R help - Mar 2011 - Incorrect degrees of freedom in SEM model using lavaan

I have been trying to use lavaan (version 0.4-7) for a simple path model,
but the program seems to be computing far less degrees of freedom for my
model then it should have.  I have 7 variables, which should give (7)(8)/2 28
covariances, and hence 28 DF.  The model seems to only think I have 13
DF.  The code to reproduce the problem is below.  Have I done something
wrong, or is this something I should take to the developer?


library(lavaan)

myCov = matrix(c(24.40, 0, 0, 0, 0, 0, 0, .03, .03, 0, 0, 0, 0, 0, 6.75, -
.08, 519.38, 0, 0, 0, 0, .36, .01, 2.74, .18, 0, 0, 0, .51, .0, -.31, .02,
.2, .0, 0, -.17, .0, -1.6, -.04, .01, .25, 0, -.1, .02, -.03, .0, -.01, .01
, .02), nrow=7, byrow=TRUE, dimnames=list(c("Internet",
"Stress3",
"HHincome", "Race", "Age", "Gender",
"Stress1"), c("Internet", "Stress3",
"HHincome", "Race", "Age", "Gender",
"Stress1")))


model = '

Internet ~ HHincome + Race + Age + Gender + Stress1

Stress3 ~ Internet + HHincome + Race + Age + Gender + Stress1

'


fit=sem(model, sample.nobs=161, sample.cov=myCov, mimic.Mplus=FALSE)


#check the number of parameters being estimated

inspect(fit, what="free")


#Note the DF for the Chi-square is 0, when it should be 28-13 = 15

summary(fit)


Andrew Miles

	[[alternative HTML version deleted]]

Your model is saturated.

I think lavaan calculates the number of degrees of freedom this way:

DF = n*(n + 1)/2 - t - n.fix*(n.fix + 1)/2

n = number of variables
t = number of free parameters
n.fix = number of fixed exogenous variables

So, if you fix the exogenous variables, as in mimic = "Mplus":

DF = 28 - 13 - 15 = 0

If you don't, as in mimic = "EQS":

DF = 28 - 28 - 0 = 0

You are probably not considering the variances and covariances of the
exogenous variables to arrive at 15 degrees of freedom:

model = '

Internet + Stress3 ~ HHincome + Race + Age + Gender + Stress1

Stress3 ~ Internet

HHincome ~~ 0*Race + 0*Age + 0*Gender + 0*Stress1
Race ~~  0*Age + 0*Gender + 0*Stress1
Age ~~ 0*Gender + 0*Stress1
Gender ~~  0*Stress1

HHincome ~~ 1*HHincome
Race ~~ 1*Race
Age ~~ 1*Age
Gender ~~ 1*Gender
Stress1 ~~ 1*Stress1
'

fit = lavaan(model, sample.nobs=161, sample.cov=myCov, int.ov.free T,
int.lv.free = F, auto.fix.first = T, auto.fix.single = T,
auto.resid.var = T, auto.cov.lv.x = T, auto.cov.y = T,
mimic = "EQS")
summary(fit)

Cheers,

Gustavo.



