Bootstrap distribution of standardized RAM path coefficients
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.
mxBootstrapStdizeRAMpaths(model, bq= c(.25, .75),
method= c('bcbci','quantile'), returnRaw= FALSE)model |
An MxModel that uses RAM expectation and has already been run through |
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 |
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.
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.
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.
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 3.0416504Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.