Example Models

# Often you will see data presented as a lower diagonal.
# the readMoments() function in the sem package is a nice helper to read this from the screen:

data = sem::readMoments(file = "", diag = TRUE)
1
.304 1
.305 .344 1
.100 .156 .158 1
.284 .192 .324 .360 1
.176 .136 .226 .210 .265 1

# terminates with an empty line: see ?readMoments for more help

# now lets fill in the upper triangle with a flipped version of the lower
data[upper.tri(data, diag=F)] = t(data)[upper.tri(data, diag=F)]

# Set up manifest variables
manifests = c("income", "occup", "educ", "church", "member", "friends")

# Use these to create names for our dataframe
dimnames(data) = list(manifests, manifests)

# And latents
latents = "social" # 1 latent, with three formative inputs, and three reflective outputs (each with residuals)

# Just to be helpful to myself, I've made lists of the formative sources, and the reflective receiver variables in this MIMIC model
receivers = manifests[4:6]
sources = manifests[1:3]

MIMIC <- mxModel("MIMIC", type="RAM",
manifestVars = manifests,
latentVars = latents,

# Factor loadings
mxPath(from = sources , to = "social" ),
mxPath(from = "social", to = receivers),

# Correlated formative sources for F1, each with variance = 1
mxPath(from = sources, connect = "unique.bivariate", arrows = 2),
mxPath(from = sources, arrows = 2, values = 1, free=F ),

# Read in an example dataset supplied with the OpenMx package
data(myFADataRaw)
# Grab three variables
df <- myFADataRaw[, c("x1","z1", "z3")]

# rename them to be more memorable
manifests = c("cont1", "ord1","ord2")
names(df) <-manifests

# For OpenMx to work with ordinal data, they must be ordered factors!
df$ord1 <- mxFactor(df$ord1, levels=0:1)
df$ord2 <- mxFactor(df$ord2, levels=0:2)

# Let's see what we're working with now
str(df)
'data.frame': 500 obs. of 3 variables:
$ cont1: num 1 1.63 1.95 2.95 3.66 ...
$ ord1 : Ord.factor w/ 2 levels "0"<"1": 2 2 2 2 2 2 2 2 2 1 ...
$ ord2 : Ord.factor w/ 3 levels "0"<"1"<"2": 1 2 2 1 2 2 1 2 1 1 ...

hist(df$cont1) # nice and normal
plot(~df$ord1) # binary - 4x as many 1s as 0s
plot(~df$ord2) # three-values: low endorsement of the highest value

# Just to help keep things simple in the model, let's list up the continuous
# and the ordinal manifests separately
ordinalVars = manifests[2:3]
continuousVars = manifests[1]

m1 <- mxModel("joint CFA", type="RAM",
manifestVars = manifests,
latentVars = "F1",
# Factor loadings
mxPath(from="F1", to = manifests, arrows=1, free=T, values=1, labels=c("l1","l2","l3")),

# Manifest continuous mean & residual variance (both free)
mxPath(from="one", to = continuousVars, arrows=1, free=T, values=0, labels="meancont1"),
mxPath(from=continuousVars , arrows=2, free=T, values=1, labels="e1" ),

# Ordinal manifests mean and variance fixed at 0 & 1
# The thresholds will be computed as being based off this underlying normal distribution)
mxPath(from="one", to = ordinalVars, arrows=1, free=F, values=0, labels=c("meanord1","meanord2")),
mxPath(from=ordinalVars , arrows=2, free=F, values=1, labels=c("e2","e3")),

# fix latent variable variance @1 & mean @0
mxPath(from="F1" , arrows=2, free=F, values=1, labels ="varF1"),
mxPath(from="one", to="F1", arrows=1, free=F, values=0, labels="meanF1"),

# Make a matrix as wide as the number of ordinal variables (2), and as many rows as the max # of thresholds (3) - 1
# In this case that is 2 * 2
# leave it free where there is a real threshold to be set, and fill the rest of each column fixed @NA
# set the column names to the name of the ordinal variables: that is how OpenMx maps into this threshold matrix
mxMatrix("Full", nrow=2, ncol=2, byrow=T, name="thresh",
dimnames = list(c(), ordinalVars),
free = c(T, T ,
F, T),
values = c(0, -1,
NA, 1)
),
# Add some data
mxData(df, type="raw"),
# tell the mxRAMObjective that we have not only A,S, F and M matrices, but also some ordinal vars with thresholds
mxRAMObjective(A="A", S="S", F="F", M="M", thresholds="thresh")
)

# run!
m1 = mxRun(m1); summary(m1)

free parameters:
name matrix row col Estimate Std.Error lbound ubound
1 l1 A cont1 F1 -0.1953311 0.04115263
2 l2 A ord1 F1 -1.0135426 NaN
3 l3 A ord2 F1 -4.3049347 NaN
4 e1 S cont1 cont1 0.9571266 0.06018277
5 meancont1 M 1 cont1 2.9876221 0.04461568
6 thresh 1 ord1 -1.3038918 NaN
7 thresh 1 ord2 -2.1373824 NaN
8 thresh 2 ord2 5.7570834 NaN