Mediators, Moderators COMBINED
Using the quiz dataset, explore how exercise moderates the association between body awareness and health. What proportion of variation in health does the interaction effect explain, above that of the main effects of exercise and body awareness? Report two decimal places. Remember a proportion is a number between 0 and 1, NOT a percentage
.13
Bootstrapping
As usual, it also turns out that the distribution of the Sobel statistic is very sensitive to normality of the residuals in the analysis - including both the bivariate analysis (X,Y) and the multivariate analysis (X,M,Y). So, as usual, a preferred approach may be to look at the bootstrap version of the Sobel test. Like bootstrapping in regression, the approach is to randomly subsample the sample of participants in your model, and to empirically derive the distribution of c - c' for each of the samples. If the 95% confidence limits for this empirical distribution don't span zero, we can be confident that it is not zero - at least with 95% confidence. if I simulated lots and lot and lots of observation like the one I've got here how often would that c-c' be greater than zero. 95% CI of the indirect effect
Now testing the mediation hypothesis -- JAMOVI N.B. This assumes that you have installed the module 'jAMM' - see Jamovi notes for mediation lecture.
Click on the module 'medmod' and choose 'GLM mediation model' • Move CPQnegco into the Dependent Variable box • Move anx_fr into the Covariates box • Move RAMattrib into the Mediators box • Initially, ensure that the 'Mediation options' asks for standard confidence intervals (not bootstrap) - this will give us our Sobel test
Step 3 - Run the Regression
Click: ANALYSE > REGRESSION > LINEAR Click Reading Comprehension (DV) into Dependent field, and the other newly created centred variables (EFF_CENT & MOT_CENT) into Independent(s). This creates a block with only main effects.
Step 2 - Create New Interaction Variable The next step is to compute the interaction term. This is a new variable representing the product of the IV and moderator (so representing the unique combination of IV and moderator that applies to the participant).
Click: TRANSFORM > COMPUTE NEW VARIABLE Come up with a name for the interaction term (in Target Variable), for instance "Eff_X_Motiv" The interaction is just the product of the two centered variables:
So actually we really need to know if the relationship between X and Y is significantly weaker after controlling for M. We are going to introduce 2 main ways of testing this:
1. Sobel test 2. Bootstrap test
How much variance is explained by the interaction, over and above what is explained by the main effects? Is this significant (cite the relevant statistic)?
3.6% It is significant F(1,116) = 6.94, p = .01
How much variance in reading comprehension can be explained just by the main effects of reading efficiency and motivation (without the interaction)? Is this significant (cite the relevant statistic)?
36.5% It is significant F(2, 117) = 33.66, p < .001
In total, how much variance do the main effects and interaction together explain? Is this significant (cite the relevant statistic)? R- square
40.1% It is significant F(3,116) = 25.90, p < .001
Sobel test
A significance test of mediation. It tests whether the relationship between a predictor variable and an outcome variable is significantly reduced when a mediator is included in the model. It tests the indirect effect of the predictor on the outcome Look at the Sobel test of the indirect effect - line 1 of the 'Indirect and Total Effects' table. What is the Sobel test telling you? The value of the indirect effect is significantly greater than zero.
example -- dichotomous IV and a continuous moderator
Imagine a scenario where we had two groups of participants - those who had consumed our drug, and those who had not. · Drug · No drug We want to know whether overall the drug increases sleepiness. But we also want to know whether the drug will interact with alcohol, so that with larger amounts of alcohol, the effect of the drug will be larger.
the difference between anova (experiemntal methods) and regression ( observational data )
In Experimental data (ANOVA) we manipulate to make things orthogonal (unrelated to each other) this makes for a much cleaner analysis. In regression, we always have this case where our variables are going to be correlated with each other (not always apparent why, hidden processes) ie; mediators, suppressor variables. this has an implication for how we do moderation. the implication is that this equation can become fairly difficult to solve if the relationships between our IV's are moderate in size. this is because the product of Ŷ = a + b1X1 + b2X2 + b3X1×X2 (interaction) is going to be highly correlated to bothŶ = a + b1X1 + b2X2 + b3X1×X2 (main effects). and the higher the correlation between X1 and X2 main effects the higher that product (b3X1×X2) is going to be correlated with them. problems with multicollinearity. But if you centre the variables around their mean the colinearity decreases. the collinearity between the product term dafuq (interaction) Ŷ = a + b1X1 + b2X2 + b3X1×X2 and the main effects Ŷ = a + b1X1 + b2X2 + b3X1×X2 is largely to do eith the off kilterness of the main effects so when centred this corrects. less problematic.
What is a mediator and what does it do?
