Mediation Flashcards
what unique information do mediation and moderation give us?
Mediation and Moderation are extremely important statistical techniques that provide us with more useful and unique information about how 3 or more variables interact sequentially and ultimately, we gain a better understanding on how psychological phenomenon are related to one another.
Are having lots of raw correlations useful?
Having a multitude of raw zero-order correlations is not very useful. • When we are looking at studies with lots of variables, we obtain a large amount of correlations that are often too big to sort through. • Furthermore, finding significant correlations only tells us about the association about exactly two variables and does not allow us to see how variables interact sequentially. • I want to be able to discuss a string or sequence between three or more variables.
*we do not have sufficient information to write a report concluding the relationship between these three variables. All we have is bits and pieces of the puzzle with no evidence of causality or direction.
What statistical methods can be used to look at a two variable relationship?
Two variable relationships are easy:
(A) Two variables at a time i.e.
concurrent data
• T-test
• Raw (zero order) correlations
• Chi-square
(B) How do we examine the
relationship between three
or more variables at a
time?
• ANOVA with 2 or more IV’s
• MANOVA with 2 or more
DV’s
*do not allow us to link 3 variable in sequence
a. Path models (mediation)
b. Partial corelation
(moderation)
*are ways to look at the world
in a nuanced and
sophisticated way which is
required within a complex
world with complex
psychological phenomena.
does the order of the three variables in a mediation model matter?
• The order of variables matter! It’s a directional relationship so it is read left to right. • Mediation is about HOW the IV predicts the DV by identifying the mechanism (MV) through which the IV effects the DV. • You order the variables to make directional predictions about the associations. • The decision on how to order your variables is made based on your theoretical understanding on how the variables interact/covary. • There should ALWAYS be a reason for why you ordered your variables in the way you did.
how many predictor variables are in a mediation model?
> technically 2.
IV predicts DV and MedV
MedV predicts DV
the basic relationship in a mediation and moderation are….
the same. a two variable relationship between the IV-DV. Which we are lookig at a third variable’s (medv or modv) effect on this basic relationship.
meditation model is equivilant to a…
hypothesis, it tells us the mechanism through which th IV effects the DV i.e. indircetly through the medv.
what is the old school method for calaculating a mediation?
• The old school way is to perform two separate regressions and then combine the outputs to generate the mediation results-a tedious method.
E.g. Regression 1: IV-MedV
Regression 2: IV and
MedV predicts DV
what is the c and c’ pathways?
> the basic IV-DV relationship without the third variable is the c pathway (the total effect because it represents the total variance in the model and is what we partition out into a, b and c’ pathways).
the basic relationship with the thrid variable in the model is the c’ pathway
the strenght of the basic relationship is calculated using…
> a linear regression between the IV-DV. Thus, the strength of the total effect equivilant to the R2 (variance in the DV explained by the IV)
what is the a pathway and the b pathway?
> the indirect effect (a + b
pathway)
the a pathway is the IV predicting the mediator variable
the b pathway is the mediator variable predicting the DV
indirect effect is the IV predicting the mediator variabe, which in turn, predicts the DV.
c’ (the c prime) ‘ indicates
‘ symbol signifies a change or modification to something already defined.
the modified basic relationship which has already been defined as the c pathway
jamovi is an example of ___ modelling
• Is an example of “statistical equation modelling” which a powerful wat to examine relationships between variables. o SEM the analysis of multiple relations among multiple variables. o This is a huge advantage over more basic analysis like a linear/multiple regression where they are restricted to a single DV.
a mediation model has 2x __ and ___
> IV's and DV's > IV predicts the DV and the Mediator variable. > the mediator variable and DV are outcome variables.
difference between medmod and scatr
1. MedMod: can only have a
single IV, MV and DV.
2. Scatr: a little more powerful
type of mediation analysis
because you can have
multiple IV[s], MV[s] and
DV[s].restrictions of medmod
In medmod: - You can only have a single IV, MV, DV. - All variables need to be continuous - Variables cannot be nominal (categorical).
