OpenMx (version 2.18.1)

mxBootstrapStdizeRAMpaths: 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.

note: Model must have already been run through mxBootstrap.

Usage

mxBootstrapStdizeRAMpaths(model, bq= c(.25, .75), 
	method= c('bcbci','quantile'), returnRaw= FALSE)

Arguments

model

An MxModel that uses RAM expectation and has already been run through mxBootstrap.

bq

vector of 2 bootstrap quantiles corresponding to the lower and upper limits of the desired confidence interval.

method

One of 'bcbci' or 'quantile'.

returnRaw

Whether or not to return the raw bootstrapping results (Defaults to FALSE: returning a dataframe summarizing the results).

Value

If 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 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.

Details

mxBootstrapStdizeRAMpaths applies mxStandardizeRAMpaths to each bootstrap replication, thus creating a distribution of standardized estimates for each nonzero path coefficient.

The default 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 bq=c(.025,.0975).

nb: ‘bcbci’ stands for ‘bias-corrected bootstrap confidence interval’ To learn more about bcbci and quantile methods, see Efron (1982) and Efron and Tibshirani (1994).

note 1: It is possible (though unlikely) that the number of nonzero paths (elements of the A and S RAM matrices) may vary among bootstrap replications. This precludes a simple summary of the standardized paths' bootstrapping results. In this rare case, if returnRaw=TRUE, a raw list of bootstrapping results is returned, with a warning. Otherwise an error is thrown.

note 2: mxBootstrapStdizeRAMpaths ignores sub-models. To standardize bootstrapped sub-models, run it on the sub-models directly.

References

Efron B. (1982). The Jackknife, the Bootstrap, and Other Resampling Plans. Philadelphia: Society for Industrial and Applied Mathematics.

Efron B, Tibshirani RJ. (1994). An Introduction to the Bootstrap. Boca Raton: Chapman & Hall/CRC.

See Also

mxBootstrap(), mxStandardizeRAMpaths(), mxBootstrapEval, mxSummary

Examples

# NOT RUN {
# }
# NOT RUN {
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

# }