Transcript Latent variable path analysis

Latent variable path analysis
• Combination of CFA and observed variable path
analysis
• More parameters estimated, so need to have a
larger sample size
• Chief advantage is that you are determining how
latent constructs are related to each other, leaving
aside error, which may distort
correlations/covariances
• State-of-the-art!!
• Is there one “right answer” to a given dataset?
What will we do today?
• First, I will show you the observed variable path
analysis (like last week)
• Then I will show you an alternative model for the
observed variable path analysis
• Talk about how to compare them
• Then I will show you a latent variable path
analysis, and the same with the alternative model
• Hopefully, you will see how these tools can be
used to usefully describe a dataset
Maruyama & McGarvey’s (1980) dataset
concerning peer acceptance
• 249 subjects (child, teacher and parent data)
• Interested in seeing how exogenous variables (like
socio-economic status) and parent evaluations
predict peer acceptance of children
• Five major potential latent variables:
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Socio-economic status
Academic abilities
Academic achievement
Adult evaluation of child
Peer evaluation of child
Original model: observed variables
f1
z1
Educ of
head
g1,1
g1,2
f2
Vocab
f3
g2,3
Mother
eval
Verbal
ach
z2
b2,1
Popular
in class
Original model: obtained results
f1
R2=.21 z1
Educ of
head
f2
.22*
.35**
Vocab
f3
.12~
Mother
eval
Verbal
ach
z2
.26*
Popular
in class
R2=.03
Alternative model: observed variables
f1
z1
Educ of
head
g1,1
g1,2
f2
Vocab
Verbal
ach
b2,1
z2
Mother
eval
b3,1
b3,2
Popular
in class
z3
Alternative model: obtained results
f1
z1
Educ of
head
f2
.22*
.35**
z2
R2=.21
Verbal
ach
.13*
R2=.02
Mother
eval
.26*
Vocab
.12~
z3
Popular
in class R2=.09
Comparison of two models
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Original model
C2(6) = 9.83
RMSEA = .05
NFI = .90
PNFI = .54
CFI = .96
RFI = .84
Crit. N = 424.98
GFI = .98
AGFI = .96
PGFI = .39
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Alternative model
C2(6) = 6.83
RMSEA = .023
NFI = .93
PNFI = .56
CFI = .99
RFI = .89
Crit. N = 611.33
GFI = .99
AGFI = .97
PGFI = .40
Now, on to latent variable path
analysis!
• Two-step process: 1) CFA on the potential latent
variables; and 2) path analysis on the latent
variables
• Need to achieve good fit with the CFA before can
proceed; may need to drop indicators and/or latent
variables
• May make sense to do the observed variable path
analysis first (as we did here), except that you
assume that you’re using the best indicators
(which may not be true)