In statistics, a mediation model seeks to identify and explain the mechanism or process that underlies an observed relationship between an independent variable and a dependent variable via the inclusion of a third hypothetical variable, known as a mediator
We want to ask an additional question: Does the relationship between reading efficiency and reading comprehension depend on the child's level of motivation? For instance, among children with higher motivation, is there a stronger relationship between reading efficiency and comprehension? Step 1: Centering the Predictor variables
In the lecture we used Z scores to center our variables. This time let's center them by simply subtracting the mean from each variable. First, find the means for your variables: ANALYZE > DESCRIPTIVES > DESCRIPTIVES Click OK, or 'paste' Note the means for your variables
A moderated theory
Is it the case that the relationship between X and Y changes at different levels of the moderator variable. when or to whom does x relate to y or under what circumstances does x relate to y. would it be true that x relates to y under some circumstances but not under others, or for some people but not other people. a ? is the variable that explains the conditions or the people under which there will be a relationship between x and y and how strong that relationship will be.
SOBEL TEST IN JAMOVI
MED MOD GLM mediation model covaritae = iV MODERATOR =M DV you can check if you unstandardised coefficient (direct effect of iv on dv) from spss matches jamovi by looking at at the mediation model in jamovi at direct an under estimate and the number should match coefficients table unstandardised for your iv. Look at indirect line. this will tell you if the indirect effect is significant. before (in spss) we could only hint at it. turn boostrapping on!
To Create centred scoresStep 1: Centering the Predictor variables
Note the means for your variablesTRANSFORM > COMPUTE NEW VARIABLE In the target variable field come up with a name for the new variable (one that denotes your centred variable), for instance "EFF_CENT" Click on the name of your predictor (Reading Efficiency) in the left-hand pane to click it into the formula box. Then simply type " - 66.5" to subtract the mean from all scores.
Based on these results, what would be the appropriate next step?
Simple slopes analysis should be conducted to examine the nature of the interaction
What kinds of variables can be used?
The IV's can be · Continuous (i.e., 'numbers') or · Dichotomous also know as a boolean (only having two levels) - if so they are assigned 'arbitrary' codes of 0 and 1 prior to analysis The DV must be continuous. If one of your IVs is multicategorical (i.e., represents several groups of people), you could create several dichotomous predictors to represent each category (dummy coding). That is complicated, however, so often better to employ an ANCOVA (we'll talk about that in a later week).
After doing more research, the research team then realized that they had their initial hypothesis wrong. What the literature stated was that attentiveness in tutorials would mediate the association between perceived usefulness of statistics and achievement. Using dataset Practice_Quiz2_401_Dataset.sav, test the four steps of Baron and Kenny mediation below, listing each as true or false:
The predictor predicts the outcome variable. A TRUE The predictor predicts the mediator. A TRUE The mediator predicts the outcome variable, with the predictor controlled for. A TRUE After controlling for the mediator, there is no longer a relationship between X and Y. B FALSE
In mediation we are testing whether controlling for a proposed mediator explains enough variance in X and Y to explain away their association with one another. In other words does the relationship between X and Y 'go away' when we control for M?
Three possibilities: 1. Yes - M completely accounts for the relationship between X and Y 2. No - M doesn't account for any of the relationship between X and Y Sort of.X and Y are still related after controlling for M, but less strongly
Regression Results Jamovi Bootstrap • Under Mediation Options tick Bootstrap (BC) • Wait a long time 😊 It will appear in the same place the Sobel test was previously. Particularly look at whether the 95% CI spans zero.
What is the bootstrap confidence interval for the indirect effect? I got CI = [.1628,3.6994] You would have gotten a different set of numbers, but that's fine. That's just how bootstrapping works. What is this telling you? With 95% confidence the value of the indirect effect is greater than zero.
Run a standard multiple regression with Couple negative communications as the DV, and the predictor (insecure attachment [anx fr]) and the mediator (RAM attributions) in 'Independent' window. You will need this to report the R2 and semipartial correlations for your model. You would also do diagnostics on this model in SPSS as per our previous workshop.
What is the overall R2 for the model? .401 Are insecure attachment and attributions both significant contributors to the model? Yes
Take a look at the simple slopes plot
What is this graph telling you? It is clear that there is a positive association between reading efficiency and comprehension (higher scores in efficiency related to higher comprehension) at each level of motivation - that is, all the lines have a positive slope. It is very clear, however, that the slope (i.e., the strength) of the relationship increases with higher motivation - this explains the interaction.
Imagine a researcher speculated as to the basis of this relationship, and conjectured that those with more secure attachment may engage in more adaptive coping, and this in turn leads to their improved outcomes in terms of well-being. How might you test this?
What we could do is use the property of collinearity that we have been discussing in regression so far... So for instance, we could run a regression with secure attachment (X) and wellbeing (Y), and control for adaptive coping (M). If secure attachment didn't predict wellbeing after controlling for adaptive coping, we would say the relationship was fully mediated. If it still predicts, but predicts less strongly we can say it is partially mediated (but we would need to establish that it is significantly less).
