S. Messing
2009-May-22 05:27 UTC
[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. 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. I believe posters reported the same
problem. It seems that the ability to invert the correlation matrix may
have something to do with this error, but solve(correl) yields a solution.
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.
John Fox
2009-May-22 13:25 UTC
[R] Confirmatory factor analysis problems using sem package (works in Amos)
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 thefollowing> 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. > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guidehttp://www.R-project.org/posting-guide.html> and provide commented, minimal, self-contained, reproducible code.