SOC 681 – Causal Models with
Directly Observed Variables
Types of SEMs
Regression Models
Path Models
Recursive
Class Exercise: Example 7
SEMs with Directly Observed Variables
Felson and Bohrnstedt’s study of 209 girls
from 6th through 8th grade
Variables
Academic: Perceived academic ability
Attract: Perceived attractiveness
GPA: Grade point average
Height: Deviation of height from the mean height
Assumptions
Relations among variables in the
model are linear, additive and causal. Curvilinear, multiplicative and
interaction relations are excluded.
Variables not included in the model
Assumptions
Variables are measured on an
interval scale.
Variables are measured without
Objectives
Estimate the effect parameters (i.e., path
coefficients). These parameters indicate the direct effects of a variable hypothesized as a cause of a variable taken as an effect.
Decompose the correlations between an
exogenous and endogenous or two endogenous variables into direct and indirect effects.
Determine the goodness of fit of the model to
AMOS Input
ASCII
SPSS
Microsoft Excel
Microsoft Access
Microsoft FoxPro
dBase
AMOS Output
Path diagram
Structural equations effect
coefficients, standard errors, t-scores, R2 values
Goodness of fit statistics
Direct and Indirect Effects
Decomposing the Effects of Variables
on Achievement
Variables Direct Indirect Total
Sex -.03 - -.03
FatherEd .17 - .17
Ethnic .17 - .17
IndTrng .23* - .23*
AStress -.17* - -.17*
ActMast .02 - .02
Goodness of Fit: Model 2
Chi-Square = 29.07
df = 15
p < 0.06
Chi-Square/df = 1.8
RMSEA = 0.086
GFI = 0.94
AGFI = 0.85
Chi Square:
2 Best for models with N=75 to N=100
For N>100, chi square is almost always significant since the magnitude is
affected by the sample size
Chi Square to df Ratio:
2/df
There are no consistent standards for what is considered an acceptable model Some authors suggest a ratio of 2 to 1
Root Mean Square Error of
Approximation (RMSEA)
Value: [ (2/df-1)/(N-1) ]
If 2 < df for the model, RMSEA is set to
0
GFI and AGFI
(LISREL measures)
Values close to .90 reflect a good fit.
These indices are affected by sample
size and can be large for poorly specified models.
Akaike Information Criterion (AIC)
Value: 2 + k(k-1) - 2(df)
where k= number of variables in the model A better fit is indicated when AIC is smaller
Not standardized and not interpreted for a given model.
Model Building
Standardized Residuals
ACH – Ethnic = 3.93
Modification Index
Goodness of Fit: Model 3
Chi-Square = 16.51
df = 14
p < 0.32
Chi-Square/df = 1.08
RMSEA = 0.037
GFI = 0.96
AGFI = 0.90
Comparing Models
Chi-Square Difference = 12.56
df Difference = 1 p < .0005
Difference in Chi Square
Value: X
2Decomposing the Effects of Variables
on Achievement
Variables Direct Indirect Total
Sex - .09 .09
FatherEd .- .06 .06
Ethnic .29 .05 .34
IndTrng .25 .04 .29
AStress -.14 -.03 -.17
Class Exercise:
Example 7
SEMs with Directly Observed Variables
Attach the data for female subjects
from the Felson and Bohrnstedt study (SPSS file Fels_fem.sav)
Fit the non-recursive model
Delete the non-significant path
between Attract and Academic and refit the model
Compare the chi square values and
Class Exercise: Example 7
SEMs with Directly Observed Variables
Felson and Bohrnstedt’s study of 209 girls
from 6th through 8th grade
Variables
Academic: Perceived academic ability
Attract: Perceived attractiveness
GPA: Grade point average
Height: Deviation of height from the mean height
