reliability-corrected single items

In modsem: Latent Interaction (and Moderation) Analysis in Structural Equation Models (SEM)

EVAL_DEFAULT <- FALSE
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  eval = EVAL_DEFAULT
)

library(modsem)

Reliablity-Corrected Single Items

If wanted, indicators for latent variables can be replaced with reliablity corrected single items, using Chronbach's $\alpha$. This can either be done using the relcorr_single_item function, returning the altered model syntax and data, or via the rcs argument in modsem. Here we can see an example using the relcorr_single_item function:

tpb_uk <- "
# Outer Model (Based on Hagger et al., 2007)
 ATT =~ att3 + att2 + att1 + att4
 SN =~ sn4 + sn2 + sn3 + sn1
 PBC =~ pbc2 + pbc1 + pbc3 + pbc4
 INT =~ int2 + int1 + int3 + int4
 BEH =~ beh3 + beh2 + beh1 + beh4

# Inner Model (Based on Steinmetz et al., 2011)
 INT ~ ATT + SN + PBC
 BEH ~ INT + PBC
 BEH ~ INT:PBC
"

corrected <- relcorr_single_item(syntax = tpb_uk, data = TPB_UK)
corrected

Here we can see that relcorr_single_item returns a new model syntax, and a new data.frame containing the generated items. Additionally, it also returns the Chronbach's $\alpha$ and average variance extraced (AVE) for the different constructs in the model. The syntax and data can be extracted using the $ operator, and used to estimate the model.

syntax <- corrected$syntax
data   <- corrected$data

est_dca <- modsem(syntax, data = data, method = "dblcent")
est_lms <- modsem(syntax, data = data, method="lms", nodes=32)
summary(est_lms)

The easiest approach however, is to use the rcs argument in the modsem function to call relcorr_single_item before estimating the model.

est_dca <- modsem(tpb_uk, data = TPB_UK, method = "dblcent", rcs = TRUE)
est_lms <- modsem(tpb_uk, data = TPB_UK, method = "lms", rcs = TRUE)

Choosing Variables

If you don't want to use reliablity-corrected single items for all of the latent variables in the model, you can use the choose argument in relcorr_single_item (orrcs.choose in modsem) to select which set of indicators to replace.

relcorr_single_item(syntax = tpb_uk, data = TPB_UK,
                    choose = c("ATT", "SN", "PBC", "INT"))

est_dca <- modsem(tpb_uk, data = TPB_UK, method = "dblcent", rcs = TRUE,
                  rcs.choose = c("ATT", "SN", "PBC", "INT", "INT:PBC"))
summary(est_dca)

modsem documentation built on Aug. 27, 2025, 9:08 a.m.