% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/probeInteraction.R
\name{probe2WayMC}
\alias{probe2WayMC}
\title{Probing two-way interaction on the no-centered or mean-centered latent
interaction}
\usage{
probe2WayMC(fit, nameX, nameY, modVar, valProbe, group = 1L,
  omit.imps = c("no.conv", "no.se"))
}
\arguments{
\item{fit}{A fitted \link[lavaan:lavaan-class]{lavaan::lavaan} or
\link[lavaan.mi:lavaan.mi-class]{lavaan.mi::lavaan.mi} object with a latent 2-way interaction.}

\item{nameX}{\code{character} vector of all 3 factor names used as the
predictors. The lower-order factors must be listed first, and the final
name must be the latent interaction factor.}

\item{nameY}{The name of factor that is used as the dependent variable.}

\item{modVar}{The name of factor that is used as a moderator. The effect of
the other independent factor will be probed at each value of the
moderator variable listed in \code{valProbe}.}

\item{valProbe}{The values of the moderator that will be used to probe the
effect of the focal predictor.}

\item{group}{In multigroup models, the label of the group for which the
results will be returned. Must correspond to one of
\code{lavInspect(fit, "group.label")}, or an integer
corresponding to which of those group labels.}

\item{omit.imps}{\code{character} vector specifying criteria for omitting
imputations from pooled results. Ignored unless \code{fit} is of
class \link[lavaan.mi:lavaan.mi-class]{lavaan.mi::lavaan.mi}. Can include any of
\code{c("no.conv", "no.se", "no.npd")}, the first 2 of which are the
default setting, which excludes any imputations that did not
converge or for which standard errors could not be computed.  The
last option (\code{"no.npd"}) would exclude any imputations which
yielded a nonpositive definite covariance matrix for observed or
latent variables, which would include any "improper solutions" such
as Heywood cases.  NPD solutions are not excluded by default because
they are likely to occur due to sampling error, especially in small
samples.  However, gross model misspecification could also cause
NPD solutions, users can compare pooled results with and without
this setting as a sensitivity analysis to see whether some
imputations warrant further investigation.}
}
\value{
A list with two elements:
\enumerate{
\item \code{SimpleIntercept}: The simple intercepts given each value of the
moderator.
\item \code{SimpleSlope}: The simple slopes given each value of the moderator.
}
In each element, the first column represents the values of the moderator
specified in the \code{valProbe} argument. The second column is the simple
intercept or simple slope. The third column is the \emph{SE} of the simple
intercept or simple slope. The fourth column is the Wald (\emph{z})
statistic, and the fifth column is the associated \emph{p} value testing
the null hypothesis that each simple intercept or slope is 0.
}
\description{
Probing interaction for simple intercept and simple slope for the
no-centered or mean-centered latent two-way interaction
}
\details{
Before using this function, researchers need to make the products of the
indicators between the first-order factors using mean centering (Marsh, Wen,
& Hau, 2004). Note that the double-mean centering may not be appropriate for
probing interaction if researchers are interested in simple intercepts. The
mean or double-mean centering can be done by the \code{\link[=indProd]{indProd()}}
function. 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. 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.

Let that the latent interaction model regressing the dependent variable
(\eqn{Y}) on the independent variable (\eqn{X}) and the moderator (\eqn{Z})
be \deqn{ Y = b_0 + b_1X + b_2Z + b_3XZ + r, } where \eqn{b_0} is the
estimated intercept or the expected value of \eqn{Y} when both \eqn{X} and
\eqn{Z} are 0, \eqn{b_1} is the effect of \eqn{X} when \eqn{Z} is 0,
\eqn{b_2} is the effect of \eqn{Z} when \eqn{X} is 0, \eqn{b_3} is the
interaction effect between \eqn{X} and \eqn{Z}, and \eqn{r} is the residual
term.

To probe a two-way interaction, the simple intercept of the independent
variable at each value of the moderator (Aiken & West, 1991; Cohen, Cohen,
West, & Aiken, 2003; Preacher, Curran, & Bauer, 2006) can be obtained by
\deqn{ b_{0|X = 0, Z} = b_0 + b_2 Z. }

The simple slope of the independent varaible at each value of the moderator
can be obtained by
\deqn{ b_{X|Z} = b_1 + b_3 Z. }

The variance of the simple intercept formula is
\deqn{ Var\left(b_{0|X = 0, Z}\right) =
       Var\left(b_0\right) + 2Z \times Cov\left(b_0, b_2\right) +
       Z^2 \times Var\left(b_2\right) },
where \eqn{Var} denotes the variance of a parameter
estimate and \eqn{Cov} denotes the covariance of two parameter estimates.