APA reporting of statistical significance:
(A) P-value less than .05
(B) Confidence Interval 95%
(alpha .05) or 99% (alpha
.01)
> if the upper and lower CI bounds include 0 than the findings is statistically non-significant. If bounds are both + or - then it will likley include 0 and be non-significant.
> CI 99% is more conservative- strictc’ is calculated by…
total effect (c-pathway) - a - b
do the a and b pathways need to be statistically significant?
Yes. Why? Because the mediation analysis is a x b. If non or one of them is insignificant than the indirect effect will be weak or insignificant. If both a and b are significant than the mediation a x b is likely to be statistically significant as well.
Jamovi mediation tells us about the strength of the indirect effect and direct effect by…
• Gives you the unstandardised coefficient and not the beta weight. • Thus, need to look at B and SE to interpret the size and direction of the association. • we can indirectly guess what the beta weight would be by looking at the b, SE and the p- value.
Jamovi output:
Mediation
(A) Path estimates box to
check if a and b pathwyas
are statistically significant
and their strength and
direction (+/-)
(B) Mediation Estimates box to
check the size of the
indirect effect and the
mediation % to see if the c'
is still significant and its
size relative to the indirect
effect.the indirect effect and direct effect can be
>
- or -
the indirect effect could be significant or non-significant
the basic relationship has to be significant but the direct effect can be significant or non-significant.
i.e. c significant and c’ signficant/non-significant
the indirect effects a and b pthways could be…
>
- or -
- and + = + indirect effect
- and - = - indirect effect
- and - = - indirect effect
Bootstrapping:
• Bootstrapping generates numerous samples based on the sample taken from the population. The associations are identified in these numerous bootstrap samples are then averaged (*bootstrap uses sample to generate 5000 bootstrap samples which are averaged and used for analysis) • Results are: o If numerous bootstrapped samples are generated (usually 5000), then the standard errors get smaller because the distribution becomes normal o Since SE gets smaller, the p- value gets smaller as well.
E.g. N=219 is a small sample size and would produce a lumpy distribution. Bootstrapping is a simple transformation technique which uses resampling to create a normal distribution. The new averaged bootstrap sample will become “periotic” sample i.e. narrow distance between -2SD and +2SD with a high peak.
Good for when you do not have the time or resources to uses a large sample. Bootstrapping allows us, to the best of our ability, to estimate the strength of the indirect effect. The smaller SE is the pay off, the reason why this technique is so important. Will have 5000 bootstrap samples with their own estimates of the strength of the indirect effect and then all 5000 of them are average to find the most accurate estimate (smaller SE and smaller p-value).
in a regressio analysis is conducted on __ samples
one sample of the population.
bootstrapping has a __ effect on the SE and p-value
small.
• The SE from the normal regression 0.062 with p- value .016 • The bootstrap SE was 0.058 with a p-value .012. • Notice the B (unstandardised estimate are the same i.e. strength and direction) but the variability around our estimate (like a SD) is smaller which leads to a smaller significance value found. o i.e. we are more confident that the “true value” is 0.148. • Notice that before bootstrapping both the B and p-value were significant. Bootstrapping, in this instance, did not turn a non- significant finding into a significant finding.
Confidence Intervals:
• Use a , not a –
• Why?
Because the point of a CI is to allow the reader to look at it and identify if the value 0 falls within the lower and upper bounds of the CI. If, it includes 0 then the finding is statistically insignificant. • Thus, using the – symbol is ambiguous, it can be read as a (-) symbol and can lead to people miss interoperating the significance of your finding. • The general rule is if + and – than it includes 0 and is non- significant.
Multiple Mediator Model
> 1x basic relationship IV-DV
2x indirect effects:
- a1 x b1
- a2 x b2
• We still have 1x direct effect
(c’)
• Thus, the total output has
three pathways
*cannot be done with a simple regression, it has to be done with a SEM (structural equation modelling) need to use GLM medmod and not the medmod analysis in Jamovi.
Key Difference between GLM Mediation Model and Medmod: • The GLM Mediation analysis allows you to place multiple mediator variables into the model. • The goal is to see if all or some of the mediator variables are statistically significant.
