Probing twoway interaction on the residualcentered latent interaction
Description
Probing interaction for simple intercept and simple slope for the residualcentered latent twoway interaction (Pornprasertmanit, Schoemann, Geldhof, & Little, submitted)
Usage
1  probe2WayRC(fit, nameX, nameY, modVar, valProbe)

Arguments
fit 
The lavaan model object used to evaluate model fit 
nameX 
The vector of the factor names used as the predictors. The firstorder factor will be listed first. The last name must be the name representing the interaction term. 
nameY 
The name of factor that is used as the dependent variable. 
modVar 
The name of factor that is used as a moderator. The effect of the other independent factor on each moderator variable value will be probed. 
valProbe 
The values of the moderator that will be used to probe the effect of the other independent factor. 
Details
Before using this function, researchers need to make the products of the indicators between the firstorder factors and residualize the products by the original indicators (Lance, 1988; Little, Bovaird, & Widaman, 2006). The process can be automated by the indProd
function. Note that the indicator products can be made for all possible combination or matchedpair approach (Marsh et al., 2004). Next, the hypothesized model with the regression with latent interaction will be used to fit all original indicators and the product terms. To use this function the model must be fit with a mean structure. See the example for how to fit the product term below. Once the lavaan result is obtained, this function will be used to probe the interaction.
The probing process on residualcentered latent interaction is based on transforming the residualcentered result into the nocentered result. See Pornprasertmanit, Schoemann, Geldhof, and Little (submitted) for further details. Note that this approach based on a strong assumption that the firstorder latent variables are normally distributed. The probing process is applied after the nocentered result (parameter estimates and their covariance matrix among parameter estimates) has been computed. See the probe2WayMC
for further details.
Value
A list with two elements:
SimpleIntercept The intercepts given each value of the moderator. This element will be shown only if the factor intercept is estimated (e.g., not fixed as 0).
SimpleSlope The slopes given each value of the moderator.
In each element, the first column represents the values of the moderators specified in the valProbe
argument. The second column is the simple intercept or simple slope. The third column is the standard error of the simple intercept or simple slope. The fourth column is the Wald (z) statistic. The fifth column is the pvalue testing whether the simple intercepts or slopes are different from 0.
Author(s)
Sunthud Pornprasertmanit (psunthud@gmail.com)
References
Lance, C. E. (1988). Residual centering, exploratory and confirmatory moderator analysis, and decomposition of effects in path models containing interactions. Applied Psychological Measurement, 12, 163175.
Little, T. D., Bovaird, J. A., & Widaman, K. F. (2006). On the merits of orthogonalizing powered and product terms: Implications for modeling interactions. Structural Equation Modeling, 13, 497519.
Marsh, H. W., Wen, Z., & Hau, K. T. (2004). Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction. Psychological Methods, 9, 275300.
Pornprasertmanit, S., Schoemann, A. M., Geldhof, G. J., & Little, T. D. (submitted). Probing latent interaction estimated with a residual centering approach.
See Also

indProd
For creating the indicator products with no centering, mean centering, doublemean centering, or residual centering. 
probe2WayMC
For probing the twoway latent interaction when the results are obtained from meancentering, or doublemean centering. 
probe3WayMC
For probing the threeway latent interaction when the results are obtained from meancentering, or doublemean centering. 
probe3WayRC
For probing the twoway latent interaction when the results are obtained from residualcentering approach. 
plotProbe
Plot the simple intercepts and slopes of the latent interaction.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27  library(lavaan)
dat2wayRC < orthogonalize(dat2way, 1:3, 4:6)
model1 < "
f1 =~ x1 + x2 + x3
f2 =~ x4 + x5 + x6
f12 =~ x1.x4 + x2.x5 + x3.x6
f3 =~ x7 + x8 + x9
f3 ~ f1 + f2 + f12
f12 ~~0*f1
f12 ~~ 0*f2
x1 ~ 0*1
x4 ~ 0*1
x1.x4 ~ 0*1
x7 ~ 0*1
f1 ~ NA*1
f2 ~ NA*1
f12 ~ NA*1
f3 ~ NA*1
"
fitRC2way < sem(model1, data=dat2wayRC, meanstructure=TRUE, std.lv=FALSE)
summary(fitRC2way)
result2wayRC < probe2WayRC(fitRC2way, c("f1", "f2", "f12"), "f3", "f2", c(1, 0, 1))
result2wayRC
