Applied Methods and Statistics - Summary

Applied Methods
and Statistics

, LECTURE 't
31/08/2020



SPURIOUS RELATIONS
⑤
#
Variable
Variable
s causes x

} × is related to
y

q g
s cause, y


-
-
- -




spurious
DIRECT AND
relationship
INDIRECT EFFECTS



Direct : Variable x causes y
⑦ -7
⑦
Indirect : Variable
Variable
x

m
causes

causes
y
m

⑦ -
② -
⑦
mediator




⑦
UNKNOWN EFFECTS


§py spurious relation


tenting
\
No statement is made about the

direction of the effect ,
I

⑦
indirect effect
↳ correlation
④ y y

RECIPROCAL EFFECTS




Variable

Variable
x



y
causes

causes
y
x
⑦ ⑦
moderator




②
CONDITIONAL EFFECTS




The size of the effect of X

L
on


of
y depends
a third
on



variable
the


.
value

⑦ →
⑦

, LECTURE I
03.10912020




FROM THEORY TO PATH DIAGRAM




F
Fr÷aaiO\
D
,




ft
ka


i .
O O
D D
'
s .




Gz
←




D
Golden rule = all variables that cause a
spurious relation between two variables with an
may
assumed causal effect between them must be included in the model

Include common causes
*
to avoid an inaccurate estimation of bi
→ we include the spurious if we have to
relation to see reject the causal
hypothesis
(i -
e .
.
be = O)

Possible
findings
•
when
testing causal hypotheses
:




bi bn




D
causal hypotheses can
only be rejected if . . .




D.
Size of spurious relation Cs) =
correlation

explained completely by spurious
→
correlation is relation
D. Two
possibilities
Size of spurious relations ) =
correlation

be O causal hypothesis rejected
→
no causal relation and
-
-



,


Size of
spurious relation Cs ) t correlation

→
There is a causal relation ,
OR

→ Not all variable that cause a
spurious relation are included in the model

, Endogenous
D
variables = a variable explained by other variables in the model

D
Exogenous variables =
a variable that is not explained in the model

United between
exogenous variables are
always included ,
even if we don't draw

them
D
Disturbance terms ( = 5 )

• 5 ( ' '

zeta
"

) represents . . .




→ Unknown variables →
endogenous
→ known variables that are omitted

→
Human unpredictability
→
Measurement variable
error in
endogenous
Bo
Disturbance terms included , if don't draw them
are
always even we


•
Assumption : disturbance terms are small ,
uncorrelated with each other and uncorrelated

with variables
exogenous
All variables that omitted effect
from the model have
relatively the
→



endogenous
are a small on


variables

All variables that omitted from the model unrelated
mutually
→ are
are


→ No spurious relations have been omitted from the model



FROM PATH DIAGRAM TO LINEAR EQUATIONS




One
equation per endogenous
D
variable with . . .




•
All variable ( direct effect)
variables that explain the
endogenous
Be An intercept
• A disturbance term