Lecture notes Mediation, moderation and CPA
Course: Topics in Causal Analysis 2021/2022
Study: Bachelor Psychology (or Data Science) Tilburg University
Topics in causal analysis
This course exist out of two topics:
1. Mediation, moderation and conditional process analysis. (Lecturer: Guy Moors)
2. Multilevel Analysis. (Lecturer: John Gelissen)
This summary covers topic 1.
Mediation, moderation and conditional process analysis
Introduction
This topic is about how variables are in an causal link with one another. It’s very
important to have a good understanding about regression analysis. To try to
understand what kind of models you can research with mediation, moderation and
conditional process analysis, it’s important to have a good understanding about the
research question. From whether there is certain relation between variables or if
there is, to how does a relationship comes into existence and when. We’re interested
in questions that reflect causal reasoning, so that one phenomenon (variable) causes
the other. To find the answer to such question we define measurement instruments,
like questionnaires, we collect data and define hypotheses, that define the expected
relationships between phenomena (make a prediction of the research question).
Example
Look at these three research questions where we could be interested in:
1. Does economic stress impact on the intention to withdraw from business among
small business owners?
2. And does the personal state of mind of business owners such as feeling
depressed influence this intention?
3. And maybe it is economic stress that makes these business owners feeling more
depressed to begin with?
Now we’re going to make a prediction of the answers on the research questions by
describing what the relationship of the variables will look like (hypotheses):
H1: The more economic stress a small business owner experiences the higher the
intention to withdraw from business.
H2: The extent to which a small business owner feels depressed affect is positively
related to withdrawal intention.
H3: The more economic stress experienced the more likely a small business owner
will show symptoms of depressed affect.
As you can see there are three variables in these questions: economic stress (ES),
withdrawal intention (WI) and depressed affect (DA). The questions are linked and
can be put in one conceptual model. This is a visualisation of how the variables could
be linked together (not defined paths are assumed to be zero but in this case every
path is defined):
, As you can see in the conceptual model there are three
bivariate hypotheses (every hypothesis links two variables
with each other) that force the researcher to ask the
following question: How does ES influences WI?, with
hypothetical answer: ES influences WI through the level of DA. The corresponding
hypothesis is thus that economic stress increases the intention to withdraw from
business because ES increases the level of depressed affect which in turn increases
WI. This is a mediation hypotheses (DA is a mediator) and is also called a
multivariate hypothesis (more than two variables are linked by the “how” question).
So the effect of ES on WI is not direct but an indirect effect via the mediator DA. It is
possible to have a partial or a full mediation (if there is a direct link as well or only an
indirect link):
If you start with only bivariate hypotheses you’ll always have a partial mediation
model , so it’s very important to make multivariate hypotheses as well. A conceptual
diagram differs of a conceptual model in two ways. Such a
diagram needs to depict all the effects that need to be
estimated; the full mediation model expects a zero or a non-
significant direct effect so it needs to be tested.
You can see that there are no more pluses and minuses,
because you have to keep an open mind about the effect and
if it will be significant in the first placed.
We can expand the how question to a when question, like can we expect ES to
influence DA in all situations? This way, we’re defining a relationship between
variables as being conditional on another variable. The corresponding hypothesis
could be that the higher the number of social ties (ST) the less economic stress will
lead to increased depressed affect. This is called moderation or a conditional
relationship. The conceptual model will look like:
We could also merge the how and when question and then we have a conditional
,process analysis:
or
It’s not enough to have a mediation or moderation hypothesis, then we need a
conditional process analysis hypothesis like:
“The more social ties (ST) a business owner has, the less likely DA will mediate the
effect of ES on WI since the effect of ES on DA is weakened by ST.”
or
“The effect of ES on WI will only be mediated by DA when the business owner has
relatively few social ties (TS) since having relatively more social ties implies that ES
will not impact on WI through DA”
or
“The lower the relative number of social ties the more DA will mediate the effect of
ES on WI since the number of ST increases the effect of ES on DA.”
