moderating variable changes the direction or magnitude of the relationship between two variables. August 2022 Psychological Statistics 3  Moderation Analysis Parental support (a) Enhancing - where increasing the moderator would increase the effect of the predictor (IV) on the outcome (DV). (b) Buffering - where increasing the moderator would decrease the effect of the predictor on the outcome. Confidence Academic Success (c) Antagonistic - where increasing the moderator would reverse the effect of the predictor on the outcome. Confidence leads to academic success “especially if” students are high in parental support. Confidence leads to academic success “depending on” the parental support received by students. August 2022 Psychological Statistics 4 Data Requirements Moderation Analysis IV is continuous DV is continuous MV is continuous OR categorical If IV is CATEGORICAL, use ANOVA If DV is CATEGORICAL use LOGISTIC REGRESSION August 2022 Psychological Statistics 5 Sample Moderation Analysis Steps  Step 1: Estimate the interaction effect Step 2: Statistical inference test Step 3: If interaction is significant, then probe the interaction by doing a simple slopes analysis (or cheat sheet). August 2022 Psychological Statistics 7  Hierarchical multiple regression is used to assess the effects of a moderating variable. To test moderation, we will, in particular, be looking at the interaction effect between X and M and whether or not such an effect is significant in predicting Y. 9/3/20XX Psychological Statistics 8 Example Does Anger Out predict Anger Expression? [ X → Y] Does Sports participation predict Anger Expression? [M → Y] Does Sports participation moderate the relationship between Anger Out and Anger Expression? [X|M →Y] Predictor – Anger Out DV – Anger Expression Moderator – Sports participation 9/3/20XX Psychological Statistics 9 To Use Jamovi Click + Modules, search and add medmod 9/3/20XX Psychological Statistics 10 9/3/20XX Presentation Title 11 9/3/20XX Presentation Title 12 9/3/20XX Psychological Statistics 13 Possible conclusions Main Effects are Present: The significant simple slopes suggest that there are meaningful relationships between the predictor (anger out) and the outcome (anger expression) at different levels of the moderator (sports). This means that anger out consistently affects anger expression, regardless of the level of the moderator. Lack of Interaction: The non-significant interaction effect implies that the strength or direction of the relationship between anger out and anger expression does not significantly change across different levels of the moderator. In other words, while the relationship exists, it is not influenced by the moderator to a degree that is statistically significant. Consistent Relationship: Since the simple slopes are significant at both low and high levels of the moderator, you can conclude that the predictor’s effect on the outcome is relatively stable, even if it varies slightly in magnitude. Caution in Interpretation: While the simple slopes analysis provides insights into the effect at specific levels of the moderator, the lack of a significant interaction means that one should be cautious about overinterpreting the differences in slopes as indicating a nuanced moderating effect. 9/3/20XX Presentation Title 14 Example Question: Does the method of teaching moderate the effect of the IQ on reading? Ho: The effect of IQ on reading is not moderated by method of teaching. Ha: The effect of IQ on reading is moderated by method of teaching. 9/3/20XX Presentation Title 15 9/3/20XX Presentation Title 16 9/3/20XX Presentation Title 17 Reporting Results To test the hypothesis that [IV] affects [DV] , and whether [M] moderates the relationship between [IV] and [DV] , a hierarchical multiple regression analysis was conducted. Results show that [IV] (B = ___, p = ___) and [M] (B = ___, p = ___)have [in]significant main effects on [DV]. The interaction between and [IV] and [M] is [also] [in]significant (B = ___, p = ___). Furthermore, it is indicated that IV leads to DV depending on the presence of M. Simple Slopes Analysis indicate that when M scores are high (B = ___, p = ___), the effect of IV on DV is _______. On the other hand, when M scores are low (B = ___, p = ___), the effect of the IV on the DV is _______. 9/3/20XX Presentation Title 18 Mediation Analysis Moderator vs. Mediator Moderator It is desirable that the moderator variable be uncorrelated with both the predictor and the criterion (DV) to provide a clearly interpretable interaction term. Unlike the mediator-predictor relation (where the predictor is causally antecedent to the mediator), moderators and predictors are at the same level in regard to their role as causal variables antecedent or exogenous to certain criterion effects. That is, moderator variables always function as independent variables, whereas mediating events shift roles from effects to causes, depending on the focus of the analysis. 