Mediation

Question 1

what unique information do mediation and moderation give us?

Answer 1

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.

Question 2

Are having lots of raw correlations useful?

Answer 2

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.

Question 3

What statistical methods can be used to look at a two variable relationship?

Answer 3

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.

Question 4

does the order of the three variables in a mediation model matter?

Answer 4

•	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.

Question 5

how many predictor variables are in a mediation model?

Answer 5

> technically 2.
IV predicts DV and MedV
MedV predicts DV

Question 6

the basic relationship in a mediation and moderation are….

Answer 6

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.

Question 7

meditation model is equivilant to a…

Answer 7

hypothesis, it tells us the mechanism through which th IV effects the DV i.e. indircetly through the medv.

Question 8

what is the old school method for calaculating a mediation?

Answer 8

• 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

Question 9

what is the c and c’ pathways?

Answer 9

> 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

Question 10

the strenght of the basic relationship is calculated using…

Answer 10

> 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)

Question 11

what is the a pathway and the b pathway?

Answer 11

> 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.

Question 12

c’ (the c prime) ‘ indicates

Answer 12

‘ symbol signifies a change or modification to something already defined.

the modified basic relationship which has already been defined as the c pathway

Question 13

jamovi is an example of ___ modelling

Answer 13

• 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.

Question 14

a mediation model has 2x __ and ___

Answer 14

> IV's and DV's
> IV predicts the DV and the 
   Mediator variable.
> the mediator variable and 
   DV are outcome variables.

Question 15

difference between medmod and scatr

Answer 15

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].

Question 16

restrictions of medmod

Answer 16

In medmod:
- You can only have a single 
   IV, MV, DV.
- All variables need to be 
  continuous
- Variables cannot be nominal 
  (categorical).

Question 17

APA reporting of statistical significance:

Answer 17

(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- strict

Question 18

c’ is calculated by…

Answer 18

total effect (c-pathway) - a - b

Question 19

do the a and b pathways need to be statistically significant?

Answer 19

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.

Question 20

Jamovi mediation tells us about the strength of the indirect effect and direct effect by…

Answer 20

• 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.

Question 21

Jamovi output:

Mediation

Answer 21

(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.

Question 22

the indirect effect and direct effect can be

Answer 22

>

• 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

Question 23

the indirect effects a and b pthways could be…

Answer 23

>

• or -
• and + = + indirect effect
• and - = - indirect effect
• and - = - indirect effect

Question 24

Bootstrapping:

Answer 24

• 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).

Question 25

in a regressio analysis is conducted on __ samples

Answer 25

one sample of the population.

Question 26

bootstrapping has a __ effect on the SE and p-value

Answer 26

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.

Question 27

Confidence Intervals:
• Use a , not a –
• Why?

Answer 27

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.

Question 28

Multiple Mediator Model

Answer 28

> 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).

Question 29

Why are Multiple Mediator Models Great?

Answer 29

• 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.

Question 30

Categorical IV’s in a Mediation Model

Answer 30

*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).

Question 31

Multiple Mediation model is unique because …

Answer 31

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).

Question 32

Example Categorical IV’s are…

Answer 32

(A) Religious or non-religious
(B) Tv or No TV
(C) Smoker or Non-Smoker
(D) High SES or Low SES

Question 33

Experimental Mediation Analysis

Answer 33

Types of variables (constraints):

IV is a dichotomous categorical variable:
(A) Treatment
(B) Control

The Mediator Variable and Dependent Variable must be continuous.

Question 34

with concurrnet data the order of variables in a mediation model are…

Answer 34

• 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.

Question 35

Experimental Mediation Analysis have the advantage of …

Answer 35

• 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.

Question 36

quasi-experimental mediation -pal longitudinal- write up:

Answer 36

“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.”

Question 37

Can you have a Dichotomous DV?

Answer 37

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.

Question 38

Summary of Mediation:

Answer 38

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.