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Carrying out latent profile analysis (LPA) by adapting code examples for a two-factor model and growth mixture models

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Picture of user. joshuarosenberg Joined: 07/06/2017
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Mixture Distribution and Latent Class Models
Hi everyone. I'm new to both OpenMX and mixture models and am trying to do a latent profile analysis, or a mixture model (initially with two classes) of a Two-factor Model.

With the good documentation and code examples for Two-factor Models and mixture models (specifically the code for a growth mixture model), I tried to combine the two. However, when I run it, I get the following error that I'm having trouble debugging:

Error: The reference 'Class1.fitfunction' is unknown in the algebra named 'Latent Profile Model.mixtureObj'

Can you help point me in the right direction? A reproducible example is given in the attached code. Thank you in advance for considering this!

Replied on Mon, 08/14/2017 - 09:33
Picture of user. jpritikin Joined: 05/23/2012

I made a few corrections to the attached code to let it run. I'm not sure whether its exactly the model you want, but it no longer fails to run.

Do you use source code control? You probably could have figured this out yourself if you did. There are lots of online tutorials to help you get up to speed such as the [one at github](https://try.github.io/)

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Replied on Mon, 08/14/2017 - 11:39
Picture of user. jpritikin Joined: 05/23/2012

Well, I might be wrong about how you put that script together. What it looked like is that you copied some working code and modified it. If you indeed followed this method then you could have examined each change to determine whether the change caused the script to break. Going back to an earlier version of the script is facilitated by source code control. In any case, I'm glad it's working now.
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Replied on Mon, 08/14/2017 - 15:41
Picture of user. joshuarosenberg Joined: 07/06/2017

In comparing them (as part of making a commit on GitHub), I now see some obvious errors (and one that was not obvious to me) - I'm sorry about that. Thanks again for the (quick) help and sorry for the (easy-to-fix) problems in the code!
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Replied on Wed, 08/16/2017 - 14:16
Picture of user. joshuarosenberg Joined: 07/06/2017

Thank you again. I'm circling back to this and noticed that the estimates for the free parameters seem to only be for Class 1 - whereas the estimates for this growth mixture model example here are for both Class 1 and Class 2.

Could I ask if you could help me to modify this code to allow both classes to have free parameters estimated in this example - now here on GitHub?

Thanks so much.

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Replied on Thu, 08/17/2017 - 12:14
Picture of user. joshuarosenberg Joined: 07/06/2017

Thank you - when I remove the labels, so change the means part of the model specification from:

means <- mxPath( from="one", to=c("x1","x2","x3","y1","y2","y3","F1","F2"),
arrows=1,
free=c(T,T,T,T,T,T,F,F), values=c(1,1,1,1,1,1,0,0),
labels=c("meanx1","meanx2","meanx3",
"meany1","meany2","meany3",NA,NA) )
To:

means <- mxPath( from="one", to=c("ce","be","ae"),
arrows=1,
free=c(T,T,T), values=c(1,1,1)
)

I now see different estimates for Class1 and Class2 mean parameters, but they have the same values (though different standard errors).

I pushed the change to the example here.

Thank you again very much for helping me work through this.

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Replied on Thu, 08/17/2017 - 15:03
Picture of user. joshuarosenberg Joined: 07/06/2017

I *think* per row - something akin to a Latent Profile Analysis or Latent Class Analysis, in which each observation is assigned a posterior probability to one of the classes (and means and residuals variances for each of the classes are estimated).
Thank you again
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Replied on Sat, 08/19/2017 - 10:07
Picture of user. AdminHunter Joined: 03/01/2013

An easy way to do standard mixture models is to use EasyMx, an R package that is a wrapper around OpenMx. Run this:


install.packages("EasyMx")
require(EasyMx)
?EasyMx # look at the help page for the package
?emxMixtureModel # look at the help page for the mixture model helper

The general idea with the mixture model helper is that you give it a list of MxModel objects and it creates the needed mixture pieces. As I understand it, a latent profile analysis is a mixture model in which each mixture component freely estimates all of its means, variances, and covariances. Here's the example latent profile model:


# Latent Profile Example
require(EasyMx)

m1 <- omxSaturatedModel(demoOneFactor)[[1]]
m1 <- mxRename(m1, 'profile1')

m2 <- omxSaturatedModel(demoOneFactor)[[1]]
m2 <- mxRename(m2, 'profile2')

mod <- emxMixtureModel(list(m1, m2), data=demoOneFactor, run=TRUE)
summary(mod)
coef(mod)

mxGetExpected(mod$profile1, 'covariance')
mxGetExpected(mod$profile1, 'means')
mxGetExpected(mod$profile2, 'covariance')
mxGetExpected(mod$profile2, 'means')

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Replied on Tue, 08/22/2017 - 10:21
Picture of user. joshuarosenberg Joined: 07/06/2017

If I can, please allow me to clarify.

