[R] Incorrect degrees of freedom in SEM model using lavaan

[Gustavo Carvalho]

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]]
>
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