Researchers wished to explore how differences in exercise intensity would moderate the association between body awareness and overall health. Using the quiz dataset, test for a moderation effect. Results indicate that:
a. A moderation effect does not exist as the interaction effect is non-significant. b. A moderation effect exists as the interaction term is significant. c. A moderation effect exists as the interaction term is non-significant. d. A moderation effect does not exist as the interaction effect is significant.
What does a 95% bootstrapped CI for the indirect effect of X on Y, tell us about the presence of a mediated pathway? Choose the best response below.
a. If the interval does not include 0, there is significant partial mediation. b. If the interval does not include 0, there is a significant indirect effect. c. If the confidence interval includes 0 there is a significant indirect effect. d. If the confidence interval includes 0 there is significant full mediation.
Researchers were interested in the relationship between Facebook logins and Self Esteem. They predicted that an increase in login frequency would be associated with a decrease in self-esteem. They also predicted that this relationship would be stronger for older participants. To test this relationship what analysis should be performed:
a. Mediation; IV=Age, Mediator=Login Frequency, DV=Self Esteem b. Moderation; IV=Login Frequency, Moderator=Age, DV=Self Esteem c. Moderation; IV=Age, Moderator=Login Frequency, DV=Self Esteem d. Mediation; IV=Login Frequency, Mediator=Age, DV=Self Esteem
Researchers were interested in testing whether low intensity exercise produces positive outcomes in cardiovascular responses to stress, partially via changes in mindfulness levels. What analysis best fits this research hypothesis?
a. Mediation; IV=Exercise, Mediator=Mindfulness, DV=Cardiovascular Stress b. Moderation; IV=Exercise, Moderator=Cardiovascular Stress, DV= Mindfulness c.Mediation; IV=Exercise, Mediator=Cardiovascular Stress, DV= Mindfulness d. Moderation; IV=Exercise, Moderator=Mindfulness, DV=Cardiovascular Stress
Researchers hypothesized that attentiveness in tutorials would moderate the association between perceived usefulness of statistics and achievement. More specifically, it was hypothesized that the relationship between usefulness and achievement would be stronger as attentiveness increased. Using dataset Practice_Quiz2_401_Dataset.sav perform a moderation analysis to test this hypothesis. Results indicate that:
a.A moderation effect does not exist as the interaction effect is significant. b.A moderation effect exists as the interaction term is significant. c.A moderation effect does not exist as the interaction effect is non-significant. d.A moderation effect exists as the interaction term is non-significant.
Using dataset Practice_Quiz2_401_Dataset.sav, test the hypothesis that attentiveness in tutorials would mediate the association between perceived usefulness of statistics and achievement. What statement below best summarizes the analysis?
a.A partially mediated relationship is evident. b.Full and partial mediation is evident. c.No mediated relationship is evident. d.A fully mediated relationship is evident.
Researchers were interested in testing whether changes in body awareness would mediate the association between exercise intensity and cardiovascular stress. Using quiz dataset examine the Sobel test and bootstrap test of the indirect effect (BC method 1000 samples). Which of the following statements would best describe the results?
a.Both the Sobel and bootstrap tests indicate that the indirect effect is significantly different from zero. b.The Sobel test indicates that the indirect effect is not significantly different from zero, however the bootstrap test does not c.The bootstrap test indicates that the indirect effect is not significantly different from zero, however the Sobel test does not d. Neither the Sobel test nor the bootstrap test indicate that the indirect effect is significantly different from zero
Researchers were interested in exploring how depression and anxiety levels predict coping skills of natural disaster victims. More specifically, researchers were interested in the amount of variability in coping skills, that can be explained by depression and anxiety. What statistical analysis would most appropriate fit the researcher's needs?
a.Heirarchical Multiple Regression b.Moderation. c.Standard Multiple Regression. d.Mediation.
Ŷ = a + b1X1 + b2X2 + b3X1×X2
b1X1 = The main (overall) effect of alcohol on sleepiness b2X2=The main (overall) effect of the drug on sleepiness what additional information is there to get by knowing the combination of those two effects on that particular participant? b3X1×X2 test for significance. if the (product term? dafuq) is significant then it indicates that we know more from knowing the combination of the two variables than knowing the main effects alone.
why can we use categorical dichotomous (Boolean) variables in multiple regression?
