# non-centered interaction terms (LMS and QML)

    library(modsem)

# Non-centered interaction terms

Using the LMS and QML approaches it is possible to estimate interaction terms where the means of the latent variables are not centered (i.e., they have non-zero means).

Here we can see an example using the `TPB` dataset:

    tpb <- '
    # Outer Model (Based on Hagger et al., 2007)
      ATT =~ att1 + att2 + att3 + att4 + att5
      SN =~ sn1 + sn2
      PBC =~ pbc1 + pbc2 + pbc3
      INT =~ int1 + int2 + int3
      BEH =~ b1 + b2

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

    # Adding Latent Intercepts
      INT ~ 1
      BEH ~ 1
      PBC ~ 1
      SN  ~ 1
      ATT ~ 1
    '

    est <- modsem(tpb, TPB, method = "lms", nodes = 32)
    summary(est)

Comparing this to the estimates we get when `PBC` and `INT` have zero means, we see that the coefficients `BEH~PBC` and `BEH~INT` are drastically changed. This is not a bug, and is a function of the interaction effect rescaling the coefficients, when not centered at zero. When using the `standardized_estimates` function, or `summary(est, standardized = TRUE)` the interaction effect is centered, and we can see that the coefficients `BEH~PBC` and `BEH~INT` are rescaled once again.

    summary(est, standardized = TRUE, centered = TRUE)

It is also possible to get the centered solution using the `centered_estimates()` function. Note, that `centered_estimates()` removes the mean structure of the model all together.

    centered_estimates(est)