[R] path analysis (misspecification?)
William Revelle
lists at revelle.net
Mon Mar 9 06:20:12 CET 2009
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/
More information about the R-help
mailing list