• A multiple mediator model is used to explicitly compare the strength of one mediator to another mediator. • Can include up to 5 mediator variables into the model. Any more than that and the model becomes too complicated.
Finding whether mediator variables are significant or non-significant is very important to know because this helps us identify targets for interventions i.e. traits to promote and traits to reduce the frequency of (adaptive vs. maladaptive).
Why are Multiple Mediator Models Great?
• The main strength is that mediator models can compare the strength and directions of the two or more indirect effects at the same time. • In our example, we learned that cognitive reappraisal mediated the relationship between PosTry and SubHap, whereas, ExpSup did not. • Both, Neither or One mediator can be found to be statistically significant!
*very good for prevention science; using higher level analytic techniques to inform social policies that can benefit society.
Categorical IV’s in a Mediation Model
*sex is a categorical IV which has been dichotomously coded into 0 and 1:
• Male = 0
• Female = 1
Important: a dichotomous categorical variable can only be used as an IV not as a MV or DV- this would lead to statistical problems for Jamovi.
Including a categorical variable is as an IV changes the mathematical analysis computed, the interpretation of the output that can be made i.e. we are now comparing one group to another (male and female).
Multiple Mediation model is unique because …
it allows for us to compare the strength and direction of two indirect effects. A multiple mediation model with a categorical IV is even more unique because it allows for us to compare two groups (i.e. males and females).
Example Categorical IV’s are…
(A) Religious or non-religious
(B) Tv or No TV
(C) Smoker or Non-Smoker
(D) High SES or Low SES
Experimental Mediation Analysis
Types of variables (constraints):
IV is a dichotomous categorical variable:
(A) Treatment
(B) Control
The Mediator Variable and Dependent Variable must be continuous.
with concurrnet data the order of variables in a mediation model are…
- concurrent data the ordering of variables is not fixed in a mediation model, continuous variables can be placed in any slot and categorical has to be the IV.
- Usually, the order of variables is determined based on theoretical research, how we predict the sequence to occur.
Experimental Mediation Analysis have the advantage of …
• Experimental Mediation Analysis have the advantage of allowing us to place variables in a particular order based on the IV: intervention or control, MV, DV: outcome variable.
• Longitudinal data: further allows us to place variables into their slots based on time i.e. the chronological order that the variables were measured in.
o Allows us to make more reliable conclusions about the temporal and causal relationship between our sequence of variables.
quasi-experimental mediation -pal longitudinal- write up:
“In our experimental mediation analysis we found that the PAL intervention predicted an increase in gratitude by the end of the 12 weeks of the intervention, which, in turn, predicted increased levels of subjective happiness six months later, B = 0.30, SE = .15, 95% CI = [.01, .59], p = .040. The indirect to total effect size ratio indicated that about 30% of the total effect between the intervention and subsequent happiness was explained by the indirect effect through increased gratitude. In sum, the effect of the PAL programme was a boost in gratitude in the immediate term, which, in turn, led to increased happiness six
months later.”
Can you have a Dichotomous DV?
In this example: • IV: Continuous (stress) • MV: Continuous (rumination) • DV: Categorical (smokers, non-smokers)
If the DV is Categorical (dichotomous) you have to compute two logistic regressions: • Stress to Cigarette Smoking (IV-DV) • Rumination to Cigarette Smoking (MV-DV)
Combining the a, b, c and c’ links are more difficult to do with a logistic regression but it is possible. Typically these are done in health psychology.
• Cannot compute two logistic
regressions in Jamovi but
can do it in R.
Summary of Mediation:
Summary of Mediation:
• Most Mediations use three categorical variables. • However, one can do a standard mediation with a dichotomous categorical IV. Mediations involving dichotomous categorical MV’s or DV’s require the use of logistical regression: they’re more difficult and requires translation of B’s and standard errors but it can be done. • The effect size tells us how much of the amount of variance in the DV goes through the mediator variable (as well as whether it is statistically significant). It could be statistically significant but the direct effect could be larger than the indirect effect. • Mediations in concurrent data provide ambiguous findings because variables can be placed in any slot. • Experimental designs are better because than can unambiguously place variables into particular slots.
