Module 2 Flashcards
What is correlation?
Correlation is when a change in one variable is associated with change in another variable
What is multiple regression?
Multiple regression is 2 or more independent variables that are being utilised to predict the value of the dependent variable
What type of questions do moderation analyses attempt to answer?
What/when questions
eg: “under what circumstances?”, “for what type of people?”, “when does the effect occur?”
What type of questions do mediation analyses attempt to answer?
How/why questions
eg: “How does X influence Y”, “Why does X influence Y?”
5
Provide 3 examples of moderation questions.
“Is the relationship between attitude towards university and where a student sits influenced by the age of the student?” - age is an inherent aspect of the individual
“Does playing violent video games for more than 6 hours a week make people more aggressive?” - 6 hours a week is a circumstance
“If employee satisfaction is high, is job turnover reduced for both male and female employees?”
Provide 3 examples of mediation questions.
“Is the relationship between attitude to university and where students sit explained by IQ?”
“Does playing violent video games that involve realistic interpersonal violence make people more aggressive?”
“If employee satisfaction is high amongst workers with high autonomy, is job turnover reduced?”
Define moderation
Moderation looks at how a third variable can change the relationship between a predictor variable (IV) and an outcome variable (DV) based on the interaction between the IV and the moderator
its like a multiple regression with 3 independent variables: the original predictor variable, the moderator, and the interaction
Why do we need to centre variables?
To avoid multicollinearity
(Multicollinearity refers to a situation in which more than two explanatory variables in a multiple regression model are highly linearly related. We have perfect multicollinearity if, for example as in the equation above, the correlation between two independent variables is equal to 1 or −1.)
What should we do after we find we have a significant interaction (moderation) effect?
Perform a simple slopes analysis to find exactly where the interaction is occurring
What is the role of a mediator variable?
A mediator variable explains part or all of the relationship between two variables.
Size is measured using R2 of the direct pathway compared to R2 of the direct effect when M is included.
In mediation, what are the 2 antecedent variables? What are the 2 consequent variables?
Antecedent = X and M Consequent = M and Y
Distinguish between direct effect, total effect, direct pathway and indirect pathway
Direct effect = c’ (X > M > Y)
Total effect = c (X > Y)
Direct pathway = X > Y
Indirect pathway = X > M > Y
How will c relate to c’ if partial mediation has occurred? How will they relate if perfect mediation has occurred?
Partial mediation - c’ will be smaller than c
Perfect mediation - c’ = 0
What are the 4 requirements to that need to be fulfilled to confirm mediation has occurred? Which of them is still debated? Why?
1) There is a significant relationship between X and Y
2) There is a significant relationship between X and M
3) M still predicts Y after controlling for X
4) The strength of the relationship between X and Y is reduced when M is in the equation
1) is still debated because alone it represents a correlation and in the same way that correlation doesn’t equal causation, lack of correlation doesn’t mean there is no causation. Thus, it shouldn’t be necessary for there to be a relationship between X and Y
According to Dr Levesque what types of questions are moderation and mediation useful for?
Moderation: Useful for When Questions
Under what conditions does X influence Y?
Explores the boundary conditions of associations
Mediation: Useful for How/Why Questions
How does X influence Y?
Explores causal factors and mechanisms of associations
What is a simple slopes analysis?
Simple Slopes Analysis provides information about the interaction effect in a moderation analysis
Creates 3 regression lines for X - Y at low, mean, and high M values
Parallel = no interaction
If high M sharper slope than low M = M increases effect of X on Y
In SPSS: Select conditioning -1SD, Mean, 1SD
Results found under “Conditional Effects of X on Y” section of output
if theres a moderation relationship then it actually doesnt tell us about the interaction effect. so we do a simple slopes analysis or a johnson method to examine the relationship between a predictor variable and an outcome variable at low, mean, and high values of a third variable
parallel lines = no interaction and moderation
What is the difference between direct, total and indirect effects in a mediation analysis?
Total Effect: Simple relationship between X and Y without M included in model
Represented by c
Direct Effect of X on Y: Effect of X on Y when M is included in model
Represented by c’
Indirect Effect of X on Y: Effect of X on Y via M
Product of a and b pathways
Product will be positive if a and b have same sign (even if both negative)
Significance tested using confidence interval (if includes 0 not significant)
How do you run a moderation analysis in SPSS?
