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Effects coding method in CFA

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pehkawn's picture
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Joined: 05/24/2020 - 19:45
Effects coding method in CFA

I am trying to run a CFA where one latent variable is regressed on four manifest variables. I am trying to constrain the pattern coefficients ($\lambda$) mean to equal one, according to Kline's (2015, p. 200) effects coding method:

$$ \frac{\lambda_1 + \lambda_2 + \lambda_3 + \lambda_4}{4} = 1 $$

Below is a code example. I tried adding an mxConstraint() function in mxModel() but the syntax is not correct. How can I apply the constraints properly?

library(OpenMx)
data <- mxData(observed = mydata, type="raw")
 
# residual variances
res_var <- mxPath(
    from = paste0("x", 1:4),
    arrows = 2,
    free = TRUE,
    values = 1, 
    labels = paste0("e_x", 1:4)
)
 
# latent variance
lat_var <- mxPath(
    from = "L", 
    arrows = 2,
    free = TRUE, 
    values = 1,
    labels = c("var_L")
)
 
# factor loadings
fac_loads <- mxPath(
    from = "L",
    to = paste0("x", 1:4),
    free = c(TRUE, TRUE, TRUE, TRUE),
    values = 1,
    arrows = 1,
    label = paste0("L__x", 1:4)
)
# means
means <- mxPath(
    from = "one",
    to = c(L, paste0("x", 1:4),
    arrows = 1,
    free = FALSE,
    values = 0,
    labels = c(paste0("mean_", student_sci_ach), "mean_stSCI")
)
 
model <- mxModel(
    "My Model", 
    type = "RAM",
    manifestVars = paste0("x", 1:4),
    latentVars = "L",
    data,
    var, lat_var,
    fac_loads,
    means,
# I tried defining a constraint here, but this obviously doesn't work.
    mxConstraint(mean(paste0("L__x", 1:4)) == 1)
)
 
results <- mxRun(model)
summary(results)
<\blockcode>
AdminRobK's picture
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Joined: 01/24/2014 - 12:15
try something like this

In an MxConstraint, both sides of the comparator (= in this case) have to be valid MxAlgebra-like expressions, evaluable in the MxModel's namespace; mere character strings aren't accepted. Try something like this:

model <- mxModel(
    "My Model", 
    type = "RAM",
    manifestVars = paste0("x", 1:4),
    latentVars = "L",
    data,
    var, lat_var,
    fac_loads,
    means,
    mxMatrix(type="Full",nrow=4,ncol=1,free=T,labels=paste0("L__x", 1:4),name="Lmat"),
    mxConstraint(mean(Lmat) == 1)
)
pehkawn's picture
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Joined: 05/24/2020 - 19:45
Thanks, that did the trick!

That worked after I added an extra line model &lt;- omxAssignFirstParameters(model) to copy the values in the A matrix into Lmat.

AdminNeale's picture
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Joined: 03/01/2013 - 14:09
Yep

That is one way to avoid trying to start parameters at different values when they appear in different places in the model. Good solution, although it's a bit less controllable than manually setting parameters to the same value wherever they appear, in this case I think changing the mxMatrix line to

  mxMatrix(type="Full",nrow=4,ncol=1,free=T, values=1, labels=paste0("L__x", 1:4),name="Lmat"),

Use of omxAssignFirstParameters() means that you don't actually know which starting value was used. Sometimes that's ok, but, (e.g., to debug bad starting values) it's not always ideal.