On Thu, Mar 17, 2011 at 9:50 AM, Andrew Miles <rstuff.miles at gmail.com>
wrote:
> I have been trying to use lavaan (version 0.4-7) for a simple path model,
> but the program seems to be computing far less degrees of freedom for my
> model then it should have. ?I have 7 variables, which should give (7)(8)/2
> 28 covariances, and hence 28 DF. ?The model seems to only think I have 13
> DF. ?The code to reproduce the problem is below. ?Have I done something
> wrong, or is this something I should take to the developer?
>
>
> library(lavaan)
>
> myCov = matrix(c(24.40, 0, 0, 0, 0, 0, 0, .03, .03, 0, 0, 0, 0, 0, 6.75, -
> .08, 519.38, 0, 0, 0, 0, .36, .01, 2.74, .18, 0, 0, 0, .51, .0, -.31, .02,
> .2, .0, 0, -.17, .0, -1.6, -.04, .01, .25, 0, -.1, .02, -.03, .0, -.01, .01
> , .02), nrow=7, byrow=TRUE, dimnames=list(c("Internet",
"Stress3",
> "HHincome", "Race", "Age",
"Gender", "Stress1"), c("Internet",
"Stress3",
> "HHincome", "Race", "Age",
"Gender", "Stress1")))
>
>
> model = '
>
> Internet ~ HHincome + Race + Age + Gender + Stress1
>
> Stress3 ~ Internet + HHincome + Race + Age + Gender + Stress1
>
> '
>
>
> fit=sem(model, sample.nobs=161, sample.cov=myCov, mimic.Mplus=FALSE)
>
>
> #check the number of parameters being estimated
>
> inspect(fit, what="free")
>
>
> #Note the DF for the Chi-square is 0, when it should be 28-13 = 15
>
> summary(fit)
>
>
> Andrew Miles
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

Dear Andrew,

The reported df in lavaan is 0 which is correct. It is because this
path model is saturated. "28" is not the df, it is the no. of pieces
of information. The no. of parameter estimates is also 28. Thus, the
df is 0.

However, you are correct that there are only 13, not 28, free
parameters reported by lavaan. It is because "fixed.x=TRUE" was
implicitly used in your example (see ?sem). Since HHincome + Race +
Age + Gender + Stress1 are predictors, they are fixed at their sample
values when "fixed.x=TRUE" was used. And their covariance elements are
not involved in calculating the df.

If you want to mirror the behaviors in other SEM packages, you may try:

fit2 <- sem(model, sample.nobs=161, sample.cov=myCov, fixed.x=FALSE)
inspect(fit2, what="free")
summary(fit2)

Hope it helps.
Mike
-- 
---------------------------------------------------------------------
?Mike W.L. Cheung? ? ? ? ? ? ?? Phone: (65) 6516-3702
?Department of Psychology? ? ?? Fax:?? (65) 6773-1843
?National University of Singapore
?http://courses.nus.edu.sg/course/psycwlm/internet/
---------------------------------------------------------------------


On Thu, Mar 17, 2011 at 8:50 PM, Andrew Miles <rstuff.miles at gmail.com>
wrote:
> I have been trying to use lavaan (version 0.4-7) for a simple path model,
> but the program seems to be computing far less degrees of freedom for my
> model then it should have. ?I have 7 variables, which should give (7)(8)/2
> 28 covariances, and hence 28 DF. ?The model seems to only think I have 13
> DF. ?The code to reproduce the problem is below. ?Have I done something
> wrong, or is this something I should take to the developer?
>
>
> library(lavaan)
>
> myCov = matrix(c(24.40, 0, 0, 0, 0, 0, 0, .03, .03, 0, 0, 0, 0, 0, 6.75, -
> .08, 519.38, 0, 0, 0, 0, .36, .01, 2.74, .18, 0, 0, 0, .51, .0, -.31, .02,
> .2, .0, 0, -.17, .0, -1.6, -.04, .01, .25, 0, -.1, .02, -.03, .0, -.01, .01
> , .02), nrow=7, byrow=TRUE, dimnames=list(c("Internet",
"Stress3",
> "HHincome", "Race", "Age",
"Gender", "Stress1"), c("Internet",
"Stress3",
> "HHincome", "Race", "Age",
"Gender", "Stress1")))
>
>
> model = '
>
> Internet ~ HHincome + Race + Age + Gender + Stress1
>
> Stress3 ~ Internet + HHincome + Race + Age + Gender + Stress1
>
> '
>
>
> fit=sem(model, sample.nobs=161, sample.cov=myCov, mimic.Mplus=FALSE)
>
>
> #check the number of parameters being estimated
>
> inspect(fit, what="free")
>
>
> #Note the DF for the Chi-square is 0, when it should be 28-13 = 15
>
> summary(fit)
>
>
> Andrew Miles
>
> ? ? ? ?[[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>