Analysis -> Regression -> Process by Hayes
Model 1 = Moderation
Outcome = Y variable, Predictor = X variable, Moderator = Moderator W
Select HC3 (Davidson MacKinnon) for Heteroscadescity
Tick Generate Code, Mean Center
Select -1SD, Mean, 1SD for Conditioning and tick Johnson Neyman
Interpreting Output
INT_1 = Interaction term - if this is significant then there is a moderation effect
Check whether confidence intervals include 0
Check Simple Slopes under Conditional effects
How do you run a Mediation analysis through SPSS?
Analyse -> Regression -> Process by Hayes
Model 4 - mediation
Outcome = Y variable, Predictor = X, Mediator = mediator
Tick Effect size, Pairwise, and Total Model
Interpreting the output - is the indirect effect significant?
1st model shows effect of predictor on mediator
2nd model shows combined effect of predictor and mediator on outcome
Under Total, Direct and Indirect effects
Check indirect effect of X on Y -> if the BOOT confidence intervals do not include 0 it is significant
How can you check for normality and missing data?
Analyse -> Descriptives -> Frequencies
Will show you any missing data, range and sample size
Analyse -> Descriptives -> Explore
Check Skewness and Kurtosis values
Close to 0 values indicate normality, positive = leptokurtic, +skew
Check Graphs of Normality
Finally check the Shapiro Wilk (significant value = not normal)
Make a educated judgement
How do you check for outliers?
Run a linear regression
Select Statistics, casewise diagnostics, MAH and Cook Distances
Z-scores; Check for any z-score > 3SD
Univariate: Check Casewise Diagnostics
If the table doesn’t appear there are no univariate outliers that need to be worried about
Multivariate: Check Mah and Cook values against critical
Mah < 13 is good for 2 IVs (indicates no major outliers)
Cook < 1 indicates no one response is too influential
How do you check for linearity, homoscedasticity, independence and multicollinearity?
Run regression - select Dyan Watson, Collinearity, Zpre-Zresid plot, Normality PLot
Zpred-Zresid Plot: assesses linearity and homescedascity
look for a random distribution
Durbin Watson; assesses independence of errors
Value between 1-3 is good. Closer to 2 the better.
Multicollinearity
Tolerance > 1 and VIF < 10 indicates no multicollinearity
Double check by verifying the correlations
Moderation model vs mediation model
MODERATION
the influence that x exerts on y is influenced of dependent on the variable M
moderating variable is also an IV
MEDIATION
X is thought to explain Y through M
M could be predictive of Y?
nor should we assume that because theres no arrow from M to Y that M doesnt predict Y. it may be that M is a significant predictor of Y and they are signficantly correlated
What do you have to do to continuous independent variables?
You have to centre continuous independent variables which will allow us to create an interaction term.
variables are centred using the SD score - mean
we do this to avoid multicollinearity where the independent variables are highly correlated
multicollinerity is a potential issue because youre using the original score already in the moderation analysis
if we use the original scores we increase the chance that multicollineratiy will be a problem
Assumption of mediation: Causality
would only recommend using causality when you are CERTAIN of a relationship and have undertaken something like a random control trial
but in mediation it is assumed that the relationships in the model are causal
- M is causally located between X and Y
- that X causes M in turn causes Y
mediators need a clear theoretical basis
mediator variable need to be amendable to change
e.g. age dont make great mediators becausre whatever teh x variable is, its unlikely to cause age but age would make a good moderator
so often you will see mediators as cognitive processes or mediators proposed
e.g. is the relationship between bullying and anxiety mediated by a childs relationship with other peers
What does Hayes say about mediation and why is it controversial?
Hayes says researchers can test causation with no experimental manipuation and in such a situation, sometimes a theory or solid argument are the only foundation upon which a causal claim can be built
Klein says mediation is a myth
nature of the data in mediation
- usually continuous
- continuous or categorical independent variable
- continuous mediator variable
- continuous outcome variable
sample size
- various ways to calculate nad one isnt more correct than an other but the key is to consider the options and justify with theory
Tabachnick and Fiddell 2014 propose an appropriate sample size as 50 + 8 per IV
Stevens 2004 uses 15 per IV
common sample size issues:
- a skewed DV
- when you need to expect a small effect size
- when theres a possibility of measurement error (measurements with unreliability)
so sample size needs to be larger if this is the case
statistical assumptions of mediation
- normality
- outliers (univariate and multivariate)
- multicollineraity and singularity
- linearity
- homoscedascity of residuals
- independence of errors
