umxCP with two latent variables that loads in only part of the indicators

Hi Luis

I can't test because tidyverse doesn't exist for my version of R (4.0.3 which has been out ~2 months). But I can tell you how to do it. umxCP sets up OpenMx models with matrices. Most of these are in the 'top' model within the model that umxCP returns.
For example, the a paths are estimated in matrix a_cp, which we can see an example of by running the example from the ?umxCP help documentation.

$a_cp
DiagMatrix 'a_cp'

$labels
[,1] [,2] [,3]
[1,] "a_cp_r1c1" NA NA
[2,] NA "a_cp_r2c2" NA
[3,] NA NA "a_cp_r3c3"

$values
[,1] [,2] [,3]
[1,] 0.3191584 0.0000000 0.0000000
[2,] 0.0000000 0.5930313 0.0000000
[3,] 0.0000000 0.0000000 0.6918959

$free
[,1] [,2] [,3]
[1,] TRUE FALSE FALSE
[2,] FALSE TRUE FALSE
[3,] FALSE FALSE TRUE

$lbound
[,1] [,2] [,3]
[1,] 0 NA NA
[2,] NA 0 NA
[3,] NA NA 0


If you wish to allow the factors to correlate, you could use the Cholesky approach, which simply means freeing up the elements in the lower triangle of the a_cp, c_cp and e_cp matrices. If you only have 2 factors, this is easy because there's only one element in the lower triangle, so you could do something like this as Step 1:

model$top$a_cp$free[2,1] <- TRUE
model$top$c_cp$free[2,1] <- TRUE
model$top$e_cp$free[2,1] <- TRUE


Step 2 is to change the factor loading matrix, which is (cryptically) in matrix cp_loadings:

$cp_loadings
FullMatrix 'cp_loadings'

$labels
[,1] [,2] [,3]
[1,] "cp_loadings_r1c1" "cp_loadings_r1c2" "cp_loadings_r1c3"
[2,] "cp_loadings_r2c1" "cp_loadings_r2c2" "cp_loadings_r2c3"
[3,] "cp_loadings_r3c1" "cp_loadings_r3c2" "cp_loadings_r3c3"
[4,] "cp_loadings_r4c1" "cp_loadings_r4c2" "cp_loadings_r4c3"
[5,] "cp_loadings_r5c1" "cp_loadings_r5c2" "cp_loadings_r5c3"
[6,] "cp_loadings_r6c1" "cp_loadings_r6c2" "cp_loadings_r6c3"

$values
[,1] [,2] [,3]
[1,] 0.234958126 0.7924620 3.0297019
[2,] 0.049709341 -0.2315207 1.5511085
[3,] -0.009447686 0.7429272 0.5365263
[4,] 3.435387889 2.2862029 1.6776101
[5,] 1.923986619 2.6755898 2.2131049
[6,] -0.701359035 -1.4013078 -1.6685230

$free
[,1] [,2] [,3]
[1,] TRUE TRUE TRUE
[2,] TRUE TRUE TRUE
[3,] TRUE TRUE TRUE
[4,] TRUE TRUE TRUE
[5,] TRUE TRUE TRUE
[6,] TRUE TRUE TRUE

You can fix values to zero with a umx function, or with base OpenMx it might be done with omxSetParameters():

omxSetParameters(model$top, labels=c("cp_loadings_r4c1","cp_loadings_r5c1","cp_loadings_r6c1"), values=0, free=FALSE)


There are various tricks for using wildcards for labels that umx has that could be handy way to find all the factor loadings in a column without having to list them all out.

Step 3 is to run the model again once it has been modified.

This error occurs when exactly? Because, at first, you're not touching OpenMx, just basically modifying a matrix with base r. I remember setting up an identical model with umxcp. However, I just let the factors correlate (correlated factors) instead of specifying Cholesky.

A 2 common pathway CP model with CP 1 loading one set of variables and CP 2loading the second set makes sense. The short answer to the question about why you can't manually add correlations after a model is built, is that the default umxCP uses a diag matrix which can't implement the off diagonal covariances you want. SO you need to say correlatedA=TRUE when creating the model. This should have been called something else but... history.

The install_github(tbates/umx") version now deprecates `correlatedA` in favour of `correlatedACE` which is more accurately named, and defaults to leaving the lower triangle fixed at zero, allowing you to free up the (few) paths you want.

To create a 2-factor CP model, just set `nFac=2`

To restrict what manifests each CP loads on, in the resultant model, delete the paths from CP1 to the set 2 manifests, and from CP2 to the set 1 manifests using labels.

Paths from cp1 are in column 1 of the `cp_loadings` matrix. and labeled as "cp_loadings_r1c1"

You can match the relevant pattern with regular expressions, or if you like more concrete or fool proof approach, make a list and drop that... e.g.:

```R
tmp = umxCP(your setup here..., correlatedACE=TRUE, auto=FALSE)
pathsToDrop = c( "cp_loadings_r5c1", "cp_loadings_r6c1", ..., "cp_loadings_r1c2", ...)
m2 = umxModify(tmp, pathsToDrop, name = "style_and_personality")
```
you would then need to free the covariance of the a paths if you think that makes sense.

Hi Luis

I don't usually have trouble changing objects within OpenMx models. One difference I notice is that you use:

m2$submodels$top$matrices$e_cp$free[2,1] <- TRUE

whereas I would use something like

m2$top$e_cp$free[2,1] <- TRUE

that is, refer to a matrix with model$matrix without either $submodels or $matrices in the string. I'm not sure that this is your issue though. Another option is to replace the whole matrix

e_cp <- m2$submodels$top$matrices$e_cp
e_cp$free[2,1]<-TRUE
m2$top <-mxModel(m2$top,tempMat)

although clumsier, the pass through mxModel has validation checks that can prevent runtime errors. HTH!