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)