Probing interaction for simple intercept and simple slope for the residual-centered latent two-way interaction (Pornprasertmanit, Schoemann, Geldhof, & Little, submitted)
probe2WayRC(fit, nameX, nameY, modVar, valProbe)The lavaan model object used to evaluate model fit
The vector of the factor names used as the predictors. The first-order factor will be listed first. The last name must be the name representing the interaction term.
The name of factor that is used as the dependent variable.
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.
The values of the moderator that will be used to probe the effect of the other independent factor.
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 p value testing whether the simple
intercepts or slopes are different from 0.
Before using this function, researchers need to make the products of the
indicators between the first-order 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
matched-pair 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 residual-centered latent interaction is based on
transforming the residual-centered result into the no-centered result. See
Pornprasertmanit, Schoemann, Geldhof, and Little (submitted) for further
details. Note that this approach based on a strong assumption that the
first-order latent variables are normally distributed. The probing process
is applied after the no-centered result (parameter estimates and their
covariance matrix among parameter estimates) has been computed. See the
probe2WayMC for further details.
Lance, C. E. (1988). Residual centering, exploratory and confirmatory moderator analysis, and decomposition of effects in path models containing interactions. Applied Psychological Measurement, 12(2), 163--175. doi:10.1177/014662168801200205
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(4), 497--519. doi:10.1207/s15328007sem1304_1
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(3), 275--300. doi:10.1037/1082-989X.9.3.275
Geldhof, G. J., Pornprasertmanit, S., Schoemann, A. M., & Little, T. D. (2013). Orthogonalizing through residual centering: Extended applications and caveats Educational and Psychological Measurement, 73(1), 27--46. doi:10.1177/0013164412445473
indProd For creating the indicator products with no
centering, mean centering, double-mean centering, or residual centering.
probe2WayMC For probing the two-way latent interaction
when the results are obtained from mean-centering, or double-mean centering
probe3WayMC For probing the three-way latent interaction
when the results are obtained from mean-centering, or double-mean centering
probe3WayRC For probing the two-way latent interaction
when the results are obtained from residual-centering approach.
plotProbe Plot the simple intercepts and slopes of the
latent interaction.
# NOT RUN {
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, std.lv = FALSE,
meanstructure = TRUE)
summary(fitRC2way)
result2wayRC <- probe2WayRC(fitRC2way, c("f1", "f2", "f12"),
"f3", "f2", c(-1, 0, 1))
result2wayRC
# }
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