thank you very much!
I definitely need more theoretical background ...
but for now;
what does that mean for this dataset?
x1 should be the intermediate variable of x2 and y1
(x2 -> x1 -> y1)
Can I test that with this kind of analysis?
or do I see know that this kind of "intermediate variable" model does
not fit the data well
and I need to set all paths to get a good model that represents the
data good enough?
Am 09.03.2009 um 06:15 schrieb William Revelle:
Martin,
hi,
I have following data and code;
cov <- c
(1.670028
,-1.197685
,-2.931445,-1.197685,1.765646,3.883839,-2.931445,3.883839,12.050816)
cov.matrix <- matrix(cov, 3, 3, dimnames=list(c("y1","x1","x2"),
c("y1","x1","x2")))
path.model <- specify.model()
x1 -> y1, x1-y1
x2 <-> x1, x2-x1
x2 <-> x2, x2-x2
x1 <-> x1, x1-x1
y1 <-> y1, y1-y1
x2 -> y1, x2-y1
summary(sem(path.model, cov.matrix, N = 422))
and I get following results;
Model Chisquare = 12.524 Df = 1 Pr(>Chisq) = 0.00040179
Chisquare (null model) = 812.69 Df = 3
Goodness-of-fit index = 0.98083
Adjusted goodness-of-fit index = 0.885
RMSEA index = 0.16545 90% CI: (0.09231, 0.25264)
Bentler-Bonnett NFI = 0.98459
Tucker-Lewis NNFI = 0.9573
Bentler CFI = 0.98577
SRMR = 0.027022
BIC = 6.4789
Parameter Estimates
Estimate Std Error z value Pr(>|z|)
x1-y1 -0.67833 0.033967 -19.970 0 y1 <--- x1
x2-x1 3.88384 0.293743 13.222 0 x1 <--> x2
x2-x2 12.05082 0.831569 14.492 0 x2 <--> x2
x1-x1 1.76565 0.121839 14.492 0 x1 <--> x1
y1-y1 0.85761 0.059124 14.505 0 y1 <--> y1
Iterations = 0
Now I wonder why the chi-square value is so bad and what
Pr(>Chisq) tells me.
Can anyone help me on this?
When I allow the path x2 -> y1 I get of course a good fit, but the
path coefficient of x2 -> y1 is pretty low (-0.084653), so I
thought I
can restrict that one to zero.
If you examine the residuals
mod1 <- sem(p.model,cov.matrix,N=422)
residuals(mod1)
You will see that you are completing ignoring the y1-x2 covariance.
When you examine your covariance matrix as a correlation matrix,
r.mat <- cov2cor(cov.matrix)
you will note that the x2-y1 relationship is very large (the
correlation is -.65)
Your original model was fully saturated and what you are reporting
is actually what I label as p.model which is your full model without
the last row.
If you compare the fully saturated model with your mod1, you will
find that the reason for the large chi square is due to not
specifying the x2-y1 path.
You might want to read some more on sem techniques. A good
introduction is a text by John Loehlin.
Bill
--
William Revelle http://personality-project.org/revelle.html
Professor http://personality-project.org/personality.html
Department of Psychology http://www.wcas.northwestern.edu/psych/
Northwestern University http://www.northwestern.edu/
Attend ISSID/ARP:2009 http://issid.org/issid.2009/
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