9/3/20XX Presentation Title 20 Moderator vs. Mediator Mediator A variable functions as a mediator when it meets the following conditions: a) variations in levels of the independent variable significantly account for variations in the presumed mediator (Path a) b) variations in the mediator significantly account for variations in the dependent variable (Path b) c) when Paths a and b are controlled, a previously significant relation between the independent and dependent variables is no longer significant, with the strongest demonstration of mediation occurring when Path c is zero. 9/3/20XX Presentation Title 21 Mediation Mediating variables form the basis of many questions in psychology: Will changing social norms about science improve children’s achievement in science? If an intervention increases secure attachment among young children, do behavioral problems decrease when the children enter school? Does physical abuse in early childhood lead to deviant processing of social information that leads to aggressive behavior? Do expectations start a self-fulfilling prophecy that affects behavior? Can changes in cognitive attributions reduce depression? Does trauma affect brain stem activation in a way that inhibits memory? Does secondary rehearsal increase image formation, which increases word recall? Questions like these suggest a chain of relations where an antecedent variable affects a mediating variable, which then affects an outcome variable. 9/3/2024 22  Mediation Mediation implies a situation where the effect of the independent variable on the dependent variable can best be explained using a third mediator variable which is caused by the independent variable and is itself a cause for the dependent variable. This answers the question “why?”. That is to say instead of X causing Y directly, X is causing the mediator M, and M is in turn causing Y. The mediator is called an intervening or process variable. The causal relationship between X and Y in this case is said to be indirect. The relationships between the independent, the mediator and the dependent variables can be depicted in form of a path diagram/model. August 2022 Psychological Statistics 23  Mediation Involves a set of causal hypotheses where an initial variable may influence an outcome variable through a mediating variable. Also referred to as a causal chain in which one variable [IV] affects a second variable [M] that, in turn, affects an outcome variable [DV]. A variable may be considered a mediator to the extent it carries the influence of a given IV to a given DV. Generally speaking, mediation is said to occur when: The IV significantly affects the mediator [M]. The IV significantly affects the DV in the absence of a mediator. The mediator has a significant unique effect on the DV. The effect of the IV on the DV shrinks upon the addition of the M to the model. 9/3/20XX 24  Mediation Social Support Self-Esteem Academic Success Each arrow in a path diagram represents a causal relationship between two variables to which a coefficient or weight is assigned. These coefficients are nothing but the standardized regression coefficients (betas) showing the direction and magnitude of the effect of one variable on the other. August 2022 Psychological Statistics 25 Summary Moderation and Mediation are used to explore the interrelationships among 3 variables If you have only two variables, do a simple correlation or linear regression. Having three variables means that one can examine their various relationships in more complicated ways. Mediation and moderation are tests of association, but structured so that particular questions can be answered. Both will require a theory, model or principle August 2022 Advanced Quantitative Research 26  Mediation Social Support Self-Esteem Academic Success Self-esteem will affect academic success “because of” social support. August 2022 Psychological Statistics 27 Mediation Instead of using the terms independent and dependent variables, it would make more sense in the context of path models to speak of exogenous and endogenous variables. Variables Exogenous Variables – variables which in the context of the model have no explicit causes. That is to say, they have no arrows pointing to them. (IV) Endogenous Variables – variables which in the context of the model are causally affected by other variables. That is to say, they have arrows pointing to them. (DV) From a regression standpoint, for every endogenous variable in the regression model should be fitted. August 2022 Psychological Statistics 28 Mediation Assumptions Continuous Measurements. All variables are assumed to be measured on a continuous scale. Normality. All variables are assumed to follow a Normal distribution. Independence. The