This is quite a difficult exercise which often gets done wrong in scientific articles. It’s
hard to make one hypothesis for the full model. When you have look at a conceptual
model you need to think about which hypotheses are necessary and which are
redundant. It’s important to include the overall specification of the mediation process
and of how the mediation process is moderated:
H1 “Economic stress increases the intention to withdraw from business because ES
increases the level of depressed affect which in turn increases withdrawal intention.”
= overall specification of the mediation process
H2 “The more social ties (ST) a business owner has, the less likely DA will mediate
the effect of ES on WI since the effect of ES on DA is weakened by ST.”
= specification of how the mediation process is moderated
Then we could make a single hypothesis out of these two:
“Only when a business owner has little or no social ties the positive indirect effect of
economic stress on withdrawal intention mediated through depressed affect will
show. With a sufficient number of social ties economic stress will not affect
withdrawal intention.”
If it’s better to have two hypothesis or one
overall hypothesis depends on how you
expect the moderation effect to be. You can
have all kinds of expectations of the
, moderation effect:
1. Expecting that the effect of X on Y will have the same sign (+ of -) for all conditions
of W (moderator) but with different strength (magnitude)
In general Y is increasing the higher the level of X gets but X is the weakest on the
lowest level of the moderator W. It’s always positive but increases with the level of
moderator. So in this example you probably will define the mediation first and then
the conditional process analysis hypothesis.
2. Expecting opposite (different sign) effects of X on Y depending on the level of W
In this case you might consider one single conditional process analysis hypothesis.
3. Expecting to only observe an effect of X on Y for particular values of W and no
effect for other values of W
4. Expecting that the moderating effect of M in the relationship between X and Y is
exponentially increasing in the level of W (= nonlinear moderation -> quadratic
moderation of linear effect)
5. Etc. (a matter of creativity)
SPSS
In SPSS we’re going to work with a SPSS macro for process analysis (it’s also called
PROCESS). We’re going to look at a conceptual diagram and make them into
statistical diagrams:
Course: Topics in Causal Analysis 2021/2022
Study: Bachelor Psychology (or Data Science) Tilburg University
Topics in causal analysis
This course exist out of two topics:
1. Mediation, moderation and conditional process analysis. (Lecturer: Guy Moors)
2. Multilevel Analysis. (Lecturer: John Gelissen)
This summary covers topic 1.
Mediation, moderation and conditional process analysis
Introduction
This topic is about how variables are in an causal link with one another. It’s very
important to have a good understanding about regression analysis. To try to
understand what kind of models you can research with mediation, moderation and
conditional process analysis, it’s important to have a good understanding about the
research question. From whether there is certain relation between variables or if
there is, to how does a relationship comes into existence and when. We’re interested
in questions that reflect causal reasoning, so that one phenomenon (variable) causes
the other. To find the answer to such question we define measurement instruments,
like questionnaires, we collect data and define hypotheses, that define the expected
relationships between phenomena (make a prediction of the research question).
Example
Look at these three research questions where we could be interested in:
1. Does economic stress impact on the intention to withdraw from business among
small business owners?
2. And does the personal state of mind of business owners such as feeling
depressed influence this intention?
3. And maybe it is economic stress that makes these business owners feeling more
depressed to begin with?
Now we’re going to make a prediction of the answers on the research questions by
describing what the relationship of the variables will look like (hypotheses):
H1: The more economic stress a small business owner experiences the higher the
intention to withdraw from business.
H2: The extent to which a small business owner feels depressed affect is positively
related to withdrawal intention.
H3: The more economic stress experienced the more likely a small business owner
will show symptoms of depressed affect.