Can I ask for help specifying models with:

- Varying means, fixed residuals and no covariances (covariances within profiles are set to 0)
- Varying means, fixed residual variances and covariances

My understanding is the model fit in the example above is:

- Varying means, varying residual variances and covariances.

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Replied on Tue, 08/22/2017 - 11:49
Picture of user. neale Joined: 07/31/2009

In many applications a latent profile model makes the same assumptions as a latent class analysis, so it has the (questionable) assumption of conditional independence of the measures, given class membership. Thus only the means and variances, not the covariances, would be free. If I controlled the nomenclature, I'd term models with non-zero covariances as general mixture distributions, of which a factor mixture model is one, and only diagonal covariance structures as latent profile, consistent with latent class models. But Hunter is as usual correct, see, e.g., http://members.home.nl/jeroenvermunt/ermss2004f.pdf
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Replied on Tue, 08/22/2017 - 20:28
Picture of user. joshuarosenberg Joined: 07/06/2017

Thanks for the clarifying info. (and the link).

If only the means and variances would be freed, how can: a) the model in which both are freed and b) the model in which only the means are freed be estimated? And am I understanding correctly that the model (using EasyMx) specified above would be the model corresponding to a) the model in which both means and variances are freely estimated?

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Replied on Wed, 08/23/2017 - 14:13
Picture of user. AdminHunter Joined: 03/01/2013

The function omxSaturatedModel is just a quick way to build a saturated model. It returns a list where the first element is the saturated model (free means, free variances, free covariances), and the second element is the independence model (i.e., has free means, free variances, and zero covariances). The input to emxMixtureModel is just a list of models and a data set. I used omxSaturatedModel just as a one-line way to build a model. You'll have to do some thinking about what model you want to specify for the components of the mixture, and build those models.

You can constrain parameters to be equal by given them the same "label".

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Replied on Mon, 01/07/2019 - 13:06
Picture of user. AdminRobK Joined: 01/24/2014

It would be something like this:

#The two mixture proportions are prior class-membership probabilities
#for drawing inferences about each participant:
pri1 <- gmmFit$expectation$output$weights[1]
pri2 <- gmmFit$expectation$output$weights[2]
#The fitfunctions of the two component models return a vector of participants'
#raw (not log) likelihoods:
lik1 <- as.vector(gmmFit$Class1$fitfunction$result)
lik2 <- as.vector(gmmFit$Class2$fitfunction$result)
#Calculate participants' marginal likelihoods (probably not be necessary):
marglik <- (pri1*lik1) + (pri2*lik2)
#Calculate participants' posterior densities:
post1 <- (pri1*lik1)/marglik
post2 <- (pri2*lik2)/marglik
#Create a matrix of participants' posterior densities for the two components,
#and then normalize them into probabilities:
posteriors <- cbind(post1,post2)/rowSums(cbind(post1,post2))
#^^^Since each row of the matrix needs to be normalized, you probably
#don't need the marginal likelihoods.

Neale or Hunter can correct me if I've made a mistake anywhere.

I wonder if this is something that should have a dedicated helper function to do it?

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Replied on Wed, 01/02/2019 - 13:19
No user picture. KB Joined: 12/19/2018

Hi,

I am also new to OpenMx and like Joshua, I am trying to run a simple LPA with two normal component densities. I was wondering, is there a way to easily change the initial values in EasyMx? Or if I want that kind of flexibility do I need to go back to working directly with OpenMx?

Thanks!

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Replied on Thu, 01/03/2019 - 08:18
Picture of user. AdminNeale Joined: 03/01/2013

Once you have used a helper function to build a generic model, it is easy to modify it for your specific application. Umx has some parameter fixing/freeing functions. The base omxSetParameters() can also be used. Finally, model elements can usually be changed directly with, e.g.,

model$matrix$values <- c(1,5)

or

model$matrix <- mxMatrix(...)

to replace a matrix inside a model.
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