errors associated with one observation are not correlated with the errors of any other observation. Linearity. Relationships among the variables are assumed to be linear. August 2022 Psychological Statistics 29 Sample Simple Mediation Analysis Steps Mediation Steps Step 1 Step 2 1. Estimate the direct Direct effect = path C Direct effect = and indirect effects Indirect effect (or Significance test (p- (thru a series of mediation effect) = (path value) regression analysis) a) x (path b) Indirect effect = 2. Statistical Inference Bootstrap confidence (test the significance interval of the indirect effect) The effects can be estimated using two regression equations. Indirect effect, just multiply a and b. August 2022 Psychological Statistics 31 Steps in Testing Mediation In order to confirm a mediating variable and its significance in the model, we must show that while the mediator is caused by the initial IV and is a cause of the DV, the initial IV loses its significance when the mediator is included in the model. In more explicit terms, we should follow these four steps: 1. Confirm the significance of the relationship between the initial IV and DV. (X → Y) 2. Confirm the significance of the relationship between the initial IV and the mediator. (X → M) 3. Confirm the significance of relationship between the mediator and the DV in the presence of the IV. (M|X → Y) 4. Confirm the insignificance (or the meaningful reduction in effect) of the relationship between the initial IV and the DV in the presence of the mediator (X|M → Y) 9/3/20XX Psychological Statistics 32 3 Main Types of Mediation 1. Indirect effect: predicts no direct effect from X to Y. However, X has a direct effect on the mediator, and the mediator has a direct effect on Y. Thus, X is said to have an indirect effect on Y. This hypothesis can only be supported if the direct effect of X to Y is insignificant before testing for indirect effects. 2. Partial mediation: predicts significant direct and indirect effects from X to Y. Thus, the unmediated relationship is significant as well as the X to the mediator and mediator to Y relationships. 3. Full mediation: predicts that the direct effect of X to Y will be significant only if the mediator is absent. When the mediator is present, this direct effect becomes insignificant, while the indirect effect is significant. Lastly, if the X to the mediator and/or the mediator-to-Y relationships are insignificant, no mediation is taking 9/30/2024 Psychological Statistics 33 3 Main Types of Mediation 1. Indirect effect: predicts no direct effect from X to Y. However, X has a direct effect on the mediator, and the mediator has a direct effect on Y. Thus, X is said to have an indirect effect on Y. x This hypothesis can only be supported if the direct effect of X to Y is insignificant before testing for indirect effects. 2. Partial mediation: predicts significant direct and indirect effects from X to Y. Thus, the unmediated relationship is significant as well as the X to the mediator and mediator to Y relationships. 3. Full mediation: predicts that the direct effect of X to x Y will be significant only if the mediator is absent. When the mediator is present, this direct effect becomes insignificant, while the indirect effect is significant. 9/30/2024 34 Testing for Mediation Baron and Kenny (1986) proposed a four step approach in which several regression analyses are conducted and significance of the coefficients is examined at each step. Take a look at the diagram below to follow the description (note that c' could also be called a direct effect). 9/30/2024 35 9/3/20XX Presentation Title 36 Example Does Control in predict Anger Expression? Does Control in predict Anger Out? Does Anger Out predict Anger Expression? Does Anger Out mediate the relationship between Control-In and Anger Expression? Predictor - Control-In Dependent Variable – Anger Expression Mediator – Anger Out 9/3/20XX Presentation Title 37 9/30/2024 38 9/3/20XX 39 9/3/20XX 40 Reporting Results Mediation analysis was performed to assess the mediating role of ____ on the relationship between ______ and _____. The results (see Table __) revealed that the total effect of ______ on ______ was significant (H1: ß = __, t = __, p < ___). With the inclusion of the mediating variable (_____), the impact of ____ on ____ was (still) found (in)significant (ß = __, t = __, p = ___). The indirect effect of _____ on ____ through _____ was found significant (ß = __, t = __, p < ___). This shows that the relationship between ____ and ____ is fully/partially/not mediated by _______. 9/3/20XX Presentation Title 41  Reporting Results Table 1. Mediation Analysis Total effect Direct effect Indirect effects of ___ on ___ (a*b) Coefficient p-value Coefficient p-value Coefficient SD t-values p-values CI H2: __->__->__ 9/3/20XX Presentation Title 42