As you can see there are three variables in these questions: economic stress (ES),
withdrawal intention (WI) and depressed affect (DA). The questions are linked and
can be put in one conceptual model. This is a visualisation of how the variables could
be linked together (not defined paths are assumed to be zero but in this case every
path is defined):
, As you can see in the conceptual model there are three
bivariate hypotheses (every hypothesis links two variables
with each other) that force the researcher to ask the
following question: How does ES influences WI?, with
hypothetical answer: ES influences WI through the level of DA. The corresponding
hypothesis is thus that economic stress increases the intention to withdraw from
business because ES increases the level of depressed affect which in turn increases
WI. This is a mediation hypotheses (DA is a mediator) and is also called a
multivariate hypothesis (more than two variables are linked by the “how” question).
So the effect of ES on WI is not direct but an indirect effect via the mediator DA. It is
possible to have a partial or a full mediation (if there is a direct link as well or only an
indirect link):
If you start with only bivariate hypotheses you’ll always have a partial mediation
model , so it’s very important to make multivariate hypotheses as well. A conceptual
diagram differs of a conceptual model in two ways. Such a
diagram needs to depict all the effects that need to be
estimated; the full mediation model expects a zero or a non-
significant direct effect so it needs to be tested.
You can see that there are no more pluses and minuses,
because you have to keep an open mind about the effect and
if it will be significant in the first placed.
We can expand the how question to a when question, like can we expect ES to
influence DA in all situations? This way, we’re defining a relationship between
variables as being conditional on another variable. The corresponding hypothesis
could be that the higher the number of social ties (ST) the less economic stress will
lead to increased depressed affect. This is called moderation or a conditional
relationship. The conceptual model will look like:
We could also merge the how and when question and then we have a conditional
,process analysis:
or
It’s not enough to have a mediation or moderation hypothesis, then we need a
conditional process analysis hypothesis like:
“The more social ties (ST) a business owner has, the less likely DA will mediate the
effect of ES on WI since the effect of ES on DA is weakened by ST.”
or
“The effect of ES on WI will only be mediated by DA when the business owner has
relatively few social ties (TS) since having relatively more social ties implies that ES
will not impact on WI through DA”
or
“The lower the relative number of social ties the more DA will mediate the effect of
ES on WI since the number of ST increases the effect of ES on DA.”
This is quite a difficult exercise which often gets done wrong in scientific articles. It’s
hard to make one hypothesis for the full model. When you have look at a conceptual
model you need to think about which hypotheses are necessary and which are
redundant. It’s important to include the overall specification of the mediation process
and of how the mediation process is moderated:
H1 “Economic stress increases the intention to withdraw from business because ES
increases the level of depressed affect which in turn increases withdrawal intention.”
= overall specification of the mediation process
H2 “The more social ties (ST) a business owner has, the less likely DA will mediate
the effect of ES on WI since the effect of ES on DA is weakened by ST.”
= specification of how the mediation process is moderated
Then we could make a single hypothesis out of these two:
“Only when a business owner has little or no social ties the positive indirect effect of
economic stress on withdrawal intention mediated through depressed affect will
show. With a sufficient number of social ties economic stress will not affect
withdrawal intention.”
If it’s better to have two hypothesis or one
overall hypothesis depends on how you
expect the moderation effect to be. You can
have all kinds of expectations of the
, moderation effect:
1. Expecting that the effect of X on Y will have the same sign (+ of -) for all conditions
of W (moderator) but with different strength (magnitude)
In general Y is increasing the higher the level of X gets but X is the weakest on the
lowest level of the moderator W. It’s always positive but increases with the level of
moderator. So in this example you probably will define the mediation first and then
the conditional process analysis hypothesis.
2. Expecting opposite (different sign) effects of X on Y depending on the level of W
In this case you might consider one single conditional process analysis hypothesis.
3. Expecting to only observe an effect of X on Y for particular values of W and no
effect for other values of W
4. Expecting that the moderating effect of M in the relationship between X and Y is
exponentially increasing in the level of W (= nonlinear moderation -> quadratic
moderation of linear effect)
5. Etc. (a matter of creativity)
SPSS
In SPSS we’re going to work with a SPSS macro for process analysis (it’s also called
PROCESS). We’re going to look at a conceptual diagram and make them into
statistical diagrams:
