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Convergence problems

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metavid's picture
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Joined: 06/23/2014 - 16:15
Convergence problems
AdminRobK's picture
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Joined: 01/24/2014 - 12:15
Oddly enough, I also

Oddly enough, I also triggered the spam filter when I tried to reply with my non-admin account.

Concerning your second question: in general, BIC isn't additive. For a given model and dataset, BIC = -2logL + log(N)p, where p = number of free parameters. If we have Model_1 and Model_2, each applied to separate and independent datasets, and having no free parameters in common,
BIC_1 = -2logL_1 + log(N_1)
p_1
BIC_2 = -2logL_2 + log(N_2)p_2
If we combine the two models into a supermodel,
overall BIC = -2logL_1 + -2logL_2 + log(N_1 + N_2)
(p_1 + p_2) != BIC_1 + BIC_2

Concerning your first question: I had to make a few small edits to your syntax to reproduce the error you're reporting. Even so, there's nothing obviously wrong with your setup, so I'm not sure why optimization fails on its first function evaluation for you. You could try the following syntax, which uses the rarely-invoked independent=T argument, and see if it does what you want:

mgroups <- mxModel("mg",
                   mxModel("g1",independent = T,
                           mxMatrix( type="Full", nrow=14, ncol=1, values=rep(1,14), free=rep(F,14),name="facLoadingsE82" ),
                           mxMatrix( type="Symm", nrow=1, ncol=1, values=1, free=F, name="facVariancesE82" ),
                           mxMatrix( type="Diag", nrow=14, ncol=14, values=rep(1,14), free=rep(F,14), name="resVariancesE82" ),
                           mxMatrix( type="Full", nrow=1, ncol=14, values=rep(3.5,14), free=rep(F,14), name="varMeansE82" ),
                           mxMatrix( type="Full", nrow=1, ncol=1, values=1, free=F,name="facMeansE82" ),
                           mxAlgebra( expression= facLoadingsE82 %&% facVariancesE82 + resVariancesE82,name="expCovE82" ),
                           mxAlgebra(expression= varMeansE82 + t(facLoadingsE82 %*% facMeansE82),name="expMeanE82" ),
                           mxData(traintE[traintE$year==1982,],type="raw"),
                           mxFIMLObjective(covariance="expCovE82", means="expMeanE82", dimnames=extn)
                   ),
                   mxModel("g2",independent = T,
                           mxMatrix( type="Full", nrow=14, ncol=1, values=rep(1,14), free=rep(F,14),name="facLoadingsE83" ),
                           mxMatrix( type="Symm", nrow=1, ncol=1, values=1, free=F, name="facVariancesE83" ),
                           mxMatrix( type="Diag", nrow=14, ncol=14, values=rep(1,14), free=rep(F,14),name="resVariancesE83" ),
                           mxMatrix( type="Full", nrow=1, ncol=14, values=rep(3.5,14), free=rep(F,14),name="varMeansE83" ),
                           mxMatrix( type="Full", nrow=1, ncol=1, values=1, free=F,name="facMeansE83" ),
                           mxAlgebra( expression= facLoadingsE83 %&% facVariancesE83 + resVariancesE83,name="expCovE83" ),
                           mxAlgebra(expression= varMeansE83 + t(facLoadingsE83 %*% facMeansE83),name="expMeanE83" ),
                           mxData(traintE[traintE$year==1983,],type="raw"),
                           mxFIMLObjective(covariance="expCovE83", means="expMeanE83", dimnames=extn)
                   ),
                   mxModel("g3",independent = T,
                           mxMatrix( type="Full", nrow=14, ncol=1, values=rep(1,14), free=rep(F,14),name="facLoadingsE84" ),
                           mxMatrix( type="Symm", nrow=1, ncol=1, values=1, free=F, name="facVariancesE84" ),
                           mxMatrix( type="Diag", nrow=14, ncol=14, values=rep(1,14), free=rep(F,14), name="resVariancesE84" ),
                           mxMatrix( type="Full", nrow=1, ncol=14, values=rep(3.5,14), free=rep(F,14) ,name="varMeansE84" ),
                           mxMatrix( type="Full", nrow=1, ncol=1, values=1, free=F,name="facMeansE84" ),
                           mxAlgebra( expression= facLoadingsE84 %&% facVariancesE84 + resVariancesE84,name="expCovE84" ),
                           mxAlgebra(expression= varMeansE84 + t(facLoadingsE84 %*% facMeansE84),name="expMeanE84" ),
                           mxData(traintE[traintE$year==1984,],type="raw"),
                           mxFIMLObjective(covariance="expCovE84", means="expMeanE84", dimnames=extn)),
                   mxAlgebra(g1.objective + g2.objective + g3.objective,
                             name="LL"),
                   mxAlgebraObjective("LL")
)
mgroupsrun <- mxRun(mgroups)

EDIT: The multigroup model above will run even without the independent=T argument under the OpenMx 2.0 beta.

metavid's picture
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Joined: 06/23/2014 - 16:15
Another question

Hi,

Thank you for your elaborate response.

I have another question.
1. Are the formulae you provided (for BIC) merely applicable to the BIC from Openmx with parameter penalty?
2. How does the formula for the BIC taking into account degrees-of-freedom penalty look like?

Again, thank you.

mhunter's picture
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Joined: 07/31/2009 - 15:26
Applies to both
  1. The formulas were given for the parameters penalty, but the same idea applies for the df penalty. Neither penalty has they additive property you're looking for.

Parameters penalty
BIC_1 = -2logL_1 + log(N_1)p_1
BIC_2 = -2logL_2 + log(N_2)
p_2

overall BIC = -2logL_1 + -2logL_2 + log(N_1 + N_2)*(p_1 + p_2) != BIC_1 + BIC_2

  1. Here's the df penalty.
    df penalty
    BIC_1 = -2logL_1 + log(N_1)df_1
    BIC_2 = -2logL_2 + log(N_2)
    df_2

overall BIC = -2logL_1 + -2logL_2 + log(N_1 + N_2)*(df_1 + df_2) != BIC_1 + BIC_2

The key is that the log(N_1 + N_2) can't be broken apart.

metavid's picture
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Joined: 06/23/2014 - 16:15
Appreciate it

Thanks again for the clarification!

metavid's picture
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Joined: 06/23/2014 - 16:15
Summary statistics

Good day,

I was able to run the code above, using independent=T. The thing now is, that I have to have the summary statistics, specifically the information criteria (AIC and BIC with both parameter and df penality). mxRun went well but now I can't seem to compute the information criteria given by summary() due to a warning: argument 'invSDs' is missing, with no default. Is there a way to resolve this or should I stick with the formulae, given that the LL for the model is provided from mxRun (but not the AIC/BIC)?

Thanks.

AdminRobK's picture
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Joined: 01/24/2014 - 12:15
Try summary(mgroupsrun$g1), etc.

Sorry, I should have mentioned that summary() works differently with independent=TRUE included in every submodel. In such a case, each submodel is handled separately from all the others, and the computer doesn't bundle them together as parts of a supermodel. You're really only getting a -2loglikelihood for the supermodel because you requested it as an algebra.

You can see a summary for each submodel with summary(mgroupsrun$g1), and likewise for g2 and g3. Since you know the formulae for BIC with different penalties, thanks to M. Hunter below, you could just use the supermodel -2loglikelihood and compute the supermodel BIC from it.

Using independent=TRUE shouldn't be necessary to do what you want to do in the first place, so the problem that prompted you to make your original post is unexpected, and is probably a bug--fortunately one not present in the 2.0 beta.

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