[R] Confirmatory factor analysis problems using sem package (works in Amos)

John Fox jfox at mcmaster.ca
Fri May 22 15:25:01 CEST 2009


Dear Solomon,

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
> Behalf Of S. Messing
> Sent: May-22-09 1:27 AM
> To: r-help at r-project.org
> Subject: [R] Confirmatory factor analysis problems using sem package
(works
> in Amos)
> 
> 
> Hello all,
> 
> I'm trying to replicate a confirmatory factor analysis done in Amos. 

Occasionally in an ill-conditioned problem, one program will produce a
solution and another won't. As a general matter, I'd expect Amos to be more
robust than sem() since Amos is written specifically for SEMs, while sem()
uses nlm(), a general-purpose optimizer.

> The
> idea is to compare a one-factor and a two-factor model.  I get the
following
> warning message when I run either model:
> 
> "Could not compute QR decomposition of Hessian.
> Optimization probably did not converge."
> 
> I have no idea what to do here.  

A general strategy is to set debug=TRUE in the call to sem() and see what
happens in the optimization. Then there are several things that you can do
to try to get the optimization to converge; see ?sem. In this case, however,
I wasn't able to get a solution.

The one-factor model is equivalent to a one-factor exploratory FA, which can
be fit by ML using factanal():

> factanal(factors=1, covmat=correl, n.obs=1100)

Call:
factanal(factors = 1, covmat = correl, n.obs = 1100)

Uniquenesses:
       pvote     jmposaff     jmnegaff     boposaff     bonegaff
obama.therm mccain.therm    oddcand.D   evencand.D 
       0.100        0.496        0.497        0.277        0.397
0.129        0.312        0.466        0.585 

Loadings:
             Factor1
pvote        -0.949 
jmposaff      0.710 
jmnegaff     -0.709 
boposaff     -0.850 
bonegaff      0.777 
obama.therm  -0.934 
mccain.therm  0.830 
oddcand.D     0.731 
evencand.D    0.645 

               Factor1
SS loadings      5.744
Proportion Var   0.638

Test of the hypothesis that 1 factor is sufficient.
The chi square statistic is 1710.03 on 27 degrees of freedom.
The p-value is 0

As you can see, the one-factor model fits the data very poorly (as does a
two-factor EFA); I suspect, but am not sure, that this is the source of the
problem in sem(). I couldn't get a solution from sem() even when I used the
factanal() solution as start values.


> I believe posters reported the same
> problem.  

In almost all cases, the models haven't been properly specified, which is
not the case here. Here, the model just doesn't fit the data.

> It seems that the ability to invert the correlation matrix may
> have something to do with this error, but solve(correl) yields a solution.

No, the input correlation matrix is positive-definite. sem() would have
complained if it were not:

> eigen(correl, only.values=TRUE)
$values
[1] 6.12561630 0.82418329 0.71616585 0.51263750 0.24467315 0.18248909
0.17024374
[8] 0.13905585 0.08493524


I'll keep your problem as a test case to see whether I can produce a
solution, possibly using a different optimizer -- as I mentioned, sem() uses
nlm().