because present or not present is a mathematical construct. present -1, not present =0 clever analysis 3 groups Jewish catholic Muslim (not dichotomous) create variables Jewish/ not Jewish 1 yes 0 no catholic/ not catholic 1 yes 0 no Muslim /not Muslim 1 yes 0 no 3rd question can be ignored as it is redundant. if we know the answers to the first two questions we can calculate the answer for the 3 rd question. this is called a dummy coding
if the two IVs (part squared) are taking up all the r2
both ivs uniquely explain all the variance the more leftover variance the stringer the chance of an indirect effect mediator
direct and
direct effect is c = x-y the relationship between the iv and dv c is the relationship before controlling for the mediator
jomovi with both iv and dv as continuous
general linear model dv in dv box this time both IV and the moderator will go in to the covariates box create interaction under model simple effects simple effects variable -IVdrug moderator - M alcohol plot IV drug -horizontal access M alcohol- SEPERATE LINES think of each line as not wether you've had a drug or not but as cumulative effect of how much of the drug you have had much the same as previous analysis but when you look at it continuously we are modelingthe continuous function or warped plane but instead of 3dimensions think of it as points alone a continuum of both drug and alcahol/
to create an APA plot
get the data upon which the jamovi plot is based by clicking estimated marginal means - include covariates generates table. copy table and past in to excel get rid of extra columns copy variables from excel into spss with (paste including variable names) graphs legacy dialogues line multiple define dv (sleepiness move to variable) click box other statistic mean. iv (drug yn) category axis m (alcohol) define lines by press ok will produce chart that can be made pretty change names colours text etc
mediation-
he how or why of a causal relationshitps
F-change in model summary tells you
if the two F's in the Anova output are significantly different from each other. in other words even if you were explaining a significant amount of the effect on the DV with just the main effects iV and M are you explaining significantly more of the effect on the dv by including the interaction on top of the main effects. if yes then report with interaction.
jamovi for moderated slopes- gamlj
import data to jamovi general liner model regression sleepy -dv drug y/n -factor alcohol- covariates model select both drug y/n and alcohol click arrow and select interaction. simple effects drugy/n - simple effects variable alcohol- moderator look at output simple effect slopes the effect of drugs on sleepiness separately for high on alcohol, vs medium or low on alcohol look in column estimate (this is the b unstandardised) positive number positive effect higher number higher effect sig y or n. plot drug -horizontal access alcohol- separate lines don't read too much into it because SD is arbitrary however is important to remember is that overall message lower alcohol less sleepy higher alcohol more sleepy
jamovi continous IV dichotomous Moderater
import data to jamovi general linear model dv in dv box dichotomous moderator will go in to the factor box IV in to covariates box create interaction under model with dichotomous M (alcohol Y/N) and continuous IV (drug) simple effects simple effects variable -IVdrug moderator - M alcohol y/n plot IV drug -horizontal access M alcohol y/n - SEPERATE LINES think of each line as not wether you've had a drug or not but as cumulative effect of how much of the drug you have had much the same as previous analysis but when you look at it continuously we are modelingthe continuous function or warped plane but instead of 3dimensions think of it as points alone a continuum of both drug and alcahol/ major difference only two lines. one represents people who had alcohol and the other is people who didnt its much the same as performing two separate regresin two separate groups. lines represent the effect of drugs on sleepiness in individuals that had no alcahol and the effect of drugs on sleepiness in individuals that had alcahol simple effects to determine amount of sleepiness and significance p value is more meaningful in this analysis as definitive meaningful question
step 1) the total effect between x and y (c)
is just the relationship at the bivariate level of X (iv) and Y (dv) before controlling for m
Simple slopes in Jamovi N.B. This assumes that you have installed the module 'gamlj - see Jamovi notes for moderation lecture. Click the "Linear Models" button and chose 'General Linear Model
o Move the DV (Reading Comprehension) into the Dependent Variable field o Move the predictor (Reading Efficiency) and the moderator (Motivation to Read) into the Predictor field o Click 'Model' and select both variables - then choose the second arrow button and click Interaction o Click 'Plots' and put 'Read_Eff' on the Horizontal and 'Motiv' as separate lines Click 'Simple Effects' and add 'Read_Eff' as the simple effects variable and 'Motiv' as moderator
f test for model including main effects and either interaction or no interaction tells you
overall do the main effects combined with the interaction (or without) explain a significant amount of variance in the DV?
R squared
proportion of variance in the DV explained by main effects alone no interaction
r squared change
represents the amount of additional variance you can capture with the interaction. It will also be equal to the squared semi partial for the interaction.
