It can be seen that lavaan has a much simpler syntax that allows to rapidly model basic SEM models. However, we were a bit unfair to OpenMx because we used a path model specification for lavaan and a matrix specification for OpenMx. The truth is that OpenMx is still probably a bit wordier than lavaan, but let's apply a path model specification in each to do a fair head-to-head comparison.
We will use the famous Holzinger-Swineford 1939 dataset here from the lavaan package to do our modeling, as follows:
hs.dat <- HolzingerSwineford1939
We will create a new dataset with a shorter name so that we don't have to keep typing HozlingerSwineford1939.
We will learn to fit the Holzinger-Swineford model in this section. We will start by specifying the SEM model using the lavaan model syntax:
hs.model.lavaan <- ' visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 visual ~~ textual visual ~~ speed textual ~~ speed ' fit.hs.lavaan <- cfa(hs.model.lavaan, data=hs.dat, std.lv = TRUE) summary(fit.hs.lavaan)
Here, we add the std.lv argument to the fit function, which fixes the variance of the latent variables to 1. We do this instead of constraining the first factor loading on each variable to 1.
Only the model coefficients are included for ease of viewing in this book. The result is shown in the following model:
> summary(fit.hs.lavaan)
…
Estimate Std.err Z-value P(>|z|)
Latent variables:
visual =~
x1 0.900 0.081 11.127 0.000
x2 0.498 0.077 6.429 0.000
x3 0.656 0.074 8.817 0.000
textual =~
x4 0.990 0.057 17.474 0.000
x5 1.102 0.063 17.576 0.000
x6 0.917 0.054 17.082 0.000
speed =~
x7 0.619 0.070 8.903 0.000
x8 0.731 0.066 11.090 0.000
x9 0.670 0.065 10.305 0.000
Covariances:
visual ~~
textual 0.459 0.064 7.189 0.000
speed 0.471 0.073 6.461 0.000
textual ~~
speed 0.283 0.069 4.117 0.000Let's compare these results with a model fit in OpenMx using the same dataset and SEM model.
The OpenMx syntax for path specification is substantially longer and more explicit. Let's take a look at the following model:
hs.model.open.mx <- mxModel("Holzinger Swineford",
type="RAM",
manifestVars = names(hs.dat)[7:15],
latentVars = c('visual', 'textual', 'speed'),
# Create paths from latent to observed variables
mxPath(
from = 'visual',
to = c('x1', 'x2', 'x3'),
free = c(TRUE, TRUE, TRUE),
values = 1
),
mxPath(
from = 'textual',
to = c('x4', 'x5', 'x6'),
free = c(TRUE, TRUE, TRUE),
values = 1
),
mxPath(
from = 'speed',
to = c('x7', 'x8', 'x9'),
free = c(TRUE, TRUE, TRUE),
values = 1
),
# Create covariances among latent variables
mxPath(
from = 'visual',
to = 'textual',
arrows=2,
free=TRUE
),
mxPath(
from = 'visual',
to = 'speed',
arrows=2,
free=TRUE
),
mxPath(
from = 'textual',
to = 'speed',
arrows=2,
free=TRUE
),
#Create residual variance terms for the latent variables
mxPath(
from= c('visual', 'textual', 'speed'),
arrows=2,
#Here we are fixing the latent variances to 1
#These two lines are like st.lv = TRUE in lavaan
free=c(FALSE,FALSE,FALSE),
values=1
),
#Create residual variance terms
mxPath(
from= c('x1', 'x2', 'x3', 'x4', 'x5', 'x6', 'x7', 'x8', 'x9'),
arrows=2,
),
mxData(
observed=cov(hs.dat[,c(7:15)]),
type="cov",
numObs=301
)
)
fit.hs.open.mx <- mxRun(hs.model.open.mx)
summary(fit.hs.open.mx)Here are the results of the OpenMx model fit, which look very similar to lavaan's. This gives a long output. For ease of viewing, only the most relevant parts of the output are included in the following model (the last column that R prints giving the standard error of estimates is also not shown here):
> summary(fit.hs.open.mx)
…
free parameters:
name matrix row col Estimate Std.Error
1 Holzinger Swineford.A[1,10] A x1 visual 0.9011177
2 Holzinger Swineford.A[2,10] A x2 visual 0.4987688
3 Holzinger Swineford.A[3,10] A x3 visual 0.6572487
4 Holzinger Swineford.A[4,11] A x4 textual 0.9913408
5 Holzinger Swineford.A[5,11] A x5 textual 1.1034381
6 Holzinger Swineford.A[6,11] A x6 textual 0.9181265
7 Holzinger Swineford.A[7,12] A x7 speed 0.6205055
8 Holzinger Swineford.A[8,12] A x8 speed 0.7321655
9 Holzinger Swineford.A[9,12] A x9 speed 0.6710954
10 Holzinger Swineford.S[1,1] S x1 x1 0.5508846
11 Holzinger Swineford.S[2,2] S x2 x2 1.1376195
12 Holzinger Swineford.S[3,3] S x3 x3 0.8471385
13 Holzinger Swineford.S[4,4] S x4 x4 0.3724102
14 Holzinger Swineford.S[5,5] S x5 x5 0.4477426
15 Holzinger Swineford.S[6,6] S x6 x6 0.3573899
16 Holzinger Swineford.S[7,7] S x7 x7 0.8020562
17 Holzinger Swineford.S[8,8] S x8 x8 0.4893230
18 Holzinger Swineford.S[9,9] S x9 x9 0.5680182
19 Holzinger Swineford.S[10,11] S visual textual 0.4585093
20 Holzinger Swineford.S[10,12] S visual speed 0.4705348
21 Holzinger Swineford.S[11,12] S textual speed 0.2829848 In summary, the results agree quite closely. For example, looking at the coefficient for the path going from the latent variable visual to the observed variable x1, lavaan gives an estimate of 0.900 while OpenMx computes a value of 0.901.