# Optimizers

## What is the numerical approximation method used to find maximum likelihood estimator from log-likelihood function in OpenMx?

What is the numerical approximation method used to find maximum likelihood estimator from log-likelihood function in OpenMx?

2. How to deal with multiple estimators when you have to maximize log likelihood function here in OpenMx? Say profile likelihood or partial derivation (may not be the case).

3. Can some of you please provide me a document on how the OpenMx works on the maximization of log likelihood function to find MLE?

Thank you so much.

Arnond

## Starting values

When reading through the optimization innards of OpenMx, I came across this piece of code:

in npsolWrap.c, l.356:

if((x[k] == 0.0) && !disableOptimizer) {

x[k] += 0.1;

}

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## Why MLEs in a CFA model are different between analyses of raw data and covariance matrix data?

sample properties of SEM and then have the following question:

I would appreciate it if you could teach me why MLEs in a CFA model are

different between analyses of raw data and covariance matrix data in

OpenMx package of R. Are the optimization methods employed different?

The maximum difference I encountered is 0.084267.

When I compare the results, I adjusted their scales, i.e., multiplied by

sqrt(N/N-1) for factor loadings and by N/N-1 for error variances.

## convergence status OK but calculated Hessian with negative eigenvalue

I just found in a run that the calculated Hessian has a negative eigenvalue (which also result in NAs for some standard errors) and some of the gradients seems large. However, the convergence code is 0 so no error or warning is displayed. Should a warning be displayed in this case?

I tried another starting value and this problem goes away, with objective function decreases about 0.28, indicating the first run does not reach the minimum.

The code and data are in the attachment.

Thanks.

- Hao

## SEM without free parameters troubles OpenMX (and myself)

Today, I felt like fixing all my free parameters and call mxRun() on my model. I expected the optimizer to converge instantly or rather not to be invoked. Instead, it seems the backend is running into an infinite loop somehow. Maybe the backend needs to check the condition of no free parameters in the model.

## Referencing Data in an Algebra for mxAlgebraObjective

## Repeatability across platforms

I attach the script and data as a test case for the limits of similarities between architectures.

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## crash with raw data and mxMLObjective

> data(demoOneFactor)

> factorModel <- mxModel("One Factor",

+ mxMatrix("Full", 5, 1, values=0.2,

+ free=T, name="A"),

+ mxMatrix("Symm", 1, 1, values=1,

+ free=F, name="L"),

+ mxMatrix("Diag", 5, 5, values=1,

+ free=T, name="U"),

+ mxAlgebra(A %*% L %*% t(A) + U, name="R",

+ dimnames = list(names(demoOneFactor),

+ names(demoOneFactor))),

+ mxMLObjective("R"),

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## Crashing R in OS X

So I've recently been working on converting an mx script to OpenMx (file attached). I might be doing something I shouldn't, but the script caused R on my Mac to close w/out explanation or warning. Everything goes fine until I hit "mxRun." I ran this under Windows XP and got the following error:

> EstModel <- mxRun(CoupledModel)

Running CoupledModel

Error in mxRun(CoupledModel) :

BLAS/LAPACK routine 'DGEMM ' gave error code -13

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## likelihood statistic returned from npsol

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