Sobel test
sobel demonstarted that you could take that distribution and look at c - c' in a completely random population and it kind of approaches a chi-square distribution. The problem of how to establish partial mediation amounts to this: If the relationship between the IV and the DV reduces after controlling for the mediator, does it reduce significantly? i.e., more than any random coefficient would reduce just by virtue of having more coefficients in the model. In other words, is the pathway between IV and DV after controlling for the mediator (c') significantly different to the pathway between IV and DV before controlling for the mediator (c). Sobel proposed a test distributed on a chi-square distribution for the quantity c-c'. So the test is whether the drop in beta is significantly greater than zero. There is some controversy about whether the p values genuinely represent the chances of the null hypothesis in the population. is it true or not? try a bootstrap
the relationship between the iv and the dv will always go doen when another variable is added so how much does that relationship need to go down in order for it to be consiodered mediated or partially mediated.
sobel test could you test the difference between c & c' ... to see if it is significantly different from zero the null hypothesis; the difference between c and c' is due to random chance the alternative hypothesis is that there is a significant real difference between c and c'
The statistical technique for exploring how a set of independent variables predict a dependent variable. The statistical technique for exploring the interaction effect of two scale independent variables, on a dependent variable. The statistical technique for exploring how an independent variable relates to a dependent variable, through another variable. The test statistic for assessing significance of an individual predictor of a mediation model. The test statistic for assessing significance of an individual predictor of a moderation model.
t-statistic B. Moderated Multiple Regression C. Multiple Regression D. Mediated Multiple Regression
What is dummy coding?
taking something categorical and turning it in to a quantity for the purpose of analysis (must be dichotomous)
model 2
test the significance of the interaction
mpderation in spss block 2 in coefficients is the interaction t-test. if the interaction is significant it means?
that yes you can get a significantly larger amount of information when you consider the interaction between the iv and the m the interaction has significantly improved the model and you are modelling your data better by incorporating the interaction.
indirect effect
the indirect effect is x-m-y (the product of a and b) the indirect effect can also be thought of as c-c' whatever has reduced in the relationship between the iv and the dv c-c' is the indirect effect of the mediator
step 2) the relationship between the IV & the mediator (a)
the iv should predict the n=mediator at a bivariate level
step 3) there should be a relationship between the IV x and the Mediator m (b)
the mediator should significantly predict the dv at a bivariate level or even the mulltivariate level wit x in the equation as long as its a predictor
if the 95% confidence interval does not span zero?
then you can be 95% confident that the difference between c and c' has dropped significantly
effect size of IV is dropping in the presence of the mediator
this is a hint that the variablels ARE INTERTACTING IN A WAY THAT IS MORE COMPLICATED THAN A STANDARD REGRESSION. LOOK AT BIVARIATE CORRELATIONS. if everything is interrelated there may be some other effects at play. take R2 for total model and subtract the two SEMI PARTIAL correlation 2 FOR YOUR MODEL. if there is leftover then there may be a background indirect effect
model 1
to test the significance of the main effect of the two IVs
how to compute interaction term
transform compute variable (this will be the product of the centred scores of the IV and M) under target variable type int (interaction) move zscoreIV (times) * and move zscoreM to b=numeric expression box ok
moderation-
when or under what condition an effect occurs.
in the 95% confidence interval if it does span zero then?
you can not be 95% confident that difference between c and c prime is not zero.
if the effect size of the IV drops in the presence of the mediator
you could run in a hierarchical sense, start running the analysis with just the iv and the dv then run again this time with the moderator
how to report effects of moderator
you need to choose a high medium and low level of the moderator, conventionally people use mean -medium high- plus one SD low-minus one SD (you can do 2 SD or 3SD) its fairly arbitrary. not critical info-need sig testing also. we need to look at simple slopes.
We can ask the same questions in regression. In a regression with 2 IVs (X1 and X2):
· Is there an overall relationship between X1 and Y (e.g., higher scores on X1 associated with higher scores on Y) - main effect of X1 · Is there an overall relationship between X2 and Y (e.g., higher scores on X2 associated with higher scores on Y) - main effect of X2
Centering
· One (easily surmountable) issue in computing the coefficients in the interactive model is that the main effects of X1 and X2 are highly linearly related to the product of X1 and X2 (the interaction). This can lead to multicollinearity in the regression coefficients. · It is easily solved because it turns out that the interaction will be relatively independent of the main effects provided the variables are numerically centered around their mean. · A simple way to center a variable around its mean is to convert to Z scores.
Interactions Recall that the interaction between two variables A and B (denoted AxB interaction), represented the question of · whether the effect of A was different at different levels of B, or alternatively · whether the effect of B was different at different levels of A
· Suppose you receive a prescription from your doctor for a new medication, and the label on the medication states "This drug may interact with alcohol". · You might assume that the effect of the drug will be different if you consume alcohol than if you don't. Suppose for instance that the drug might have the effect of making you feel sleepy, potentially this effect might be greater if you also consume alcohol
In a design with two predictor variables, it may not always be obvious which is the independent variable, and which is the moderator. · In this case it may be helpful to ask - what are you most interested in?
· The thing which you are most interested in can be considered the independent variable · So, for instance in the example of the effect of a drug (say in terms of whether the drug impairs your concentration) depending on whether you have consumed alcohol, the independent variable is the drug - it is the way in which this variable affects the DV which is interesting. · Whether or not you have consumed alcohol is the moderator - the effect of alcohol on concentration is not of interest, it is whether or not the presence of alcohol changes the effect of the drug on concentration. In some designs it may be less obvious which variable is the moderator and which is the independent variable, but in many cases the distinction is useful, and helps to guide how we analyse the results.