Regards,
 John


> 
> Here are my correlation matrix and model specifications:
> 
> --------------------------- R CODE BEGIN
> ------------------------------------------------
> 
> library(sem)
> correl <- matrix(
> c(1.0000000,-0.6657822,0.6702089,0.7997673,-0.7225454,0.8992372,
> 				-0.8026491,-0.6715168,-0.5781565,-
> 0.6657822,1.0000000,-0.5107568,
> 				-0.5030886,0.6971188,-
> 0.6306937,0.7200848,0.5121227,0.4496810,
> 				0.6702089,-0.5107568,1.0000000,0.7276558,-
> 0.3893792,0.6043672,
> 				-0.7176532,-0.5247434,-0.4670362,0.7997673,-
> 0.5030886,0.7276558,
> 				1.0000000,-0.6251056,0.8164190,-0.6728515,-
> 0.6371453,-0.5531964,
> 				-0.7225454,0.6971188,-0.3893792,-
> 0.6251056,1.0000000,-0.7760765,
> 				0.6175124,0.5567924,0.4914176,0.8992372,-
> 0.6306937,0.6043672,
> 				0.8164190,-0.7760765,1.0000000,-0.7315507,-
> 0.6625136,-0.5814590,
> 				-0.8026491,0.7200848,-0.7176532,-
> 0.6728515,0.6175124,-0.7315507,
>
1.0000000,0.5910688,0.5096898,-0.6715168,0.5121227,-
> 0.5247434,
> 				-0.6371453,0.5567924,-
> 0.6625136,0.5910688,1.0000000,0.8106496,
> 				-0.5781565,0.4496810,-0.4670362,-
> 0.5531964,0.4914176,-0.5814590,
> 				0.5096898,0.8106496,1.0000000),
,nrow=9,ncol=9)
> 
> rownames(correl) = c("pvote", "jmposaff", "jmnegaff",
> 		"boposaff","bonegaff",
> 		"obama.therm", "mccain.therm",
> 		"oddcand.D", "evencand.D" )
> 
> colnames(correl) = c("pvote", "jmposaff", "jmnegaff",
> 		"boposaff","bonegaff",
> 		"obama.therm", "mccain.therm",
> 		"oddcand.D", "evencand.D" )
> 
> #One Factor Model:
> model.all <- specify.model()
> allmeasures -> pvote,				b1, NA
> allmeasures -> obama.therm,			b2, NA
> allmeasures -> mccain.therm,		b3, NA
> allmeasures -> jmposaff,			b4, NA
> allmeasures -> jmnegaff,			b5, NA
> allmeasures -> boposaff,			b6, NA
> allmeasures -> bonegaff,			b7, NA
> allmeasures -> oddcand.D,			b8, NA
> allmeasures -> evencand.D,			b9, NA
> allmeasures <-> allmeasures,		NA,1
> pvote <-> pvote,					v1, NA
> obama.therm <-> obama.therm,		v2, NA
> mccain.therm <-> mccain.therm,		v3, NA
> jmposaff <-> jmposaff,				v4, NA
> jmnegaff <-> jmnegaff,				v5, NA
> boposaff <-> boposaff,				v6, NA
> bonegaff <-> bonegaff,				v7, NA
> oddcand.D <-> oddcand.D,			v8, NA
> evencand.D <-> evencand.D,			v9, NA
> 
> 
> sem.all <- sem(model.all, correl, 1100)
> 
> summary(sem.all)
> 
> #Two Factor Model:
> model.vi <- specify.model()
> verbal -> pvote,					b1, NA
> verbal -> obama.therm,				b2, NA
> verbal -> mccain.therm,				b3, NA
> verbal -> jmposaff,					b4, NA
> verbal -> jmnegaff,					b5, NA
> verbal -> boposaff,					b6, NA
> verbal -> bonegaff,					b7, NA
> imp -> oddcand.D,					b8, NA
> imp -> evencand.D,					b9, NA
> imp <-> imp,						NA, 1
> verbal <-> verbal,					NA, 1
> pvote <-> pvote,					v1, NA
> obama.therm <-> obama.therm,		v2, NA
> mccain.therm <-> mccain.therm,		v3, NA
> jmposaff <-> jmposaff,				v4, NA
> jmnegaff <-> jmnegaff,				v5, NA
> boposaff <-> boposaff,				v6, NA
> bonegaff <-> bonegaff,				v7, NA
> oddcand.D <-> oddcand.D,			v8, NA
> evencand.D <-> evencand.D,			v9, NA
> imp <-> verbal,						civ, NA
> 
> sem.vi <- sem(model.vi, correl, 1100)
> summary(sem.vi)
> 
> --------------------------- R CODE END
> ------------------------------------------------
> 
> Thanks very much.
> 
> -Solomon
> --
> View this message in context: http://www.nabble.com/Confirmatory-factor-
> analysis-problems-using-sem-package-%28works-in-Amos%29-
> tp23664618p23664618.html
> Sent from the R help mailing list archive at Nabble.com.
> 
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