This is a package which allows you to perform interactions between latent variables (i.e., moderation) in CB-SEM. See https://kss2k.github.io/intro_modsem/ for a tutorial.

```
# From CRAN
install.packages("modsem")
# Latest version from Github
install.packages("devtools")
devtools::install_github("kss2k/modsem")
```

There are a number of approaches for estimating interaction effects in SEM. In `modsem()`

, the `method = "method"`

argument allows you to choose which to use.

`"ca"`

= constrained approach (Algina & Moulder, 2001)- Note that constraints can become quite complicated for complex models, particularly when there is an interaction including enodgenous variables. The method can therefore be quite slow.

`"uca"`

= unconstrained approach (Marsh, 2004)`"rca"`

= residual centering approach (Little et al., 2006)`"dblcent"`

= double centering approach (Marsh., 2013)- default

`"pind"`

= basic product indicator approach (not recommended)`"lms"`

= The latent moderated structural equations approach- note: now implemented with multiple endogenous variables however it does not allow interactions between two enodgenous variables, it does however allow interactions between exogenous:endogenous and exogenous:exogenous
- do
`optimize = TRUE`

for faster convergence (experimental feature)

`"qml"`

= The Quasi Maximum Likelihood estimation of latent moderated structural equations.- note: only works with a single endogenous variable.

`"mplus"`

- estimates model through Mplus, if it is installed

- New function for plotting interaction effects (
`plot_interaction()`

)

```
library(modsem)
m1 <- '
# Outer Model
X =~ x1 + x2 +x3
Y =~ y1 + y2 + y3
Z =~ z1 + z2 + z3
# Inner model
Y ~ X + Z + X:Z
'
# Double centering approach
est1Dblcent <- modsem(m1, oneInt)
summary(est1Dblcent)
# Constrained approach
est1Ca <- modsem(m1, oneInt, method = "ca")
summary(est1Ca)
# QML approach
est1Qml <- modsem(m1, oneInt, method = "qml")
summary(est1Qml)
# LMS approach
est1Lms <- modsem(m1, oneInt, method = "lms")
summary(est1Lms)
```

```
tpb <- "
# Outer Model (Based on Hagger et al., 2007)
ATT =~ att1 + att2 + att3 + att4 + att5
LSN =~ sn1 + sn2
PBC =~ pbc1 + pbc2 + pbc3
INT =~ int1 + int2 + int3
BEH =~ b1 + b2
# Inner Model (Based on Steinmetz et al., 2011)
# Causal Relationsships
INT ~ ATT + LSN + PBC
BEH ~ INT + PBC
BEH ~ PBC:INT
"
# double centering approach
estTpbDblCent <- modsem(tpb, data = TPB, method = "dblcent")
summary(estTpbDblCent)
# Constrained approach using Wrigths path tracing rules for generating
# the appropriate constraints
estTpbCa <- modsem(tpb, data = TPB, method = "ca")
summary(estTpbCa)
# LMS approach
estTpbLms <- modsem(tpb, data = TPB, method = "lms")
summary(estTpbLms)
```

```
est2 <- modsem('y1 ~ x1 + z1 + x1:z1', data = oneInt, method = "pind")
summary(est2)
## Interaction between an obsereved and a latent variable
m3 <- '
# Outer Model
X =~ x1 + x2 +x3
Y =~ y1 + y2 + y3
# Inner model
Y ~ X + z1 + X:z1
'
est3 <- modsem(m3, oneInt, method = "pind")
summary(est3)
```

```
m4 <- '
# Outer Model
X =~ x1 + x2 +x3
Y =~ y1 + y2 + y3
Z =~ z1 + z2 + z3
G =~ g1 + g2 + g3
H =~ h1 + h2 + h3
# Inner model
Y ~ X + Z + G + H + X:Z + G:H
'
# Using unconstrained approach
est4 <- modsem(m4, twoInt, method = "uca")
summary(est4)
```

```
m5 <- '
# Outer Model
X =~ x1 + x2 +x3
Y =~ y1 + y2 + y3
Z =~ z1 + z2 + z3
G =~ g1 + g2 + g3
# Inner model
Y ~ X + Z + G + X:Z:G
'
# Residual centering approach
est5 <- modsem(m5, tripleInt, standardizeData = TRUE, method = "rca")
summary(est5)
```