soc 681 – causal models with directly observed variables
DESCRIPTION
SOC 681 – Causal Models with Directly Observed Variables. James G. Anderson, Ph.D. Purdue University. Types of SEMs. Regression Models Path Models Recursive Nonrecursive. Class Exercise: Example 7 SEMs with Directly Observed Variables. - PowerPoint PPT PresentationTRANSCRIPT
SOC 681 – Causal Models with Directly Observed Variables
James G. Anderson, Ph.D.Purdue University
Types of SEMs
Regression Models Path Models
Recursive Nonrecursive
Class Exercise: Example 7SEMs 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 Weight: Weight adjusted for height Rating: Rating of physical attractiveness
GPA
HEIGHT
WEIGHT
RATING
ACADEMIC
ATTRACT
e1
e2
1
1
GPA
HEIGHT
WEIGHT
RATING
ACADEMIC
ATTRACT
e1
e2
1
1
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 but subsumed under the residuals are assumed to be not correlated with the model variables.
Assumptions
Variables are measured on an interval scale.
Variables are measured without error.
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 the data (i.e., how well the model reproduces the observed covariances/correlations among the observed variable).
AMOS Input
ASCII SPSS Microsoft Excel Microsoft Access Microsoft FoxPro dBase Lotus
AMOS Output
Path diagram Structural equations effect
coefficients, standard errors, t-scores, R2 values
Goodness of fit statistics Direct and Indirect Effects Modification Indices.
Model One
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
SelfCon .42* - .42*
Model Two
Goodness of Fit: Model 2
Chi-Square = 29.07df = 15
p < 0.06 Chi-Square/df = 1.8 RMSEA = 0.086 GFI = 0.94 AGFI = 0.85 AIC = 67.82
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 is also affected by the size of correlations in the model: the larger the correlations, the poorer the fit
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 In general, a lower chi square to df ratio
indicates a better fitting model
Root Mean Square Error of Approximation (RMSEA)
Value: [ (2/df-1)/(N-1) ] If 2 < df for the model, RMSEA is set to
0 Good models have values of < .05;
values of > .10 indicate a poor fit.
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.
These are usually not the best measures to use.
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. For two models estimated from the same
data, the model with the smaller AIC is preferred.
Model Building
Standardized ResidualsACH – Ethnic = 3.93
Modification IndexACH – Ethnic = 10.05
Model Three
Goodness of Fit: Model 3
Chi-Square = 16.51df = 14
p < 0.32 Chi-Square/df = 1.08 RMSEA = 0.037 GFI = 0.96 AGFI = 0.90 AIC = 59.87
Comparing Models
Chi-Square Difference = 12.56df Difference = 1
p < .0005 AIC Difference = 7.95
Difference in Chi Square
Value: X2diff = X2 model 1 -X2
model 2
DFdiff = DF model 1 –DFmodel 2
Decomposing 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
ActMast - .13 .13
SelfCon .44 - .44
Class Exercise: Example 7SEMs 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 the AIC values for the two models
Class Exercise: Example 7SEMs 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 Weight: Weight adjusted for height Rating: Rating of physical attractiveness
GPA
HEIGHT
WEIGHT
RATING
ACADEMIC
ATTRACT
e1
e2
1
1
GPA
HEIGHT
WEIGHT
RATING
ACADEMIC
ATTRACT
e1
e2
1
1