Path Analysis Path Analysis • Primary goal – to explain the associations among variables with our a priori model(s) – i.e., we are trying to explain why variables are correlated using a "temporally-sequenced" model – draw and test a mathematical model • with underlying equations • Variables can be based on any type of data • We care about (a) overall model fit and (b) relations within the model
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Path AnalysisPath Analysis
• Primary goal– to explain the associations among variables
with our a priori model(s)– i.e., we are trying to explain why variables are
correlated using a "temporally-sequenced" model
– draw and test a mathematical model•with underlying equations
• Variables can be based on any type of data• We care about (a) overall model fit and (b)
relations within the model
Path AnalysisPath Analysis• Two traditions to path analysis
– old tradition•the model explains R•solves equations one at a time
–using OLS regression•no determination of overall model fit
– new tradition•the model explains and R•equations of a model are solved simultaneously
–using ML estimation in EQS, LISREL, AMOS, etc.
•determination of overall fit
Path AnalysisPath Analysis• Advantages of path analysis
– ability to test overall models and individual parameters
– ability to test models with multiple DVS– ability to model (multiple) mediator variables
(processes)• Primary disadvantage of path analysis
– cannot reduce the impact of measurement error•only have observed variables•do not have multiple indicators of a latent
variable
Path-Analytic ModelPath-Analytic Model
• Always start with a path diagram
Challenge (1)
Depression (5)
Threat (2)
Problem-Focused (3)
p31
r12
p54
p53
e5
e3
Emotion-Focused (4)
e4
p42
The ProcessThe Process• Model specification based on the path diagram
– you write equations to specify each endogenous variable•three equations comprise the model
–PF = p31(Challenge) + e3
–EF = p42(Threat) + e4
–Depression = p53(PF) + p54(EF) + e5
– this model attempts to explain the variance-covariance matrix () or correlation matrix (R)
Types of effectsTypes of effects
• Direct effects
Challenge (1)
Depression (5)
Threat (2)
Problem-Focused (3)
p51r12
p54
p53
e5
e3
Emotion-Focused (4)
e4
p42
p31
Types of effectsTypes of effects• Indirect effects
– the magnitude of an indirect effect is determined by multiplying compound paths
• ChallengeDepression = p31 * p53
Challenge (1)
Depression (5)
Threat (2)
Problem-Focused (3)
p42
r12
p54
p53
e5
e3
Emotion-Focused (4)
e4
p31
p51
Types of effectsTypes of effects
• Unanalyzed association
Challenge (1)
Depression (5)
Threat (2)
Problem-Focused (3)
p42
r12
p54
p53
e5
e3
Emotion-Focused (4)
e4
p31
p51
Path AnalysisPath Analysis• Calculating and using implied correlations
– we can calculate the correlations among the variables in R based on our model•for each pair of variables there is a correlation
implied by the model– the ultimate goal is to compare observed R to
implied R– use tracing rules to calculate implied R
•we highlight all possible routes between pairs of variables
–multiply compound paths within a route–add up all possible routes
Path AnalysisPath Analysis
– using tracing rules to calculate implied R•3 primary rules to calculate the implied
correlations–No loops: you cannot go through the
same variable twice in a single route–No going forward and then backward
•You can go backward first and then forward
–A maximum of 1 unanalyzed association per route
Tracing Rule 1Tracing Rule 1
D
C
E
A
B
•No loops: cannot go through the same variable twice•Implied rA,B = ACB (YES!!!)•Implied rA,B = ACDECB (NO!!!)