When X1 and X2 are purely additive, our simple linear equation we have used until now holds fine:
Ŷ = a + b1X1 + b2X2 In an additive linear equation.It describes a flat plane in 3 dimensions.
Moderated multiple regression is the extension of what we learned in factorial ANOVA (in undergrad) to what we now know about regression. Specifically: Now that we know how to find the unique effect of each variable (analogous to a main effect in ANOVA) Can we also incorporate in interaction term o Represents whether the effect of one variable (we'll just call it our IV) differs according to the level of the other variable (we'll call it a moderator) It means adding a third term to the regression equation.
Ŷ = a + b1X1 + b2X2 + b3(X1×X2)
To model an interaction we want to consider the idea that the regression surface is not a flat plane - it is warped. That is, a situation where at, say high levels of X2 there would be a strong relationship between X1 and Y, whereas perhaps at low levels of X2 there might be a weak (or opposite) relationship. The formula for an interaction like this involves a multiplicative term in the regression equation
Ŷ = a + b1X1 + b2X2 + b3X1×X2 Think of the first two bs as representing the individual contributions of each variable, and the third one as representing the combination of the two X's. As in ANOVA, it is helpful to conceive of one variable as the focal variable (or IV) and the other as the moderator.
R2 change is commonly reported for the effect size of the interaction
(this will actually be the same quantity as the squared semi-partial correlation for the interaction, so you could also report that)
R Square Change
F-test of the interaction. null hypothesis is that the interaction explains no additional variance
fill in the numbers we have done so far; Remember there are 4 conditions of mediation according to Baron & Kenny (1986). Have we met them?
1. The predictor predicts the outcome variable (model 1) Yes 2. The predictor predicts the mediator (model 2) Yes 3. The mediator predicts the outcome variable, with the predictor taken into account / controlled for (model 3) Yes 1. After controlling for the mediator there is no longer a relationship between X and Y No.The relationship is weakened, but it is still a sizeable relationship
The steps of the Baron and Kenny approach are:
1. There should first be a significant relationship between the IV and the DV (marked c in the diagram) 2. There should be a significant relationship between the IV and the mediatior (a) 3. There should be a significant relationship between the mediator and the DV (b) 4. After controlling for the mediator, the IV should no longer predict the DV (marked c' on the diagram) Referring to the diagram above, Baron and Kenny refer to c as the total effect of X on Y, c' as the direct effect of X on Y, and the quantity c-c' as the indirect effect. The idea is that after controlling for the indirect effect (X M Y) there should no longer be any direct association between (X Y).
sample mediation write up
A mediated multiple regression was conducted examining whether negative attributions would significantly[PL1] mediate the association between insecure attachment and negative couple communication. A path model describing the predicted associations is shown in Figure 1. Table 1 shows the bivariate correlations among the variables used. [PL1] I haven't repeated the diagnostics here because I covered this in the last example. But you would need to do the full diagnostics on this analysis also. Figure 1. Path model representing theoretical variables in the model, and observed values Table 1. Bivariate correlations between variables. Insecure attachment RAM attributions Couple neg communic 0.46** 0.58** Insecure attachment 0.38** RAM attributions * p < .05, **p < .001 To examine the component parts of the model, as per convention, we first examined the bivariate association between the independent variable (insecure attachment) and dependent variable (negative communication) - denoted c on the model diagram above. There was a significant bivariate association, b = 1.36, p < .001. Overall more insecure attachment is associated with more negative couple communication. We then examined the bivariate association between the independent variable (insecure attachment) and mediator (negative attributions), denoted a in the model above. This bivariate association was also significant, b = 1.54, p = .003. Overall more insecure attachement is associated with more negative attributions. In a multivariate model including both insecure attachment and negative attributions predicting negative communication, negative attributions was a significant predictor of negative communications after controlling for insecure attachment, b = .338, p < .001 (denoted b in the model).More negative attributions were associated with more negative couple communications, uniquely explaining 18.75% of the variance in couple communication.Insecure attachment was still a significant predictor of negative communication even after controlling for negative attributions, b = .836, p = .014 (denoted c' in the model). More insecure attachment was associated with more negative couple communication, uniquely explaining 6.9% of the variance in couple communication. The multivariate model is highly significant, F(2,58) = 18.72, p < .001, explaining 40% of the variance in couple negative communication (adjusted R2 = .38). Although the association between insecure attachment and negative communication is reduced after controlling for attribution (from c =1.36 to c' = .836), it does not drop to zero and remains significant in the model. Therefore attribution does not fully mediate the association. To test whether there was a significant partial mediation taking place, we conducted both a Sobel and a bootstrap test of the indirect effect insecure attachment -> attributions -> negative communication. Both the Sobel test (Z = 2.54, p = .011) and the bootstap 95% CI = [.16, 3.7], indicated that the indirect effect was significantly greater than zero. Therefore the relationship between insecure attachment and negative communication does reduce significantly after controlling for attribution, indicating partial mediation in this instance.
