Why mxTryHardOrdinal（）dosen't report start values?

I am a novice user and don't understand the terms and theories of SEM and Cholesky thoroughly.

1.What I can tell from your suggestions is that it is **MxConstraints** that induce the warning. So, I delete the line:
mxMatrix( type="Unit", nrow=nv, ncol=1, name="Unv" ),
mxConstraint( expression=diag2vec(V)==Unv, name="VarL" )
and then no such warnings reported.

Acctually, I don't understand why the demo codes must constrain A+C+E=1, since without this constrain I can also get standardized h2, c2,e2 and rA, rC, rE through these lines:
mxAlgebra( expression=A+C+E, name="V" ),
mxMatrix( type="Iden", nrow=nv, ncol=nv, name="I"),
mxAlgebra( expression=solve(sqrt(I*V)), name="iSD"),
mxAlgebra( expression=solve(sqrt(I*V))%&%V, name ="Rph" ),
mxAlgebra( expression=solve(sqrt(I*A))%&%A, name ="Ra" ), #cov2cor()
mxAlgebra( expression=solve(sqrt(I*C))%&%C, name ="Rc" ),
mxAlgebra( expression=solve(sqrt(I*E))%&%E, name ="Re" ),
# Algebra to compute standardized variance components
mxAlgebra( expression=A+C+E, name="V" ),
mxAlgebra( expression=A/V, name="h2"),
mxAlgebra( expression=C/V, name="c2"),
mxAlgebra( expression=E/V, name="e2"),
mxAlgebra(expression=iSD %*% a,name="stda"),
mxAlgebra(expression=iSD %*% c,name="stdc"),
mxAlgebra(expression=iSD %*% e,name="stde")
I am not sure if this is right.

2. Another theory I become aware of is that Cholesky parameterization constrains the A, C, and E covariance matrices must be positive-definite, and direct-symmetric parameterization does not. What's more, when I use Cholesky parameterization, the summary of the model report that:

**Information matrix is not positive definite (not at a candidate optimum).
Be suspicious of these results. At minimum, do not trust the standard errors.**

It seems that my model violate the assumption of Cholesky parameterization. So I turn to use the "direct-symmetric" parameterization with such lines:
baseACE <- mxModel('Base',
mxMatrix( type="Full", nrow=2, ncol=2, free=T, values=svb,labels=labeta, name="Beta"),
mxMatrix( type="Zero", nrow=1, ncol=2, name="meanG" ), # or type="Zero"

)
Similarly, I **delete the constraint of A+C+E=1** from the demo codes I found. And then I try to fit AE-ACE, ACE-AE and ACE-ACE without C overlap through such lines:
#C for p1 dropped,
dropcp1 <- omxSetParameters(AceModel,labels="Base.C[1,1]",free=F,values=0,name="dropcp1")
#C for p2 dropped,
dropcp1 <- omxSetParameters(AceModel,labels="Base.C[2,2]",free=F,values=0,name="dropcp2")
#C for p1p2 overlap dropped,
dropcp1 <- omxSetParameters(AceModel,labels="Base.C[1,2]",free=F,values=0,name="dropcp1p2")

Ultimately, the results reported by Cholesky parameterization and direct-symmetric parameterization are similar. So, I decide to use Cholesky parameterization and just delete the constraint of A+C+E=1 as I mentioned above.

I'm not sure if I truely get your point and really lookforward to your comment and suggestions.

Thanks again.

1. I truely run set.seed(1) firstly whenever running mxTryHardOrdinal() and mxTryHard(), but the numbers in the forth/fifth decimal place of parameters are different, please see picture. Is such slight inconsistency normal?

2. After I run this line:
mxOption( NULL, "mvnRelEps", value= mxOption(NULL, key="mvnRelEps")/5)
mxTryHard() can find solutions, but the results are still instable. It might find solutions after different attempts, or sometimes it still showed"solution not found". I don't know if this is normal,too.

> set.seed(190503)
> eCTCToFit<- mxTryHard(eCTCToModel, intervals=F,extraTries = 10,finetuneGradient=FALSE)

Solution found! Final fit=5350.5776 (started at 9974.4539) (1 attempt(s): 1 valid, 0 errors)

3. Now it seems that I can still trust the results of mxTryHardOrdinal() , since mxTryHard() also works and the estimated parameters are relatively stable(unless the parameters should be exactly the same whenever I run the same code).

And I need to set exhaustive=T , but I still unsure about the number of *extratries*. Because I don't want to spend a lot of time running models(especially I need to fit about 10 nested models), and on the other hand I'm afraid of the small number of attempt I set is not enough to find the best result. If you don't have another suggestions, I would set extratries=15.

At last, maybe such issues I struggled with are really unnecessary, really thanks for your time!

I wanted to calcualte how much of the observational association between two phenotypes is due to A,C and E, and I added these lines to the models:

# the proportion of ace influences contributing to the overlap
mxAlgebra( expression=sqrt(h2[1,1])*sqrt(h2[2,2])*Ra[1,2]/Rph[1,2],name = "pa"),
mxAlgebra( expression=sqrt(c2[1,1])*sqrt(c2[2,2])*Rc[1,2]/Rph[1,2],name = "pc"),
mxAlgebra( expression=sqrt(e2[1,1])*sqrt(e2[2,2])*Re[1,2]/Rph[1,2],name = "pe")

Subsequently I found that if Ra/Rc/Re is negative, then pa/pc/pe is also might be negative, but they represent proportions and should be positive and less than 1. I don't know how to explain.

Thank you very much!

I aim to fit nested ACE models by dropping A/C/E step by step and to test if these nested models result in a significant deterioration of the fit(all these models are compared to full ACE model).

As it shows in the uploaded picture, A for smoke, overlap and E for overlap can be dropped from the full ACE model, but the best-fitting model is the model with A for smoke and overlap dropped( model NO.15) . If I choose to report the results of NO.15 model, then the CI of rE (E correlation) contains 0.

So, my question is that which model I should choose, the best-fitting model(model NO.15) or the model dropping all the variances/covariances that can be dropped(model NO.16).

Thanks!

Many thanks!