Tilburg University Conditional Process Analysis 2019-2020
Causal Analysis in Data Science
CONDITIONAL PROCESS ANALYSIS (DR. MOORS)
Lecture 1
Data analysis: two types of questions
- If/ whether there are relationships between certain variables
o Does economic stress impact on the intention to withdraw?
- How and when do these relationships arise?
o How does economic stress influences withdrawal intention?
Causal reasoning: the relationship between a cause and its effect
- These questions reflect “causal reasoning” = one phenomenon ‘causing’ the other
- Thus, there are expected relationships between phenomena
To find answers to these questions, you need to take some steps:
1. Defining measurement instruments (for instance questionnaires or experiments e.g.)
2. Collecting data
3. Defining hypotheses = defining the expected relationships between phenomena
Hypotheses: a proposed explanation for a phenomenon
- What variables are involved?
- What is the direction of the dependent variable? (it is positively related to … )
Direction of hypotheses: positive or negative?
- Positive → Increase (or decrease) in A, leads to increase (or decrease) in B
- Negative → Increase in A leads to decrease in B (or vice versa)
Mediation hypothesis: → the ‘how’ question → multivariate hypothesis
- Mediating the effect of the independent variable to the dependent variable
- How does economic stress (ES) influences withdrawal intention (WI)?
- The hypothetical ‘answer’ is: ES influences WI through the level of depressed affect (DA)
- Corresponding hypothesis: “Economic stress increases the intention to withdraw from
business because ES increases the level of depressed affect which in turn increases
withdrawal intention.”
Full or Partial mediation?
- Do we have found the full answer on how ES lead to WI by referring to DA?
o If that is the case, there is no direct effect from ES on WI because it is fully mediated
by DA Full mediation
- Partial mediation → However, there might still be an effect from ES on WI regardless of the
effect of DA
- Partial mediation implies that the mechanism through M does not entirely account for the
association observed between X and Y
1
,Tilburg University Conditional Process Analysis 2019-2020
Conceptual model versus conceptual diagram: two main differences
- A conceptual diagram needs to include all the effects that need to be estimated. In the "full
conceptual" model, there is no arrow between ES and WI, because no direct effect between
these variables is expected because it is fully mediated by DA. In a conceptual diagram, you
still include this potential relationship.
- Diagram no longer uses pluses and minuses. It is an open idea of what the relation might be.
While doing research you start with a conceptual model and think about the implied effects related
to it. Then you do your analysis and evaluate whether these implied 0-effects are found in your data.
The “when” question: Extending the research question: can we expect economic stress to influence
depressed affect in all situations?
- A relationship between variables can depend on situations
- Hypothesis: The higher the number of social ties the less economic stress
will lead to increased depressed affect.
- The situation in this example is ‘the number of social ties’
- = moderation or conditional relationship
Conditional Process Analysis: Merging “how” and “when”
- Mediation is indicating how the mediation process is
moderated: i.e. how ES will lead to WI
- Important: the whole is more than the sum of its parts
- Hypothesis should:
o Indicate that an indirect effect will be moderated by a moderator
o Indicate at which part of the mediation process this moderation will occur
“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.”
What hypotheses are truly necessary and what hypotheses are redundant?
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
You could use only one single hypothesis: “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.”
2
, Tilburg University Conditional Process Analysis 2019-2020
Reflection: complexity and creativity in defining moderation hypotheses – examples
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)
2. Expecting opposite (different sign) effects of X on Y depending on the level of W
3. Expect to only observe an effect of X on Y for some values of W and no effect for other values 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)
This information will help deciding whether to use one single hypothesis or two multivariate
hypotheses! Usually you start your model with a bivariate hypothesis, then start thinking about the
full picture and whether this really adds something to the model. What you observe in the full
picture is not always essential.
General issues related to course material:
Note: All models should be recursive = no loops, causality in one direction only
Related concepts:
(a) Conceptual model
- Build from a set of hypotheses:
- Paths defined by hypotheses → implies expected direction of effect
- Not-defined paths are assumed to be zero
(b) Conceptual diagram
- Used to estimate the effects that you need estimate given the conceptual model
- Adding model-assumed zero-effects + dropping sign of effects
- model-assumed effects → decision rule:
- “If a variable A has an effect on a variable B it also needs to include an effect
on any other variable C that has an assumed effect of B”
(c) Statistical diagram
- Used when reporting results from the analysis
- The estimates that we need to include in our regression analysis
You must be careful about removing zero-effects. It is dangerous to say that there is absolutely no
relationship between variables. This depends on your data and its power. A non-significant
relationship is not necessarily a zero-effect.
Lecture 2
Regression equations: A statistical model describes what is generally defined as a 'path model'. It
brings variables together (linked to each other) and tries to find estimates that indicate how one
variable is linked to the next one. This is usually performed by a series of regression equations.
- You need as many regression equations as there are mediators, plus one for the dependent
variable (regression equation for each mediator, that has an intercept, slope, and error term)
- In mediation, we assign a specific letter to specific paths in the diagram / model
- An A effect is an effect of an independent variable on a mediator
- The B effect is an effect of a mediator on the dependent variable
- The C’ effect is an direct effect of an independent variable (X) on the dependent variable (Y)
- The slope effect of X consists of two parts → A*B + C’ (= total effect)
- C = total effect of X on Y
3
Causal Analysis in Data Science
CONDITIONAL PROCESS ANALYSIS (DR. MOORS)
Lecture 1
Data analysis: two types of questions
- If/ whether there are relationships between certain variables
o Does economic stress impact on the intention to withdraw?
