02b Structural Equation Models with Directly Observed Variables

Structural Equation Models with
Directly Observed Variables II
James G. Anderson, Ph.D.
Purdue University

Identification
• Over Identified
• Just Identified
• Under Identified

GPA

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Example 7
A nonrecursive model
Felson and Bohrnstedt (1979)
(Female subjects)
Over Identified Model
No. of Variances/Covariances = 21
No. of Parameters Estimated = 19
DF = 2

GPA

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Example 7
A nonrecursive model

Felson and Bohrnstedt (1979)
(Female subjects)
Over Identified Model
No. of Variances/Covariances = 21
No. of Parameters Estimated = 20
DF = 1

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Over Ideridentified Model
Number of variances/covariances = 21
No. of parameters estimated =20
DF =1

GPA

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Example 7
A nonrecursive model
Felson and Bohrnstedt (1979)
(Female subjects)
Just Identified Model
No. of Variances/Covariances = 21
No. of Parameters Estimated = 21
DF = 0

GPA

academic

1

error1

height

weight

attract

1

error2

rating

Example 7
A nonrecursive model
Felson and Bohrnstedt (1979)
(Female subjects)
Just Identified Model
No. of Variances/Covariances = 21
No. of Parameters Estimated = 21
DF = 0

GPA

academic

1

error1

height

weight

attract

1

error2

rating

Example 7
A nonrecursive model
Felson and Bohrnstedt (1979)
(Female subjects)
Under Identified Model
No. of Variances/Covariances = 21
No. of Parameters Estimated = 22
DF = - 1

Covariances
•

•
•
•

Among observed variables
Among exogenous variables
Among measurement errors
Among errors in the equations

Covariances among Observed
Variables
rowtype

varname

n

perform

knowl

98

value

98

sat

98

train

98

98

cov

perform

0.022

cov

knowl

0.017

0.053

cov

value

0.024

0.028

0.121

cov

sat train

0.004

0.004

-0.006

0.09

cov

train

0.018

0.018

0.035

-0.006

0.094

0.058

1.379

2.877

2.461

2.117

mean

Covariances among Exogenous
Variables
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Underidentified Model
Number of variances/covariances = 21
No. of parameters estimated =22
DF =0

Covariances among Measurement
Errors
var_a

var_a

var_p

eps1

eps2

1

1

anomia67

1

eps3

powles67
path_p

67
alienation

1

anomia71

powles71

1

path_p

71
alienation

ses
1
educatio

eps4

1

1

zeta1

var_p

SEI

1

1

delta1

delta2

Example 6: Model C
Exploratory analysis
W heaton (1977)
Model Specification

1

zeta2

Covariances among the Errors in
the Equations
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Example 7
A nonrecursive model
Felson and Bohrnstedt (1979)
(Female subjects)
Over Identified Model
No. of Variances/Covariances = 21
No. of Parameters Estimated = 20
DF = 1

Class Exercise
• Create a new model:
– From the menu choose File/New

• Specify the Data file:
– Choose File/Data Files
– Browse to the tutorial folder. The path is:
• C:\Program Files\Amos 6\Examples
• In the Files of type list select SPSS
• Select Fels_mal.sav

• Estimate the Parameters of the different models
and compare their fit statistics