[R] path analysis (misspecification?)
Martin Batholdy
batholdy at googlemail.com
Mon Mar 9 05:29:40 CET 2009
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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