[R] path analysis (misspecification?)

[Martin Batholdy]

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/