A mediated theory
A mediated theory is when you have a definite IV that you think is definitely a causal agent in your theory and you want to know if some intervening variable correlated with your iv and DV explains away some of the relationships between your iv and DV. You are basically wanting to know; when you add this part into your equation Ŷ = a + b1X1 + b2X2 does variable Ŷ = a + b1X1 + b2X2 become trivial, non-significant or less interesting having controlled for x2 the ? kind of explains how or why the IV affects the DV. why is it that X causes Y is it because of M
interpret output dichotomous IV continuous M moderator centred z scored iv and m calculated interaction hierarchical wit 2 models
Block 1 in coefficients represents the main effects does iv impact dv look at t test sig (yes) does M impact DV look at t test sig (yes) once you know the result of the two main effects can you get a significantly larger amount of information by also knowing the combination of the IV with the M block 2 in coefficients is the interaction t-test. if the interaction is significant it means? that yes you can get a significantly larger amount of information when you consider the interaction between the iv and the m the interaction has significantly improved the model and you are modelling your data better by incorporating the interaction. report r square for block one found in model summary and the r square for block 2 and the r square change in block 2. r square change- the amount the r square is increasing having introduced the interaction into the model. it will also be equal to the squared semi partial for the interaction ANOVA BOX F tests. f test for the model with just main effects this tells you overall do the main effects combined explain a significant amount of variance in the DV and f test for model including main effects and interaction this tells you overall do the main effects combined with the interaction explain a significant amount of variance in the DV F-change in model summary tells you if the two F's in the Anova output are significantly different from each other.
Step 3 - Run the Regression Select these options in 'Statistics' to get the R2 change statistics
Can you understand the output? Try labelling the bits circled here.....
ANOVA table significance test
F test of main effects model
Using dataset Practice_Quiz2_401_Dataset.sav, test the hypothesis that attentiveness in tutorials would mediate the association between perceived usefulness of statistics and achievement. What is the unstandardized indirect effect of perceived usefulness of statistics on achievement? Report two decimal places.
I used estimate in the mediation indirect and direct effect box. 0.41
plots where to put what!!!!
IV on X axis DV on Y axis moderator should be the legend variable ( seperate lines
Simple slopes Once you know that the effect of one variable depends on the effect of the other variable, the next question of interest is - · what is the effect of X1 (the independent variable) at higher levels of the moderator, and · what is the effect of X1 at lower levels of the moderator for instance · what is the effect of my drug on people's sleepiness when they have consumed small amounts of alcohol, and · what is the effect of my drug on people's sleepiness when they have consumed large amounts of alcohol
Modelling the relationship between the IV and the DV at higher as well as lower levels of the moderator, allows you to describe the interaction. in anova the aim of the simple effects was to exokain the interaction- we have an interaction between variables ie; alcohol and drug- whats the effect of the drug when you have had alcohol and what s the effect of the drug when you haven't had alcohol and is that effect significant? same in multiple regression except its called simple slopes- which solves a local regression equation between the iv and dv at a nominally high level of the moderator variable and a nominally low level if the moderator variable. from these mini regressions, we can see how the relationship between the IV and the DV changes at different levels of the moderator
Mediation doesn't test causation!
The only way to tell if something is really causally related is to manipulate something in an experiment. Mediation just tests whether a proposed mediator 'explains' (i.e., accounts for) the variance shared between some X and Y variables.
Write a sentence about each simple slope. What do they mean?
There is a significant positive relationship between reading efficiency and comprehension at high levels of motivation. Among those high in motivation, higher scores on reading efficiency predict higher scores on comprehension. Among those with an average level of motivation, again, those with higher reading efficiency tended to score higher on comprehension. For participants with low levels of motivation, similarly, better reading efficiency predicted better comprehension. For a participant at 1 SD above the mean on motivation, a 1 unit increase in efficiency would lead to a .442 unit increase in reading comprehension (SE = .0768[PL1] ). [PL1] Note: I've written each of these a different way - there are millions of other ways I could have phrased this and they are not necessarily wrong, these are just my words. The important thing is what you are trying to say, not the words themselves. Also just remember that there is one way of phrasing things which is completely forbidden, and that is copying someone else's words (Plagiarism - very dangerous!)
step 4) both m and x predict y
There should be a smaller almost negligible association between x and y. If that were the case then we would say that m has explained away the relationship between x and y (c') c prime.
