Summary and help for applied methods and statistics
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Course
Applied methods and statistics (424526B6)
Institution
Tilburg University (UVT)
In this document, I included lecture notes, important information and necessary figures from the powerpoints with additional explanation, important terminology with explanation (in an organized glossary at the end of the document), and additional exercises. I also marked important parts in red and ...
The following document includes information from the PowerPoints, a summary of the
lectures, important exercises and a glossary where terminology is explained.
Lecture 1: Path model
Goal = to capture theories in a formal form and to examine whether the assumed theory
corresponds to observed correlations in reality
BASIC ELEMENTS PATH MODEL
1 Variables
2 Relations 1. Covariation (correlation)
2. causation
3 Types of relations 1. direct
2. indirect
3. unknown
4. spurious
5. reciprocal
6. conditional effects
RELATIONS BETWEEN VARIABLES
COVARIATION Not directional
Not a ‘because’
One does not cause the other
They often have a common cause though
Can be turned around ‘being happy occurs with being healthy’ → NOT causal!
CAUSATION Change in X leads to change in Y
Turning around changes the meaning
Directional
TYPES OF RELATIONS
DIRECT ‘Feeling blue leads to neglecting self-care ‘
Causation
INDIRECT ‘Feeling blue leads to neglecting self-care’ and ‘neglecting self-care leads to bad
health’ → indirect relation between feeling blue and bad health, ‘neglecting self-
care’ is a mediator
UNKOWN Not making statement about direction of effect (double headed arrow)
Double arrow = correlation
SPURIOUS ‘More ice cream sold (x) → more shark attacks’ (y)
No causation, merely covariation
Common cause: weather (s)
RECIPROCAL Set of direct effects that go in opposite direction
Happiness causes health and health causes happiness – not one double headed
arrow!!
Often not explicitly mentioned as such
CONDITIONAL A variable affects an effect, not another variable = moderator
EFFECTS
,Lecture 2: From theory to path diagram
Learning goals:
1. draw path model
2. know when H0 is rejected or not (never proven!)
3. ‘Golden rule’ and path model extensions
4. Identify endogenous and exogenous variables
5. Know meaning of assumptions and disturbance terms
6. Convert path model into linear regression equations
Steps towards path diagram:
1. Make a list of variables
2. Establish causal order
3. Formulate causal hypotheses
Causal hypotheses cannot be proven with correlations → a spurious relation can be an
alternative explanation → we only test whether two variables go together, not whether a
causal hypothesis is true
Golden rule
- Testing (not proving) causal hypotheses
- All variables that may cause a spurious relation between two variables with an
assumed causal effect between them, must be included in the model
- Necessary model extension: common causes
, What if ? = parental pressure
Possible findings after estimating path coefficients:
B1 is the path coefficient between ‘peer relations’ and ‘self-concept’. If this is 0, there is no
causal relation, but a common cause.
- Causal hypothesis is rejected if: size of spurious relation(s) = correlation
o B1 = 0
If size of spurious relation is not equal to correlation:
a. There is a causal relation
b. Not all variables that cause a spurious relation are included in the model →
omitting a spurious relation leads to inaccurate estimation of b 1. → why we have
the golden rule
Endogenous and exogenous variables
Endogenous = a variable explained by other variables in the model (at least one arrow points
at it at least one dependent variable)
, Exogenous = a variable that is not explained by other variables and has no arrow pointing at
it.
Unknown effects (correlations) between exogenous variables are always included, even if we
don’t draw them
Necessary model extensions: disturbance terms
Anxiety leads to worse peer relations
- Also other variables affecting the dependent variable (peer relations)
‘zeta’ represents:
1. Unknown variables → endogenous
2. Known variables that are omitted
3. Human unpredictability
4. Measurement error in endogenous variable
Always included, even when not drawn!
Assumptions about disturbance terms:
- Small
- Uncorrelated to each other and to exogenous variables
- All omitted variables have a relatively small effect on the endogenous variables
- Omitted variables are mutually unrelated
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