Using probe2WayMC when the dependent variable is binary in lavaan

Question

Is it possible to use the probe2WayMC function of semTools when sem(ordered="dep"), or only when the DV is continuous? I've tried it but I'm receiving this error message: Error in est$beta[nameY, nameX] : subscript out of bounds

Answer 1

Original Answer

The product-indicator method literally calculates products of (numerical values of) indicators. You can only do this with ordinal data by treating the (arbitrarily numbered) category labels as though they were really numbers. Here is a simulation study comparing that approach to LMS estimation while treating indicators as ordinal:

https://doi.org/10.1177/0013164419865017

Treating them as numeric may be the most expedient approach if there are several categories (so approximately continuous). Otherwise, you could use the parameter-moderation approach:

https://doi.org/10.1037/met0000501

Post-comment addition:

If only the outcome is an observed ordinal variable (e.g., binary like the OP's, or more categories like the reprex below), the probe2WayMC() function still works:

library(semTools)
dat2wayMC <- indProd(dat2way, 1:3, 4:6)

## make an ordinal outcome from f3's indicators
dat2wayMC$DV <- cut(rowSums(dat2wayMC[paste0("x", 7:9)]),
                    breaks = 3, labels = FALSE)
table(dat2wayMC$DV)


mod <- "## measurement models for predictors
    f1 =~ x1 + x2 + x3
    f2 =~ x4 + x5 + x6
    f12 =~ x1.x4 + x2.x5 + x3.x6
## mean centering makes correlations with interaction zero
    f12 ~~ 0*f1 + 0*f2
## regress ordinal outcome
    DV ~ f1 + f2 + f12
"
fit <- sem(mod, data = dat2wayMC, ordered = "DV")
summary(fit)
probe2WayMC(fit, nameX = c("f1", "f2", "f12"), nameY = "DV",
            modVar = "f2", valProbe = c(-1, 0, 1))

If (as in the OP's case, described in a comment below this answer) the moderator is also binary, then product indicators are not necessary because a multigroup SEM allows for moderation by the group= variable:

# not dat2wayMC (unnecessary)
dat2way <- data.frame(dat2way)
dat2way$D <- cut(rowSums(dat2way[paste0("x", 4:6)]),
                   breaks = 2, labels = FALSE)
dat2way$DV <- cut(rowSums(dat2way[paste0("x", 7:9)]),
                    breaks = 2, labels = FALSE)
table(moderator = dat2way$D,
      outcome = dat2way$DV)

mod2 <- "
## measurement model for focal predictor
## with metric-invariance constraints
    f1 =~ c(L1, L1)*x1 + c(L2, L2)*x2 + c(L3, L3)*x3
## threshold invariance for binary outcome
    DV | c(th1, th1)*t1
## regress ordinal outcome on focal predictor
## with unique labels per group
    DV ~ c(b1, b2)*f1
## slope difference across groups
## (moderating effect)
    b2_vs_b1 := b2 - b1
"
fit2 <- sem(mod2, data = dat2way, ordered = "DV",
            group = "D")
summary(fit2)

Note that the slopes are only (validly) comparable given invariance constraints on thresholds and loadings, so that the scales are linked across groups for the latent factor f1 and the latent response underlying DV. The MG-SEM approach is also less restrictive because it allows (residual) variances to differ across groups, whereas a single-group approach (using product indicators) would assume homoskedasticity.

https://doi.org/10.1080/10705511.2020.1766357

https://doi.org/10.1007/978-3-319-77249-3_20 (tutorial with lavaan examples)