- How and when do these relationships arise?
o How does economic stress influences withdrawal intention?
Causal reasoning: the relationship between a cause and its effect
- These questions reflect “causal reasoning” = one phenomenon ‘causing’ the other
- Thus, there are expected relationships between phenomena
To find answers to these questions, you need to take some steps:
1. Defining measurement instruments (for instance questionnaires or experiments e.g.)
2. Collecting data
3. Defining hypotheses = defining the expected relationships between phenomena
Hypotheses: a proposed explanation for a phenomenon
- What variables are involved?
- What is the direction of the dependent variable? (it is positively related to … )
Direction of hypotheses: positive or negative?
- Positive → Increase (or decrease) in A, leads to increase (or decrease) in B
- Negative → Increase in A leads to decrease in B (or vice versa)
Mediation hypothesis: → the ‘how’ question → multivariate hypothesis
- Mediating the effect of the independent variable to the dependent variable
- How does economic stress (ES) influences withdrawal intention (WI)?
- The hypothetical ‘answer’ is: ES influences WI through the level of depressed affect (DA)
- Corresponding hypothesis: “Economic stress increases the intention to withdraw from
business because ES increases the level of depressed affect which in turn increases
withdrawal intention.”
Full or Partial mediation?
- Do we have found the full answer on how ES lead to WI by referring to DA?
o If that is the case, there is no direct effect from ES on WI because it is fully mediated
by DA Full mediation
- Partial mediation → However, there might still be an effect from ES on WI regardless of the
effect of DA
- Partial mediation implies that the mechanism through M does not entirely account for the
association observed between X and Y
1
,Tilburg University Conditional Process Analysis 2019-2020
Conceptual model versus conceptual diagram: two main differences
- A conceptual diagram needs to include all the effects that need to be estimated. In the "full
conceptual" model, there is no arrow between ES and WI, because no direct effect between
these variables is expected because it is fully mediated by DA. In a conceptual diagram, you
still include this potential relationship.
- Diagram no longer uses pluses and minuses. It is an open idea of what the relation might be.
While doing research you start with a conceptual model and think about the implied effects related
to it. Then you do your analysis and evaluate whether these implied 0-effects are found in your data.
The “when” question: Extending the research question: can we expect economic stress to influence
depressed affect in all situations?
- A relationship between variables can depend on situations
- Hypothesis: The higher the number of social ties the less economic stress
will lead to increased depressed affect.
- The situation in this example is ‘the number of social ties’
- = moderation or conditional relationship
Conditional Process Analysis: Merging “how” and “when”
- Mediation is indicating how the mediation process is
moderated: i.e. how ES will lead to WI
- Important: the whole is more than the sum of its parts
- Hypothesis should:
o Indicate that an indirect effect will be moderated by a moderator
o Indicate at which part of the mediation process this moderation will occur
“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.”
What hypotheses are truly necessary and what hypotheses are redundant?
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
You could use only one single hypothesis: “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.”
2
, Tilburg University Conditional Process Analysis 2019-2020
Reflection: complexity and creativity in defining moderation hypotheses – examples
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)
2. Expecting opposite (different sign) effects of X on Y depending on the level of W
3. Expect to only observe an effect of X on Y for some values of W and no effect for other values 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)
This information will help deciding whether to use one single hypothesis or two multivariate
hypotheses! Usually you start your model with a bivariate hypothesis, then start thinking about the
full picture and whether this really adds something to the model. What you observe in the full
picture is not always essential.
General issues related to course material:
Note: All models should be recursive = no loops, causality in one direction only
Related concepts:
(a) Conceptual model
- Build from a set of hypotheses:
- Paths defined by hypotheses → implies expected direction of effect
- Not-defined paths are assumed to be zero
(b) Conceptual diagram
- Used to estimate the effects that you need estimate given the conceptual model
- Adding model-assumed zero-effects + dropping sign of effects
- model-assumed effects → decision rule:
- “If a variable A has an effect on a variable B it also needs to include an effect
on any other variable C that has an assumed effect of B”
(c) Statistical diagram
- Used when reporting results from the analysis
- The estimates that we need to include in our regression analysis
You must be careful about removing zero-effects. It is dangerous to say that there is absolutely no
relationship between variables. This depends on your data and its power. A non-significant
relationship is not necessarily a zero-effect.
Lecture 2
Regression equations: A statistical model describes what is generally defined as a 'path model'. It
brings variables together (linked to each other) and tries to find estimates that indicate how one
variable is linked to the next one. This is usually performed by a series of regression equations.
- You need as many regression equations as there are mediators, plus one for the dependent
variable (regression equation for each mediator, that has an intercept, slope, and error term)
- In mediation, we assign a specific letter to specific paths in the diagram / model
- An A effect is an effect of an independent variable on a mediator
- The B effect is an effect of a mediator on the dependent variable
- The C’ effect is an direct effect of an independent variable (X) on the dependent variable (Y)
- The slope effect of X consists of two parts → A*B + C’ (= total effect)
- C = total effect of X on Y
3