The variance of the simple slope formula is
\deqn{ Var\left(b_{X|Z}\right) = Var\left(b_1\right) + 2Z \times
       Cov\left(b_1, b_3\right) + Z^2 \times Var\left(b_3\right) }

Wald \emph{z} statistic is used for test statistic (even for objects of
class \link[lavaan.mi:lavaan.mi-class]{lavaan.mi::lavaan.mi}).
}
\examples{

dat2wayMC <- indProd(dat2way, 1:3, 4:6) # double mean centered by default

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 + 0*f2 # not necessary, but implied by double mean centering
"

fitMC2way <- sem(model1, data = dat2wayMC, meanstructure = TRUE)
summary(fitMC2way)

probe2WayMC(fitMC2way, nameX = c("f1", "f2", "f12"), nameY = "f3",
            modVar = "f2", valProbe = c(-1, 0, 1))


## can probe multigroup models, one group at a time
dat2wayMC$g <- 1:2

model2 <- "
f1 =~ x1 + x2 + x3
f2 =~ x4 + x5 + x6
f12 =~ x1.x4 + x2.x5 + x3.x6
f3 =~ x7 + x8 + x9
f3 ~ c(b1.g1, b1.g2)*f1 + c(b2.g1, b2.g2)*f2 + c(b12.g1, b12.g2)*f12
f12 ~~ 0*f1 + 0*f2
"
fit2 <- sem(model2, data = dat2wayMC, group = "g")
probe2WayMC(fit2, nameX = c("f1", "f2", "f12"), nameY = "f3",
            modVar = "f2", valProbe = c(-1, 0, 1)) # group = 1 by default
probe2WayMC(fit2, nameX = c("f1", "f2", "f12"), nameY = "f3",
            modVar = "f2", valProbe = c(-1, 0, 1), group = 2)

}
\references{
Tutorial:

Schoemann, A. M., & Jorgensen, T. D. (2021). Testing and interpreting
latent variable interactions using the \code{semTools} package.
\emph{Psych, 3}(3), 322--335. \doi{10.3390/psych3030024}

Background literature:

Aiken, L. S., & West, S. G. (1991). \emph{Multiple regression: Testing
and interpreting interactions}. Newbury Park, CA: Sage.

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003). \emph{Applied
multiple regression/correlation analysis for the behavioral sciences}
(3rd ed.). New York, NY: Routledge.

Marsh, H. W., Wen, Z., & Hau, K. T. (2004). Structural equation models of
latent interactions: Evaluation of alternative estimation strategies and
indicator construction. \emph{Psychological Methods, 9}(3), 275--300.
\doi{10.1037/1082-989X.9.3.275}

Preacher, K. J., Curran, P. J., & Bauer, D. J. (2006). Computational tools
for probing interactions in multiple linear regression, multilevel modeling,
and latent curve analysis. \emph{Journal of Educational and Behavioral
Statistics, 31}(4), 437--448. \doi{10.3102/10769986031004437}
}
\seealso{
\itemize{
\item \code{\link[=indProd]{indProd()}} For creating the indicator products with no
centering, mean centering, double-mean centering, or residual centering.
\item \code{\link[=probe3WayMC]{probe3WayMC()}} For probing the three-way latent interaction
when the results are obtained from mean-centering, or double-mean centering
\item \code{\link[=probe2WayRC]{probe2WayRC()}} For probing the two-way latent interaction
when the results are obtained from residual-centering approach.
\item \code{\link[=probe3WayRC]{probe3WayRC()}} For probing the two-way latent interaction
when the results are obtained from residual-centering approach.
\item \code{\link[=plotProbe]{plotProbe()}} Plot the simple intercepts and slopes of the
latent interaction.
}
}
\author{
Sunthud Pornprasertmanit (\email{psunthud@gmail.com})

Terrence D. Jorgensen (University of Amsterdam; \email{TJorgensen314@gmail.com})
}