A question on sex limitation model

Hi, I was running the sex limitation model script from http://www.vipbg.vcu.edu/HGEN619_2014/twinHet5AceCon.R and I'm quite surprised that although the initial model fitting shows that the standardized af, cf, ef and am, cm, em values differ greatly, mxCompare reveals no significant difference between the initial model and the homogeneity ACE model. Is there any possible explanation for this?

Thanks!

Here's what I got:
> QualAceSum <- summary(QualAceFit)
> QualAceSum$pa
name matrix row col Estimate Std.Error lbound ubound lboundMet uboundMet
1 af11 af 1 1 -0.04197853 0.069535675 NA NA FALSE FALSE
2 cf11 cf 1 1 0.10788236 0.027485716 NA NA FALSE FALSE
3 ef11 ef 1 1 0.09560371 0.008996776 NA NA FALSE FALSE
4 am11 am 1 1 -0.12227226 0.027188245 NA NA FALSE FALSE
5 cm11 cm 1 1 0.05321686 0.054393710 NA NA FALSE FALSE
6 em11 em 1 1 0.05450773 0.011454815 NA NA FALSE FALSE
7 meanf MZf.expMeanGf 1 STTidTrans1 0.36583189 0.014897526 NA NA FALSE FALSE
8 meanm MZm.expMeanGm 1 STTidTrans1 0.39985695 0.025581764 NA NA FALSE FALSE
9 rc11 DZo.rc 1 1 1.00000000 1.791567033 0 1 FALSE TRUE

> round(QualAceFit@output$estimate,4)
af11 cf11 ef11 am11 cm11 em11 meanf meanm rc11
-0.0420 0.1079 0.0956 -0.1223 0.0532 0.0545 0.3658 0.3999 1.0000

> round(cbind(QualAceFit$VarsZf@result,QualAceFit$VarsZm@result),4)
Af Cf Ef SAf SCf SEf Am Cm Em SAm SCm SEm
[1,] 0.0018 0.0116 0.0091 0.0782 0.5163 0.4055 0.015 0.0028 0.003 0.7204 0.1365 0.1432
>
> QualSat <- mxRefModels(QualAceFit, run=TRUE)
Running Saturated QualACE
Running Independence QualACE
> mxCompare(QualSat,QualAceFit)
base comparison ep minus2LL df AIC diffLL diffdf p
1 Saturated QualACE 25 -268.5467 182 -632.5467 NA NA NA
2 Saturated QualACE QualACE 9 -250.7103 198 -646.7103 17.83638 16 0.333565
3 Independence QualACE 20 -220.9663 187 -594.9663 NA NA NA
4 Independence QualACE QualACE 9 -250.7103 198 -646.7103 -29.74397 11 1.000000
>
> # ------------------------------------------------------------------------------
> # FIT SUBMODELS
>
> # Run non-scalar Sex Differences ACE model
> QuanAceModel <- mxModel( QualAceFit, name="QuanACE" )
> QuanAceModel <- omxSetParameters( QuanAceModel, labels="rc11", free=FALSE, values=1 )
> QuanAceFit <- mxRun(QuanAceModel)

Running QuanACE
> round(QuanAceFit@output$estimate,4)
af11 cf11 ef11 am11 cm11 em11 meanf meanm
-0.0420 0.1079 0.0956 -0.1223 0.0532 0.0545 0.3658 0.3999
> round(cbind(QuanAceFit$VarsZf@result,QuanAceFit$VarsZm@result),4)
Af Cf Ef SAf SCf SEf Am Cm Em SAm SCm SEm
[1,] 0.0018 0.0116 0.0091 0.0782 0.5163 0.4055 0.015 0.0028 0.003 0.7204 0.1365 0.1432
>
> # Run Homogeneity ACE model
> HomAceModel <- mxModel( QuanAceFit, name="HomACE" )
> HomAceModel <- omxSetParameters( HomAceModel, labels=c("af11","am11"), free=TRUE, values=.6, newlabels='a11' )
> HomAceModel <- omxSetParameters( HomAceModel, labels=c("cf11","cm11"), free=TRUE, values=.6, newlabels='c11' )
> HomAceModel <- omxSetParameters( HomAceModel, labels=c("ef11","em11"), free=TRUE, values=.6, newlabels='e11' )
> HomAceFit <- mxRun(HomAceModel)

Running HomACE
> round(HomAceFit@output$estimate,4)
a11 c11 e11 meanf meanm
0.0681 -0.0961 0.0901 0.3671 0.3972

> round(cbind(HomAceFit$VarsZf@result,HomAceFit$VarsZm@result),4)
Af Cf Ef SAf SCf SEf Am Cm Em SAm SCm SEm
[1,] 0.0046 0.0092 0.0081 0.211 0.4197 0.3692 0.0046 0.0092 0.0081 0.211 0.4197 0.3692
>
> # ------------------------------------------------------------------------------
>
> # Print Comparative Fit Statistics
> AceNested <- list(QuanAceFit,HomAceFit)
> mxCompare(QualAceFit,AceNested)
base comparison ep minus2LL df AIC diffLL diffdf p
1 QualACE 9 -250.7103 198 -646.7103 NA NA NA
2 QualACE QuanACE 8 -250.7103 199 -648.7103 -1.818989e-12 1 1.0000000
3 QualACE HomACE 5 -245.5911 202 -649.5911 5.119166e+00 4 0.2752874
>
> round(QualAceFit@output$estimate,4)
af11 cf11 ef11 am11 cm11 em11 meanf meanm rc11
-0.0420 0.1079 0.0956 -0.1223 0.0532 0.0545 0.3658 0.3999 1.0000

> round(QuanAceFit@output$estimate,4)
af11 cf11 ef11 am11 cm11 em11 meanf meanm
-0.0420 0.1079 0.0956 -0.1223 0.0532 0.0545 0.3658 0.3999

> round(HomAceFit@output$estimate,4)
a11 c11 e11 meanf meanm
0.0681 -0.0961 0.0901 0.3671 0.3972
> round(rbind(cbind(QualAceFit$VarsZf@result,QualAceFit$VarsZm@result),
+ cbind(QuanAceFit$VarsZf@result,QuanAceFit$VarsZm@result),
+ cbind(HomAceFit$VarsZf@result,HomAceFit$VarsZm@result)),4)

Af Cf Ef SAf SCf SEf Am Cm Em SAm SCm SEm
[1,] 0.0018 0.0116 0.0091 0.0782 0.5163 0.4055 0.0150 0.0028 0.0030 0.7204 0.1365 0.1432
[2,] 0.0018 0.0116 0.0091 0.0782 0.5163 0.4055 0.0150 0.0028 0.0030 0.7204 0.1365 0.1432
[3,] 0.0046 0.0092 0.0081 0.2110 0.4197 0.3692 0.0046 0.0092 0.0081 0.2110 0.4197 0.3692