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\name{mxBootstrapStdizeRAMpaths}
\alias{mxBootstrapStdizeRAMpaths}
\title{Bootstrap distribution of standardized RAM path coefficients}
\description{
Uses the distribution of a bootstrapped RAM model's raw parameters to create a bootstrapped estimate of its standardized path coefficients.
\emph{note}: Model must have already been run through \code{\link{mxBootstrap}}.
}
\usage{
mxBootstrapStdizeRAMpaths(model, bq= c(.25, .75),
method= c('bcbci','quantile'), returnRaw= FALSE)
}
\arguments{
\item{model}{An MxModel that uses \link[=mxExpectationRAM]{RAM expectation} and has already been run through \code{\link{mxBootstrap}}.}
\item{bq}{vector of 2 bootstrap quantiles corresponding to the lower and upper limits of the desired confidence interval.}
\item{method}{One of 'bcbci' or 'quantile'.}
\item{returnRaw}{Whether or not to return the raw bootstrapping results (Defaults to \code{FALSE}: returning a dataframe summarizing the results).}
}
\details{
\code{mxBootstrapStdizeRAMpaths} applies \code{\link{mxStandardizeRAMpaths}} to each bootstrap replication, thus creating a distribution of standardized estimates for each nonzero path coefficient.
The default \code{bq} (bootstrap quantiles) of c(.25, .75) correspond to a 50\% CI. This default is chosen as many more
bootstraps are required to accurately estimate more extreme quantiles. For a 95\% CI, use \code{bq=c(.025,.0975)}.
\emph{nb}: \sQuote{bcbci} stands for \sQuote{bias-corrected bootstrap confidence interval} To learn more about bcbci and quantile methods, see Efron (1982)
and Efron and Tibshirani (1994).
\emph{note 1}: It is possible (though unlikely) that the number of nonzero paths (elements of the \code{A} and \code{S} RAM matrices) may vary among bootstrap replications. This precludes a simple summary of the standardized paths' bootstrapping results. In this rare case, if \code{returnRaw=TRUE}, a raw list of bootstrapping results is returned, with a warning. Otherwise an error is thrown.
\emph{note 2}: \code{mxBootstrapStdizeRAMpaths} ignores sub-models. To standardize bootstrapped sub-models, run it on the sub-models directly.
}
\value{
If \code{returnRaw=FALSE} (default), it returns a dataframe containing, among other things, the standardized path coefficients as estimated from the real data, their bootstrap SEs, and the lower and upper limits of a bootstrap confidence interval. If \code{returnRaw=TRUE}, typically, a matrix containing the raw bootstrap results is returned; this matrix has one column per non-zero path coefficient, and one row for each successfully converged bootstrap replication or, if the number of paths varies between bootstraps, a raw list of results is returned.
}
\references{
Efron B. (1982). \emph{The Jackknife, the Bootstrap, and Other Resampling Plans}. Philadelphia: Society for Industrial and Applied Mathematics.
Efron B, Tibshirani RJ. (1994). \emph{An Introduction to the Bootstrap}. Boca Raton: Chapman & Hall/CRC.
}
\seealso{
\code{\link{mxBootstrap}()}, \code{\link{mxStandardizeRAMpaths}()}, \code{\link{mxBootstrapEval}}, \code{\link{mxSummary}}
}
\examples{
\donttest{
require(OpenMx)
data(myFADataRaw)
manifests = c("x1","x2","x3","x4","x5","x6")
# Build and run 1-factor raw-data CFA
m1 = mxModel("CFA", type="RAM", manifestVars=manifests, latentVars="F1",
# Factor loadings
mxPath("F1", to = manifests, values=1),
# Means and variances of F1 and manifests
mxPath(from="F1", arrows=2, free=FALSE, values=1), # fix var F1 @1
mxPath("one", to= "F1", free= FALSE, values = 0), # fix mean F1 @0
# Freely-estimate means and residual variances of manifests
mxPath(from = manifests, arrows=2, free=TRUE, values=1),
mxPath("one", to= manifests, values = 1),
mxData(myFADataRaw, type="raw")
)
m1 = mxRun(m1)
set.seed(170505) # Desirable for reproducibility
# ==========================
# = 1. Bootstrap the model =
# ==========================
m1_booted = mxBootstrap(m1)
# =================================================
# = 2. Estimate and accumulate a distribution of =
# = standardized values from each bootstrap. =
# =================================================
tmp = mxBootstrapStdizeRAMpaths(m1_booted)
# name label matrix row col Std.Value Boot.SE 25.0% 75.0%
# 1 CFA.A[1,7] NA A x1 F1 0.8049842 0.01583737 0.7899938 0.8124311
# 2 CFA.A[2,7] NA A x2 F1 0.7935255 0.01373320 0.7865666 0.8045558
# 3 CFA.A[3,7] NA A x3 F1 0.7772050 0.01629684 0.7698374 0.7907878
# 4 CFA.A[4,7] NA A x4 F1 0.8248493 0.01315534 0.8150299 0.8351416
# 5 CFA.A[5,7] NA A x5 F1 0.7995083 0.01479210 0.7869158 0.8057788
# 6 CFA.A[6,7] NA A x6 F1 0.8126734 0.01527586 0.8012809 0.8218805
# 7 CFA.S[1,1] NA S x1 x1 0.3520004 0.02546392 0.3399556 0.3759097
# 8 CFA.S[2,2] NA S x2 x2 0.3703173 0.02171159 0.3526899 0.3813130
# 9 CFA.S[3,3] NA S x3 x3 0.3959524 0.02529583 0.3746547 0.4073505
# 10 CFA.S[4,4] NA S x4 x4 0.3196237 0.02163979 0.3025384 0.3357263
# 11 CFA.S[5,5] NA S x5 x5 0.3607865 0.02364008 0.3507206 0.3807635
# 12 CFA.S[6,6] NA S x6 x6 0.3395619 0.02476480 0.3245124 0.3579489
# 13 CFA.S[7,7] NA S F1 F1 1.0000000 0.00000000 1.0000000 1.0000000
# 14 CFA.M[1,1] NA M 1 x1 2.9950397 0.08745209 2.9368758 3.0430917
# 15 CFA.M[1,2] NA M 1 x2 2.9775235 0.07719970 2.9109289 3.0197492
# 16 CFA.M[1,3] NA M 1 x3 3.0133665 0.08645522 2.9598062 3.0779683
# 17 CFA.M[1,4] NA M 1 x4 3.0505604 0.08210810 2.9952130 3.1103674
# 18 CFA.M[1,5] NA M 1 x5 2.9776983 0.07973619 2.9362410 3.0311999
# 19 CFA.M[1,6] NA M 1 x6 2.9830050 0.07632118 2.9360469 3.0416504
}
}
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