sample moderation write up
To investigate whether the relationship between reading efficiency and reading comprehension depends[PL1] on a child's level of motivation, a moderated multiple regression analysis was conducted. Prior to analysis, scores on reading efficiency and motivation were mean-centered, and a product term representing the interaction between them was computed based on the mean-centered data. This was done to reduce potential multi-collinearity between the predictors in the moderated model. Table 1 below shows the bivariate correlations among the variables. [PL1] Again I have left out all the diagnostics here since we have covered this. But all of it would need to be done and reported here as well... Table 1. Bivariate correlations between variables. Reading efficiency Motivation Reading comprehension 0.54** 0.45** Reading efficiency 0.37** Motivation * p < .05, **p < .001 The model was tested using a hierarchical method, with the main effects of the two predictors (mean-centered) entered at step 1, and the interaction term alone entered at step 2. In Step 1, with the main effects of the two predictors in the equation, the model was able to explain 36.5% of the variance in reading comprehension (adjusted R2 = .354, F(2, 119) = 33.66, p <.001). In the main effects model, higher scores on reading efficiency are associated with higher scores on reading comprehension (b = .317, p < .001), uniquely explaining 16.57% of the variance in reading comprehension scores. Higher scores on motivation were also associated with higher scores on reading comprehension (b = .294, p < .001), uniquely explaining 6.9% of the variance in reading comprehension in the main effects model. In Step 2, with the main effects and interaction entered simultaneously, the model was able to explain 40% of the variance in reading comprehension (adjusted R2 =.386, F(3, 119) = 25.9, p < .001). Thus the model including the interaction is able to explain 3.6% more variance that with the main effects alone (Fchang[PL1] e(1,116) = 6.94, p = .01). [PL1] Or you can call this FΔ. I prefer to always use English words if I can... A simple slopes analysis was conducted to follow up the significant interaction. Simple slopes were computed at the mean, and at ± 1 SD away from the mean (see Figure 1). The analysis showed that at high (+1SD) levels of motivation, there is a strong and significant relationship between reading efficiency and reading comprehension (b = .44, p < .001), while at mean levels of motivation there was a reduced (albeit still significant) association between reading efficiency and reading comprehension (b = .322, p < .001). At low (+1SD) levels of motivation there is still a significant association between reading efficiency and reading comprehension, however it is far weaker (b = .203, p = .005). Thus the nature of the interaction in this data is that the strength of the relationship between reading efficiency and reading comprehension becomes weaker with reduced motivation[PL1] . [PL1] Or becomes stronger with increased motivation - it's the same thing 😊 Figure 1. Simple slopes showing the relationship between reading efficiency and reading comprehension at high (+1SD), medium (Mean), and low (-1SD) levels of motivation in this sample.
mediation and moderation
are theory driven and require testing.
jamovi mediator modeling
add x, y and m on mediator options click individual regressions in the out put regression results =c iv-dv mediator model =a iv-m full model =b m-dv (controlling for the iv in the same model) full model 2nd line =c' what is the relationship between the iv and the dv after you've controlled for the mediator. Baron and Kenny steps 1-3 were met (significant correlations) step 4 is not meant to be correlated or significant but in this example, it is (is there still a significant relationship after controlling for the mediator.) YES the estimate was x and the beta was .482 in the first line (regression equation) iv-dv in the last line, they were still correlated but the beta had decreased .382 so is this a partial correlation? look at the sobel test up higher under mediation- indirect and total effects. look at the first line under z .299 p=.003 so according to the sobel test it has gone down a significant amount for a robust analysis its time to bootstrap go to confidence intervals column and change from standard to bootstrap bc. look under mediation-indirect and total effects. report confidence inetrevals in the first line thee drop in the regression coefficient between iv-dv it has dropped by somewhere between .0706-.276 so we can be 95% confident that the drop in the regression coefficient is significantly greater than zero (because the above numbers do not span zero) in this instance, we can conclude that although there is still a significant relationship between attachment and well being, after you control for coping, that relationship has been significantly mediated by coping this only relevant if the arrows cant point back the other way!
how to centre in spss
analyse descriptives descriptives move iv and m to variables box tick save standardised values as variables (which wil give z scores) press ok. you can see the two z score columns now in the data view
hierarchical regression (must have a good reason to do so) in this case we are trying to answer if we should include the interaction in the equation if the interaction is non significant. in this case there will be a contingency plan model 1; contains main effects only in case interaction is non sig model 2; contains main effects and interaction in case int is sig this is about telling the most honest story about your data. if the interaction is not significant you shouldn't be incorporating it in the analysis.
analyse regression linear DV -into dependents z score IV and z score M -into independents click next DV -into dependents interaction -independent box statistics tick r squared change part and partial (descriptives and colinearity are useful also)
